The Book and Printed Culture of Mathematics in England and Canada, 1830-1930

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Paper Index of the Mind: The Book and Printed Culture of Mathematics in England and Canada, 1830-1930

Sylvia M. Nickerson

A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Institute for the History and Philosophy of Science and Technology University of Toronto

Paper Index of the Mind: The Book and Printed Culture of Mathematics in England and Canada, 1830-1930

Sylvia M. Nickerson

Doctor of Philosophy

Institute for the History and Philosophy of Science and Technology University of Toronto

2014 Abstract

This thesis demonstrates how the book industry shaped knowledge formation by mediating the selection, expression, marketing, distribution and commercialization of mathematical knowledge. It examines how the medium of print and the practices of book production affected the development of mathematical culture in England and Canada during the nineteenth and early twentieth century.

Chapter one introduces the field of book history, and discusses how questions and methods arising from this inquiry might be applied to the history of mathematics.

Chapter two looks at how nineteenth century printing technologies were used to reproduce mathematics. Mathematical expressions were more difficult and expensive to produce using moveable type than other forms of content; engraved diagrams required close collaboration between author, publisher and engraver.

Chapter three examines how editorial decision-making differed at book publishers compared to mathematical journals and general science journals. Each medium followed different editorial processes and applied distinct criteria in decision-making about what to publish.

Daniel MacAlister, Macmillan and Company’s reader of science, reviewed mathematical manuscripts submitted to the company and influenced which ones would be published as books.

Chapter four explores economic aspects of mathematical book publication. Macmillan and

Company’s mathematical authors profited from the successful publication of textbooks. Both author and publisher augmented their prestige, influence and image through successful author-publisher liaison.

Nation building and the definition of a national identity are explored in chapter five as factors influencing the development of mathematical publishing. It is shown how the capacity to print mathematics locally was important to the development of a Canadian culture of mathematics. John Charles Fields’ production of the Proceedings of the International

Mathematical Congress, Toronto, 1924 is identified as a major turning point within this development.

Chapter six concludes that publishers, not just mathematical authors, shaped nineteenth century British mathematics. While an increase in mathematical book production during the nineteenth century stimulated popular engagement with mathematics, British publishers perpetuated conservative mathematical values through the mass production of textbooks. In distributing these textbooks to domestic and foreign markets, publishers perpetuated a moribund image of mathematics inside and outside Britain.

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Acknowledgments

Many memorable life events have occurred during my time engaged in doctoral study. Marriages were made, children were born, and deaths recorded. My wonderful husband and son, John and Colin, have enriched my life enormously and supported this project. My grandparents Frederick and Mary Barton always believed in the transformative power of education and I hope the present work would have made them proud.

I am also grateful to the organizations that furnished the necessities of life while I completed this project. I was supported along the way by a Canada Graduate Scholarship from the Social Sciences and Humanities Research Council of Canada (SSHRC). The Michael Smith Foreign Study Supplement (SSHRC funded), as well as travel grants from the Institute for the History and Philosophy of Science and Technology at the University of Toronto, enabled me to spend a significant amount of time in England completing archival research. I am very grateful to have benefitted from financial support that made researching and writing this dissertation both possible and enjoyable.

I also acknowledge the people I have met along the way, from whose work and mentorship I have learned much. Trevor Levere, Nicholas Griffin and June Barrow-Green provided guidance and inspiration when I was just getting a handle on my project, as well as detailed advice on the final product. In her role as Librarian at Massey College, Marie Korey opened up the world of ancient books and printing when she allowed me to volunteer and later, work in the Robertson Davies print shop. Both Massey College and the Institute for the History and Philosophy of Science and Technology allowed me to go on historical and intellectual adventures through the many wonderful people I connected with through these institutions. To my supervisor Craig Fraser, thank you for being my guide to the history of mathematics. Before coming to Toronto you recommended I read Joan Richard’s Mathematical Visions. This book continues to be an inspiration and a guide for me in my academic work.

Librarians are often the gateway to the knowledge that historians seek. Several librarians and archivists assisted me while I completed research during my doctorate. Alysoun Sanders (Archivist, Palgrave-Macmillan), John Shoesmith (Thomas Fisher Rare Book Library), Adam Green (Wren Library, Trinity College), Catherine Harpham and Anne Barrett

(Imperial College London), Dan Mitchell (Special Collections, University College London), Carl Spadoni and Kenneth Blackwell (Bertrand Russell Research Center) and Loryl MacDonald (University Archivist, University of Toronto) all assisted me. Some of this assistance was for research I completed on the nineteenth century British mathematician William Kingdon Clifford, which I still hope will one day come to publishable light. I probably would have asked Richard Landon (formerly of the Thomas Fisher Rare Book Library) for his opinion on the present work if he were still alive.

To my friends and my extended family too numerous to name, thank you for your encouragement and patience. To my parents, Ann Marie and James, and to my parents-in-law Hilary and Peter, your support has in so many ways made it possible for our family to continue to fulfill our dreams and goals. I dedicate this work to you.

Table of Contents

Acknowledgments ...... iv

Table of Contents ...... vi

List of Tables ...... ix

List of Plates ...... x

List of Figures ...... xi

Note to the Reader ...... xiii

Chapter 1 Introduction ...... 1 1. Mathematical books ...... 1 2. Journals versus books ...... 5 3. Passage into print ...... 8 4. Science publishing ...... 11 5. Plan for the work ...... 15

Chapter 2 “Never put together such crabbed stuff”: Printing Mathematics Using Moveable Type and Engraving ...... 18 1. Introduction ...... 18 2. Printing in the nineteenth century ...... 22 3. Difficulties of printing mathematics ...... 26 4. British printers of mathematics ...... 36 5. Populist printers William Clowes and A&R Spottiswoode ...... 37 6. Scholarly printers Oxford University Press and Cambridge University Press ...... 43 7. Journal printers Taylor and Francis ...... 50 8. Mathematical typesetting at Cambridge, Principia Mathematica (1910) ...... 52 9. Mathematical illustrations in print ...... 55 10. Engraved diagrams for Todhunter's Plane Co-ordinate Geometry (1855) ...... 63 11. Conclusion ...... 70

Chapter 3 Referees, Publisher’s Readers and the Image of Mathematics in Journals and Books ...... 73 1. Introduction ...... 73 2. Emergence of mathematical authors ...... 75 vi

3. Refereeing at mathematical journals ...... 78 4. Origin of the publisher’s reader ...... 83 5. Macmillan & Co. as publishers of science and mathematics ...... 85 6. Manuscripts on scientific and mathematical topics from Macmillan’s “slush pile” ...... 96 7. Macmillan’s reader of mathematics Donald MacAlister ...... 102 8. Conclusion ...... 110

Chapter 4 Mathematics for the World: The Business of Publishing Mathematics at Macmillan and Company ...... 113 1. Introduction ...... 113 2. Nineteenth century British publishing and Macmillan ...... 115 3. Macmillan’s publication record in mathematics and science ...... 120 4. Macmillan’s mathematical books ...... 122 5. Contracts, royalties, and revenues from publishing ...... 127 6. Promotion and advertising ...... 139 7. Mathematics for the world ...... 147 8. Conclusion ...... 154

Chapter 5 Enabling a Mathematical Culture: The Development of Mathematical Printing and Publishing in Canada ...... 157 1. Introduction ...... 157 2. Printing and publishing mathematics in pre-confederation Canada ...... 158 3. Mathematical and scientific culture in Canada ...... 169 4. John Lovell, John Herbert Sangster and Lovell’s series of schoolbooks ...... 176 5. James G. MacGregor’s An Elementary Treatise on Kinematics and Dynamics (1887) ...... 184 6. John Charles Fields and the University of Toronto Press ...... 188 7. Conclusion ...... 200

Chapter 6 Conclusion ...... 203 1. The communications circuit ...... 203 2. Mathematics in popular culture ...... 206 3. Authors, typographic culture and mathematics in print ...... 209 4. Economics, book production and the image of mathematics ...... 211 5. Fashioning a history of science publishing ...... 214

Bibliography ...... 217

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Acronyms ...... 217 Archival Sources ...... 217 Published sources ...... 217

Appendices ...... 238 A. Mathematical manuscripts received by Macmillan, 1867-1896 ...... 238 B. Some of Macmillan’s readers of science, 1867-1896 ...... 244

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List of Tables

Table 1 Proportion of Macmillan’s publications on topics in mathematics and science, 1843-1889 (Source: Foster 1891) ...... 121

Table 2 Macmillan’s mathematical books with print runs greater than 100,000, 1843- 1889 (Source: Macmillan’s First Editions Book, British Library) ...... 124

Table 3 Revenues obtained from the publication of popular Victorian novels (Source: Haythornthwaite 1984: 101-102) ...... 130

Table 4 Isaac Todhunter’s publications with Macmillan 1843-1889 (Source: Macmillan’s First Editions Book, British Library) ...... 150

List of Plates

Plate 1 Sir Donald MacAlister, first baronet (1854-1934); photograph by Olive Edis; picture credit © National Portrait Gallery, London ...... 104 Plate 2 Proceedings of the International Mathematical Congress, Toronto, August 11-16, 1924, 2 Vols., edited by J. C. Fields with the collaboration of the editorial committee, Toronto, University of Toronto Press, 1928 (Photo credit: Sylvia Nickerson) ...... 193

List of Figures

Figure 1 Frege’s conceptual writing (Source: Vilkko 1998: 415) ...... 2 Figure 2 The printing forme ...... 23 Figure 3 A sentence set in type ...... 29 Figure 4 Examples of difficult justification (Source: Spottiswoode et al 1876: 338) ...... 29 Figure 5 Mathematical expressions not involving justification (Source: Spottiswoode et al 1876: 339) ...... 30 Figure 6 Two typographical forms expressing indicies; (a) showing an exponential function requiring justification and (b) showing an equivalent form composed by machine (Source: Hitchings 1964: 83) ...... 32 Figure 7 Woodcut illustrations from Robert Simson’s Euclid (1762); the figure on the left is from Book I, proposition 2; the figure on the right is from Book II, proposition 25 (Source: Simson 1762: 7, 218) ...... 58 Figure 8 Wood engravings from Richard Potter’s An Elementary Treatise on Mechanics (1846); the figure on the left illustrates the addition of moments of force; the figure on the right illustrates finding the center of gravity of a pyramid whose base is a polygon (Source: Potter 1846: 13, 47) ...... 58 Figure 9 Illustrations printed intaglio from John Henry Pratt’s The Mathematical Principles of Mechanical Philosophy (1845) (Source: Pratt 1845: Figures 10, 56, 75) ...... 59 Figure 10 Proposition 6, Book I from Oliver Byrne’s The First Six Books of the Elements of Euclid (1847) (Source: Byrne 1847: 6) ...... 61 Figure 11 Wood engravings from Todhunter’s Plane Coordinate Geometry (1855); William Dodd’s engraving (left); William Dickes engraving (right) (Source: Todhunter 1855: 146, 282) ...... 67 Figure 12 Frontispiece from Charles Kingsley’s Glaucus, or, Wonders of the Shore (1856); William Dickes signature is visible in the bottom right hand corner of the engraving (Source: Kingsley 1856: iv) ...... 69 Figure 13 1870 Advertisement for Macmillan and Co.’s Scientific Publications (Source: Nature, vol. 1, no. 16, 17 February 1870, p. 419) ...... 143 Figure 14 1880 Advertisement for Messrs. Macmillan and Co.’s New Books (Source: The Publisher’s Circular, 17 January 1880, p. 17) ...... 144 Figure 15 ‘Beechenhurst’, The Residence of Dr. J. H. Sangster, Port Perry, Ontario Co. Canada (Source: Beers 1877: 29) ...... 184

Figure 16 Route map showing transcontinental excursion, Toronto to Vancouver and Victoria, August 17 to September 3, 1924; places where stops were made are indicated in solid black (Source: Fields 1928, Vol 1: Insertion after p. 70)...... 195 Figure 17 Three pages from Carl Størmer (University of Oslo, Norway), “Modern Norwegian Researches on the Aurora Borealis”, showing different illustration techniques used in the Proceedings (Source: Fields 1928, Vol 1: 141, Fig. 25, 26, 33) ...... 197 Figure 18 Examples of mathematical typesetting; (left) J. V. Uspensky, “On Some New Class- Number Relations”; (right) P. A. MacMahon, “Expansion of Determinants and Permanents in Terms of Symmetric Functions” (Source: Fields 1928, Vol. 1: 317, 325) ...... 197 Figure 19 Robert Darnton’s ‘communications circuit’ (Source: Darnton 1982: 68) ...... 204 Figure 20 The ‘reading’ man, from Richard Corbould Chilton’s Helluones Liborum (Devourers of books), aquatint by Fracis Jukes, engraving by J. K. Baldrey (Source: Topham 2000: 318) ..... 205

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Note to the Reader

References

I have adhered to a version of the Chicago Manual of Style author-date system for the references in this work. For published sources, the author and date of publication are specified, e.g. (Adams 1844). If referring to a specific section of text, the author and date is followed by a page number, or span of pages, for example (Adams 1844: 187) or (Adams 1844: 20-21). If the author has more than one publication in a given year listed in the bibliography, the author and date may be further distinguished by the addition of a letter, as in (De Morgan 1842a). If a book has two authors or editors, the name of both is given, or if there are more than two authors, then the lead author is specified followed by ‘et al’. Anonymous works appear under the authorship ‘Anonymous’ in the bibliography, and cited using ‘Anon.’ in place of the author’s name, e.g. (Anon. 1856: 5).

References to archival materials are given in the footnotes, with the name of the collection and the accession number. The name and location of all archives consulted are listed in the bibliography.

Records for Macmillan and Company, a business about which this work makes many comments, are held in several collections. There are documents from Macmillan held at several locations in the United Kingdom: at the Palgrave-Macmillan head offices in Basingstoke, in the Special Collections department at Reading University, and in the Department of Manuscripts at the British Library. This thesis has made particularly extensive use of the last of these collections. The Macmillan Archive (British Library Add MS 54786- 56035) comprises nineteenth and twentieth century correspondence and business records from the publishing firm. In referring to the British Library’s collection of Macmillan Papers, this thesis employs the acronym “MP” followed by an accession number, followed by either a page reference or a date reference (for correspondence) to locate the source within a volume of documents (e.g. MP 56016, p. 15). In official British Library citation style, the same document would be cited as BL Ad. MS 56016, fo. 15.

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Included in Macmillan's many extensive records of their publishing activity are a series of production ledgers, the Editions Books, which list the number of books ordered, date of publication, name of printer, type and date of paper ordered, etc., for each published title. The first Editions Book covering Macmillan's publications to the year 1892 is held at the Palgrave-Macmillan head office in Basingstoke. Subsequent volumes are found in the British Library. For convenience sake, the British Library holds a CD-ROM copy of the first Editions Book as a complement to their Macmillan collections, and it was the British Library's CD-ROM copy consulted by this author. References to Macmillan’s first Editions Book have been given in the footnotes by “Macmillan’s first Editions Book, Macmillan Archive, British Library”, followed by a page number. However it should be noted that this source is not officially a part of the British Library's manuscript collections, and so the CD- ROM is not listed in their catalogue or in the records of manuscripts. By bringing attention to this I hope to alleviate any confusion for the reader wishing to locate this source.

Currency

Occasionally this thesis makes remarks about amounts or prices in British currency. Prior to decimalization, one pound was divided into 20 shillings, and each shilling into 12 pence. When money is discussed, s. is used to denote shillings, and d. pence. For example, one pound, seven shillings and eleven pence is written £1 7s. 11d.

xiv 1

Chapter 1 Introduction

And from my pillow, looking forth by light

Of moon or favouring stars, I could behold

The antechapel where the statue stood

Of Newton with his prism and silent face,

The marble index of a mind for ever

Voyaging through strange seas of Thought, alone.

The Prelude, Book third, Residence at Cambridge. William Wordsworth (Wordsworth 1888)

1. Mathematical books

In his book Begriffsschrift (Conceptual notation, 1879), Gottlob Frege created a logical language he hoped to apply towards forming a rigorous theoretical foundation for mathematics. Using his language of pure thought, Frege imagined giving greater rigor and formality to mathematical proofs, formulating definitions for the operations of arithmetic and the idea of number. Frege’s Begriffsschrift is often cited as the work that began the logicist movement in the philosophy of mathematics (Van Heijenoort 1967; Nagel and Newman 1958: 42-3; Tiles 1989: 138-9). Legends surrounding the book frequently include the detail that Frege’s Begriffsschrift was a difficult publishing venture, as were Frege’s later books.

Frege’s conceptual writing was two-dimensional in nature, spreading across a page both vertically and horizontally. When mathematician and logician Ernst Schröder reviewed the Begriffsschrift he referred to Frege's notation as a “monstrous waste of space” (quoted in Vilkko 1998: 416). The criticism of Frege’s reviewers focused on both the impracticality of Frege’s symbolism and the fact that Frege had seemingly ignored the work of the algebraic logicians,

2 who were his contemporaries (i.e. George Boole, William Stanley Jevons, Robert Grassmann and Schröder himself).1

In Schröder’s review of Frege’s book, he argued that the notation used by the algebraic logicians was better than the one designed by Frege. When you compare the two, Schröder said, an expression in algebraic form was easier to understand than the same statement made in Frege’s two-dimensional language. Schröder used the following example. The argument “a is true or b is true but not both”, in Schröder’s algebraic expression can be written as: ab1 + a1b = 1 or ab + a1b1 = 0 (where the subscript 1 stands for negation). Using conceptual writing, the Fregean version of the same expression is the following (courtesy of Vilkko 1998: 415):

Figure 1 Frege’s conceptual writing (Source: Vilkko 1998: 415)

Despite its recognition today as a signal work in philosophy, the two-dimensional notation Frege introduced in the Begriffsschrift was never adopted by logicians (Vilkko 1998: 416). Only one symbol coined by Frege continues to be used today. Frege’s turnstile is a symbol that when preceding a statement, implies that statement is a fact. Bertrand Russell and A. N. Whitehead adopted this symbol and used it as Frege did, although they referred to the symbol as an assertion sign (Vilkko 1998: 416).

There have been many suggestions by historians of science that mathematical books were difficult or expensive to print and publish (Rider 1993; Secord 2009; Topham 2000a, 2000b). Gottlob Frege's Begriffsschrift is one example of a nineteenth century mathematical book with an intriguing history. The aim of the present study is to discover how the forming of mathematical works into printed books might have presented unusual, unique or difficult challenges to the printers who applied their technologies to reproduce them, and what special methods, if any,

1 When comparing his system with that of Peano’s, Frege wrote in 1896, “The convenience of the typesetter is not however the highest Good” (Frege quoted in Gilles 2013: 82).

3 publishers applied to the planning, marketing and distribution of these books. Did mathematicians have to accommodate the printing and publishing trades when they had their mathematical works translated into print? As print was the conduit through which their findings would reach a critical audience, mathematicians had no choice but to work with printers and publishers. The present study aims to discover more details about the nature of these relationships and their effect on the communication of mathematics. Finally, the conclusion of this thesis will relate its findings to received ideas about nineteenth century British history of mathematics.

From an intellectual point of view, Frege’s reviewers criticized his two-dimensional notation as unnecessarily cumbersome. From a printing and publishing point of view, the adoption of Frege’s concept-script may have been prohibitively costly and technically impractical (see section 1.2 in chapter one). Both of these points together may explain why no logician, even ones who closely studied him, ever adopted Frege’s two-dimensional language as the medium for further work in symbolic logic.

John Herschel once wrote to Edward Bromhead, on the occasion of the publication of the Analytical Society’s 1813 Memoirs, “the publication of Mathematical work, particularly if it goes one step beyond the comprehension of elementary readers is a dead weight and a loss to its author” (quoted in Topham 2000a: 325). Many examples confirm Herschel’s suggestion that the publication of higher mathematics was a trial for both author and publisher, and that neither expected to come out of the endeavor more financially successful. As publisher Daniel Macmillan wrote to P. G. Tait with regards to the publication of Tait’s Dynamics of a Particle, “as these high subjects never sell enough to cover expenses we shall be in no hurry about it”.2

Now considered a masterpiece in the development of modern vector analysis, Hermann Grassman's book Ausdehnungslehre (Theory of Extension, 1844) is another remarked upon

2 Daniel Macmillan to P. G. Tait, 7 January 1856, 55379 Letter-Book 1855-1856, p. 467, Macmillan Archive, British Library, UK.

4 example of a failed publishing venture in the history of mathematics.3 In 1864 Grassman’s publisher remaindered the book, recycling 600 copies as waste paper. In 1876 he wrote to Grassman apprising him of the situation, noting that what was left after the discard were “a few odd copies, [which] have now been sold, with the exception of one copy which remains in our library” (quoted in Crowe 1967: 65; Engel 1911: 331).

What mathematical authors such as Frege, Grassman, Tait, and members of the Analytical Society had in common is that their mathematical work challenged accepted norms within mathematics. For this reason, “high” books in mathematics did not necessarily find a ready audience able to understand their new ideas, or at least not right away. The publication occurred within the parameters of commerce and business, and therefore in the case of publication, market forces and economic costs had certain effects on intellectual work. It merits questioning under what circumstances publishers and authors could afford to undertake the publication of mathematical works destined for small, specialized audiences. Did mathematicians meet with resistance at the printing and publishing stage, even before their work could be entertained, favourably or unfavourably, by a broader audience? Would a publisher’s association with an esteemed author outweigh a financial loss on publishing academic work? The present study aims to find out.

In contrast to “high” books, publishers were very aware of how valuable a successful textbook could be, especially if required by a captive audience. Daniel and Alexander Macmillan were enthusiastic publishers of mathematical textbooks, often eager to seize upon the student market before another publisher could. In 1854 Daniel Macmillan wrote to well-known textbook author Isaac Todhunter, “We have not above 100 copies of your Calculus left. There will be some in the Trade, and with our agents, but not many. So we think we ought to go to press by Xmas, or sooner if you are ready. It would be a mistake to let it be out of print even for a day”.4 With regards to a new edition of Barnard Smith’s Arithmetic, Macmillan wrote:

3 Grassman was not a well-known author when he released this book, and many have also commented that his writing itself was obscure. In this case, these are the reasons why Grassman’s book sold badly (not the typographical complexity of it). 4 Daniel Macmillan to Isaac Todhunter, 3 November 1854, 55376 Letter-Book 1854-1855, p. 79, Macmillan Papers, Macmillan Archive, British Library, London UK. Hereafter references to the British Library’s Macmillan Papers will be abbreviated MP.

Even if we could save £10 – which we doubt – by this plan, it would be ill saved money if it holds back the book even for a week. For the sales now in hand show that the book is pressingly wanted; and if we, by delay, miss any who now will decide to adopt another book we shall be throwing away money while we fancy we are saving it. So we should now blaze on through against all other considerations and think only of getting the complete book out by Easter. And keep pressing the Printer. And give him no cause for delay.5

Macmillan heavily promoted some of their mathematics textbooks. In 1861, 14,000 prospectuses were prepared to advertise the publication of Todhunter’s Theory of Equations (1862) (Barrow-Green 2001: 187 f.n.51). They also produced some of their mathematical books in very large quantities, for example, H. S. Hall’s various mathematical books for India enjoyed sales upwards of three million copies (Chatterjee 2002: 156).

By examining the promotion and distribution machinery that publishers like Macmillan applied to their mathematical textbooks, we may discover that publishers played a role in the advancement of a particular view of mathematics, as the publisher disseminated these mathematical ideas en mass into an educational setting. John Feather, who has written extensively about the history of British publishing, has described the publisher as a capitalist whose trade is in ideas (Feather 1988). It will be one aim of the present work to find out which mathematical ideas were heavily capitalized upon by publishers, and whether the choice of publishers to invest money and organization into a certain image of mathematics shaped mathematics in Britain and in other English-speaking countries.

2. Journals versus books

In recent years historians of mathematics have paid attention to the founding and development of mathematical journals (Crilly 2004; Barrow-Green 2002; Lützen 2002; Despeaux 2002b; Kent 2008, etc.). These histories have offered us a picture of how specialized publications arose, particularly in the nineteenth century, to support burgeoning research-oriented mathematical communities in continental Europe, Britain, and America (Parshall and Rice 2002). Some of the

5 Daniel Macmillan to Barnard Smith, 6 March 1856, MP 55378, p. 36.

6 mathematical journals that have received historical attention are Journal für die reine und angewandte Mathematik (Crelle's Journal, f. 1826), Journal de Mathématiques Pures et Appliquées (Liouville's Journal, f. 1836), and the American Journal of Mathematics (f. 1878).

In the British context, a number of journals that published mathematics developed in the nineteenth century, including the Cambridge Mathematical Journal and its related descendant journals. The Mathematician was a short-lived publication out of Woolwich Military Academy, and The Ladies and Gentleman’s Diary was a general interest periodical that included a section for mathematical recreations (Albree and Brown 2009). Proceedings and transactions of the many learned societies offered paths through which mathematicians could communicate their work to an interested audience. The Royal Society of London, The Royal Society of Edinburgh, The Royal Irish Academy, and the British Association for the Advancement of Science all published reports or transactions. For students of mathematics, Transactions of the Cambridge Philosophical Society (later, Proceedings of the Cambridge Philosophical Society) offered an important early outlet for mathematical publication at Cambridge. From the 1860s onward, the Proceedings of the London Mathematical Society carried mathematical articles arising out of activities of the society. General science journals such as the Philosophical Magazine included important articles in physical science. For research mathematics, Crelle’s Journal and Liouville's Journal remained the most esteemed vehicles for publication.

At the same time that many mathematical practitioners sought out publication in journals, a number of examples demonstrate that mathematicians continued to develop and showcase new and important ideas in the format of research monographs and books. Landmark Writings in Western Mathematics contains several examples of groundbreaking new approaches to mathematics first presented or most comprehensively demonstrated in book form, for example, the analytical approach contained in Joseph Louis Lagrange’s Méchanique analitique (1788) or the theory of limits contained in A. L. Cauchy’s Cours d’analyse (1821) (Grattan-Guinness et al. 2005). Landmark Writings mentions several books as important to the advancement of research mathematics published in the second half of the nineteenth century. These titles included William Rowan Hamilton’s Lectures on Quaternions (1853), George Boole’s Laws of Thought (1854), Johann Peter Gustav Lejeune Dirichlet’s Vorlesungen über zahlentheorie (1863), William Thomson and P. G. Tait’s Treatise on Natural Philosophy (1867), Stanley Jevons’ The Theory of Political Economy (1871), James Clerk Maxwell’s A Treatise on Electricity and

Magnetism (1873), Lord Rayleigh’s Theory of Sound (1877-1878), Richard Dedekind’s Stetigkeit und irrationale zahlen (1872) and Oliver Heaviside’s Electrical Papers (1892). Frege’s Begriffsschrift and Grassman’s Ausdehnungslehre have already been mentioned as examples. Another signal monograph in nineteenth century mathematics is Hilbert’s Grundlagen der Geometrie (1899). Hilbert’s re-axiomatization of geometry as presented in this small book has been credited for giving rise to what some commentators have described as modernism in mathematics.6

Many of the nineteenth century journals in which mathematicians published have been studied and written about. As such the role of the periodical in nineteenth century mathematics has been, to a certain degree, explored. To date, historians have not explored the case of mathematical books in the nineteenth century, and how their publication, production, and marketing may have shaped the culture or practice of mathematics. Although no histories have been written about this topic, some historians have indicated their desire to know more. In her article about the career of prolific textbook author Isaac Todhunter, June Barrow-Green notes the difficulty of interpreting certain facts about her subject's publication career given that a larger account of the publishing and sale of mathematical books is not available. She comments that “the relationship between mathematical authors and their publishers, and the general influence of the book trade on nineteenth century mathematics have not been explored [here] although they clearly merit further research” (Barrow-Green 2001: 187, f.n.51).

Likely historians of mathematics have focused more on journals because important papers by now-famous mathematicians appeared frequently in these publications. In the opening passages of Tony Crilly's article about the Cambridge Mathematical Journal, Crilly expresses a value judgment commonly held by historians of mathematics about mathematics itself. He states that original research, and the circulation of original research through publication, is the most important aspect of mathematical development (Crilly 2004: 455). Due to similar sorts of value judgments, historians of mathematics have tended to focus on the historical development of what

6 David Rowe looks at different perspectives on Hilbert in his paper (Rowe 1997), as does Herbert Mehrtens in Moderne – Sprache – Mathematik (Frankfurt am Main: Suhrkamp 1990), where he suggests Hilbert’s work in foundations initiated modernism in mathematics. Jeremy Gray’s book Plato’s Ghost traces the rise of modernist practices and approaches to mathematics during the years 1890 to 1930 (Gray 2008).

8 contemporary mathematicians consider to be highly original mathematics. Recognized mathematical innovations of the nineteenth century more commonly appeared in journals than in books. It is likely for this reason that mathematical journals have received more substantial study.

The present examination, by contrast, seeks to offer a more nuanced story of mathematical development than what a history focused on the summits of mathematical research can provide. A focus on research-oriented mathematical publication will not be an exclusive focus here. I aim to include mathematical works considered historically important as well as books that may now be unknown. If the work existed in book form, and can be identified as mathematical (using broad criteria as introduced by Wallis and Wallis 1986: v), then I have considered it equally important to the present study.

3. Passage into print

The topic of this thesis has arisen from the author’s interest in nineteenth century British history of mathematics and her desire to apply certain intriguing perspectives offered by the discipline of book history and print culture to this subject. Before venturing forward, a brief introduction to the discipline of book history and print culture seems warranted.

In art history, an artists’ use of paint as a medium for his or her expression is often considered a subject of equal importance to the content of the painting. The premise at the heart of the book history and print culture discipline is similar. The study of book history examines the printed word as a medium for the expression and communication of knowledge. It asks the question: If the book is a medium, what effect does that medium have on the content represented there? Choosing to focus on the printed form as a communications medium puts an emphasis on questions about how all the mechanisms of print, from the physical form of the book to the organization of its publication, distribution and eventual use, mediated the communication and reception of the knowledge contained therein. Book history and print culture asks whether there are characteristics common to all printed texts, and if so then how those characteristics have affected how printed knowledge has been generated or received.

While Marshall McLuhan’s famous catchphrase “the medium is the message” has become something of a cultural cliché, this concept, presented in his book, The Gutenberg Galaxy, is one

9 of the ideas that launched the study of book history and print culture. Elizabeth Eisenstein took inspiration from McLuhan for the premise of her book, The Printing Press as an Agent of Change: Communications and Cultural Transformation in Early-Modern Europe first published in 1979. Eisenstein’s two-volume work sets out to document the effect of the “communications- shift” that occurred when Western countries moved from a reliance on manuscripts to printed texts (see Eisenstein 1979: vol. 1, x, xi). An ambitious work that took fifteen years to write, The Printing Press as an Agent of Change put forward Eisenstein’s perspective on how the invention of moveable type printing affected the subsequent developments of the Reformation, the Renaissance and the Scientific Revolution. Eisenstein’s opinions expanded from McLuhan’s initial suggestion about how communication affects knowledge production. For Eisenstein, the medium through which communication takes place has an effect on the message, or ultimate reception and cultural meaning, of the knowledge contained therein. Although McLuhan’s Gutenberg Galaxy was too cryptic a work for most to digest, Eisenstein’s 1979 book, and the conversations it subsequently provoked, are associated with the development of book history and print culture into a recognized, albeit interdisciplinary, field of study.

Eisenstein proposes that printed culture has three characteristics that differentiate it from the preceding manuscript culture. These characteristics are standardization, dissemination, and permanence. Roughly speaking, printing brought an authority to a particular version (the printed version) of a text, with more copies of that text made available than ever before. According to her thesis, the production of numerous identical copies of the same text fixed and objectified knowledge (literally), whereas the sharing of knowledge in script and oral culture had been more fluid. Eisenstein claims these characteristics endemic to print affected how people acquired knowledge, what kinds of knowledge people had access to, and how many people could access it. In particular, she claims that because printing technology brought more reliability and objectivity to texts, these characteristics enabled subsequent social-cultural changes to take place in religion, in the humanities and in science. Because these movements relied on using texts in a way made possible by print, she suggests these fundamental changes to Western belief systems would not have been possible without a transformation from the previous manuscript-reliant culture to the ensuing printed culture brought about by the invention of the printing press and its eventual adoption across Europe.

Since the publication of The Printing Press as an Agent of Change, Eisenstein’s book has inspired much debate about how Western culture evolved over the five hundred years in which the printed word has been a dominant communications medium. While still acknowledged as a founding work in book history, Eisenstein’s account has since been criticized as overly deterministic in its theoretical approach (Finkelstein and McCleery 2006: 2). Subsequent historians of the book have significantly revised both Eisenstein’s account of the print medium and her claims about its transformative effect on culture. While Eisenstein assumed that printed books arrived with many of the values we associate with printed knowledge today, Adrian Johns’ counters that the value of “intrinsic reliability” cast upon printed texts was concocted over time by the printing industry itself. Johns’ claims this image of print was constructed to ensure printers’ own cultural and commercial success (Johns 1998: 2-3). John’s well-received The Nature of the Book (1998) challenges Eisenstein’s account of printing and claims that her description of the transformative power of print stands “outside of history” because she places the printing press itself beyond her historical analysis (Johns 1998: 19).

Eisenstein claims that the effect of the printing press on culture was revolutionary as opposed to evolutionary (Eisenstein 2005: 15). Subsequent historians of the book have not wanted to venture as far. While Johns claims that Eisenstein sees the scientific revolution as inconceivable without the preceding printing revolution, this is not an entirely fair assessment. Eisenstein writes, “printing is an agent, not the agent, let alone the only agent, of change in Western Europe… the very idea of exploring the effects produced by any particular innovation arouses suspicion that one favours a monocausal interpretation or that one is prone to reductionism and technological determinism” (Eisenstein 2005: xviii).

David Finkelstein and Alistair McCleery have solidified the discipline of book history in the new millennium with their compilations An Introduction to Book History (2005) and The Book History Reader (2002). In his chapter “What Is the History of Books?” Robert Darnton’s formulation of the communications circuit attempts to position the book as an artifact that should be analyzed through its interaction with people in society (Darnton 2006: 12). Darnton’s influential article described how books circulate from author to typesetter, printer, binder, shipper and bookseller and then on to the reader who completes the circuit. This is an attempt to see books in a more complicated way than the assumed linearity of a ‘diffusionist’ model, where books progress from the author’s creation to publication to reception. Darnton attempts to close

11 that path by reminding us that we are all readers and writers both, and writers must be readers first. Mindful of this, we may consider the role of books in society to be more circular than linear.

Darnton and D. F. MacKenzie have been identified as leaders of a new movement in the history of the book (see Howsam 2000: 189, 190; Darnton 2006) who have sought to integrate book history with cultural history, simultaneously taking a cautious approach towards adopting theoretical frameworks for how books function in culture. The new book history describes itself as having grown up from previous approaches to studying the book, including bibliography and a previously exclusive focus on literary works, both of which were familiar occupations to English scholars. The Society for the History of Authorship, Reading and Publishing (SHARP) founded in 1993 symbolizes the openness of the redefined genre with an interest in stories not just about literary books but about all books, including ones that tell us about religion, science, politics, food, homemaking and education, etc.

Approaches from the book history and print culture discipline have inspired the questions I pose in this thesis. McLuhan, Eisenstein, Johns, and Darnton have all provided ways to conceptualize the interaction of books in culture. To a large extent, the study of book history and print culture offers a web of interdisciplinarity too diverse to offer one methodology or a single approach for describing how the print medium has transformed culture and knowledge. However, in the conclusion of this thesis, I will return to perspectives from book history and print culture, in order to examine how we might see the history of mathematical printing and publishing through these frameworks.

4. Science publishing

We know that publication was important, in science and in mathematics. In their history of mathematics in Canada, Tom Archibald and Louis Charbonneau recognized the important role printers and publishers played in the development of a nascent mathematical community. In order to have a mathematical culture, they write, one must have some cultural value placed on the acquisition of mathematical skills, an educational infrastructure to develop those skills, and good teachers who inspire students. In addition, they recognize that “an additional aspect of the local setting [for mathematics] is the book trade: publishers and printers played an important role in the diffusion of basic mathematical knowledge” (Archibald and Charbonneau 1995: 2).

James Secord has drawn similar conclusions about the increasing importance publication played in the growth of nineteenth century science. He has noted that while other vectors of professionalization, such as vocational societies, institutions of learning and positions of employment have been examined, the role of print culture in the professionalization of the scientist has been less studied. The nineteenth century saw changes in the way that mathematics was practiced, with the gentlemanly ideal merging into the role of the specialist practitioner.7 However, within a new structure wherein professionalism was defined by academic positions, membership in professional organizations, meetings and conferences etc., “an approach informed by the history of print shows that this view of the changing structure of science is radically incomplete and sometimes just plain wrong. For it ignores, or at best treats as peripheral, the forms in which knowledge appeared, assuming that publication in specialist periodicals was already established as the only legitimate means for announcing new discoveries” (Secord 2009: 444). Secord continues:

it presupposes that specific forms of communicating knowledge were ready to hand, and firmly in the control of a well-defined group of specialists. Except works devoted to book history, the transmission of knowledge into print is usually treated as relatively transparent. Carrying out procedures in the laboratory, creating scientific organizations and attracting new practitioners: all these are assumed to require work. But the forms of publication, with few exceptions, have been taken for granted (Secord 2009: 444).

Jonathan Topham, who along with Secord has written about the history of science from the print culture perspective, has raised the point that publishing increased the cultural influence and power of the scientist. He writes that one area worthy of further exploration

concerns the involvement of the incipient scientists in managing the new print media to secure their ends, and there has been increasing historical interest in the rhetorical strategies by which practitioners sought to construct audiences and to make their science public. However, this work has tended to be carried out with little consideration either of the rapidly changing print culture through which such rhetoric was mediated to audiences, or of the nature of new reading audiences themselves. This arguably testifies to the lingering

7 On the evolving perception and self-perception of mathematicians in England at this time, John Heard’s doctoral thesis The Evolution of the Pure Mathematician in England, 1850-1920 is particularly useful (Heard 2004).

presence in our historiography of one of the assumptions of the diffusionist model—that the communication of scientific ideas and practices operates (at least when successful) in an unmediated, unidirectional manner from the scientist to the lay public (Topham 2000b: 561).

While science was becoming professionalized in the later nineteenth century, there existed limited positions of responsibility in science, and these positions often offered small financial compensation. Besides a professor’s salary, marrying into money or patenting a successful invention, another option for financial advancement of the scientist was publishing material for a general audience (Meadows 2004: 121). Publishing, however, held more potential than merely supplemental income. Being sought out by a publisher and its attendant audience recognized the scientist’s cultural authority on a particular topic. Over time, scientists’ participation in science publishing further legitimized and added respectability to the profession. Jack Meadows recognizes the 1850s to the 1870s as the time of the greatest pace of change in the Victorian scientific community. In this same period Macmillan and Company became one of the most prolific publishers of science in the English language. It grew from a small bookshop into one of the largest London publishers over these thirty years. In this thesis I make a case that both the scientist-authors and the publishers at Macmillan and Co. used one another to bolster the other’s prestige. Publishers could associate themselves with the cultural cachet of eminent scientists, and market their books as if the product contained some of this mystique. Meanwhile, the scientist’s authority was legitimized through publication. Most often career advancement in the scientific profession and the commercial interest of the publishing business brought these groups together to work in mutual self-interest. The relationships formed between publisher and scientist were influential bonds that effectively curated the scientific knowledge available in print.

In the year 2000 the British Journal for the History of Science published a special issue on book history and the sciences (BJHS vol.33 no. 2, June 2000). Leslie Howsam’s article in this issue discusses the design and production of the International Scientific Series, and how Victorian men of science such as T. H. Huxley, John Tyndall and Herbert Spencer used these books to broadcast an image of science they wished to promote. In her introduction she writes

Even some more recent scholarship discusses scientific books as if they had emerged straight from the minds and consciousness of their authors, to be decanted on the page, unmediated by any influence from the publishing and printing trades. Publishing does not work that way now, and it did

not work that way in the past. The bland package of a printed and bound book may conceal a complex history of networking and power-broking among authors and publishers (Howsam 2000: 187).

It has been shown how nineteenth century science was organized by professional organizations such as the Royal Society, the British Association for the Advancement of Science and the London Mathematical Society (Morrell 1981; Hall 1984; Rice et al, 1995). Other histories have demonstrated how specific sites of training and pedagogy, such as the University of Cambridge, were important in molding and influencing mathematical research communities and knowledge production (Warwick 2003). As Andrew Warwick has mentioned in his history of mathematical teaching at Cambridge, historians of science have at times taken for granted that mathematicians and scientists were able to communicate easily with one another and create innovations in their field, without asking what social structures and material resources put them in a position to do so. Histories of professional organizations and educational structures (of which Warwick’s book Masters of Theory is an example), have attempted to reverse these assumptions by grounding the history of mathematics in the realm of social history, with a sensitivity to and an awareness of how labour and material culture had an impact.

The very idea of basing a history of mathematics in material culture may seem unusual, as the practice of mathematics has often been regarded as one of the most socially or culturally neutral human pursuits that exists (Warwick 2003:12). Mathematics is often considered one of the most privileged forms of knowledge, and its association with perfect or God-like knowledge continues in Western culture to this day. Perhaps the fact that Euclid is the second most frequently printed book in history, next only to the Bible itself, is a sign of how culturally esteemed mathematical knowledge has been (Barrow-Green 2001: 193). Movements in the Sociology of Scientific Knowledge have attempted to undermine these beliefs by deconstructing the production of mathematical knowledge (see chapter four, “Constructing quaternions” in Pickering 1995) or by socially engaging it (see Bloor 1981).

The common assumption that mathematical knowledge is not affected by labour and material culture is motivation to make more visible what has so far been less explored. In the book history and print culture field, it has been demonstrated how “invisible” factors had an effect on the book trade. Transportation and trade-routes including railways, barge and stage-coach, the labour market, population growth, geo-political forces, raw materials and improvements to public

15 education, were all part of the nexus of the production and circulation of books. This study acknowledges that material realities had an impact on the production and distribution of ideas in their physical manifestation as books. As such this work will demonstrate that mathematics too, in its transmission through print, was in certain ways subject to these limitations. Very material and pedestrian conditions may have had an impact on the evolution on mathematics, this most immaterial of subjects.

5. Plan for the work

Chapter two explores how translating mathematical ideas into print presented technical challenges. It was complex and expensive to typeset works laden with mathematical symbols and diagrams. Composing mathematical symbolism using a system designed to mimic alphabetic script presented challenges that were not covered in the standard printers’ manuals (Secord 2009: 466). Mathematical diagrams had to be engraved with a high degree of precision to preserve the meaning the author intended. The engraver who translated the author’s diagrams into wood or copper may have done so without understanding what aspects of the image were crucial to its meaning. Because of all this, printing mathematics was a specialized art within the printing trade, and not every printer undertook it. Chapter two demonstrates how difficult and costly it could be to compose and print texts that were heavily laden with special mathematical symbols and diagrams. Commercial printers William Clowes and A&R Spottiswoode, the university presses at Oxford and Cambridge, and London-based journal printer Taylor and Francis are explored as printers and publishers of mathematics. Two further case studies are presented that illustrate the difficulties of printing mathematics: typesetting Bertrand Russell and Alfred North Whitehead’s Principia Mathematica (Cambridge University Press, 1910-13) and the production of woodcut illustrations for Issac Todhunter’s Plane Coordinate Geometry (Macmillan, 1855).

Although the relationship between publisher and literary author has been a subject of study since the 1970s, the relationship between publisher and scientific author has been less frequently attended (MacLeod 1980: 63). The mingling of publisher and mathematical author, especially in the case of the publication of research monographs or books, is unexplored. Chapter three examines how mathematical publishing was pursued and managed at mathematical and general science journals compared to at a book publisher. The roles of referees and editors are explored at the mathematical journals Cambridge and Dublin Mathematical Journal and Acta

Mathematica. It is revealed how the values applied to the decision-making process differed at general science journals compared to mathematical journals. Chapter three introduces Macmillan and Company as major publishers of mathematical books, and introduces Donald MacAlister as Macmillan’s professional reader of science and mathematics. MacAlister reviewed almost all mathematical manuscripts submitted to the press between 1880 and 1900. MacAlister’s readers’ reports reflect what mathematics he considered beneficial for publication. Differing values applied to the decision-making process at mathematical journals, general science journals and books resulted in different images of mathematics cultivated in each print media.

Chapter four provides a quantitative study of mathematical books published at Macmillan and Company, looking at the quantities in which Macmillan produced its mathematical books and how lucrative these books were for their authors and publisher. The amount of scientific books Macmillan produced and the pattern in which it produced them is compared to what is known about mathematics and science publishing in the nineteenth century British book market generally (Eliot 1994, 1995, 2002). From statistics about Macmillan’s mathematical books (title, year of publication, print run, etc.), trends in Macmillan’s mathematical publications are observed. Author-publisher contracts suggest that authors of Macmillan’s mathematical textbooks could find significant financial benefit from a successful title. For Macmillan, their mathematical textbook sales provided a consistent source of income upon which they could found riskier ventures, such as the publication of higher books on special mathematical subjects. Both textbooks and academic books had their purposes. While textbooks were profitable, academic publishing also had an affirmative role. Publishing specialized materials in mathematics gave Macmillan’s textbooks further legitimacy. Also, publishing projects in higher areas of science became a way of developing relationships with authors who might later write educational products. Both author and publisher came together for mutual benefit in the commercialization of knowledge. Schoolbooks and academic books coexisted within the publishing program to mutual benefit; each product reinforced the success of the other.

Chapter five presents the development of mathematical printing and publishing in nineteenth and early twentieth century English-speaking Canada. Nationalism and nation building are revealed as important motives for the development of local printing and publishing of mathematics. Local production of mathematical books in the Canadas was at first restricted to reprinting American or British mathematical schoolbooks. Locally produced textbooks in mathematics were developed

17 for political reasons, as a response to changes in educational structures or to reinforce political loyalties. John Lovell’s series of schoolbooks on mathematical subjects written by John Herbert Sangster are explored as an early example of native authorship and publication. Throughout the nineteenth century, researchers, when they existed in Canada, sought publication outside Canada for their work. Into the twentieth century scientists found Canadian printers inadequate for the production of original technical works. James MacGregor’s An Elementary Treatise on Kinematics and Dynamics, published by Macmillan in 1887, and John Charles Fields’ Theory of the Algebraic Functions of a Complex Variable prepared in Berlin by Mayer & Müller and produced in Sweden by Almqvist & Wiksell in 1906, are examples in which Canadian researchers published abroad. Out of this context Field’s collaboration with the University of Toronto Press on the Proceedings of the International Congress of Mathematics, Toronto, 1924 (University of Toronto, 1928) was an important turning point, as it developed the capability of the University of Toronto Press to handle specialized mathematical printing. This capability in turn facilitated the creation of Canadian journals and research monographs. These materials showcased research being done in Canada, and in turn assisted a fledgling mathematical culture that was identifiably Canadian.

Chapter 2 “Never put together such crabbed stuff”: Printing Mathematics Using Moveable Type and Engraving

The subject of mathematical printing has never been methodically treated, and many

details are left to the compositor which should be attended to by the mathematician. Until

some mathematician shall turn printer, or some printer mathematician, it is hardly to be

hoped that this subject will be properly treated.

Augustus De Morgan, from “Symbols and Notation”, Penny Cyclopedia (De Morgan 1842a)

1. Introduction

The British mathematician Augustus De Morgan was a teacher, logician, and historian of mathematics. In 1826 he became a member of the populist Society for the Diffusion of Useful Knowledge, and over the course of his life he wrote some 850 articles for its Penny Cyclopaedia (Stephen 2004). When, in one of these articles, De Morgan stated that “many details [of printed notation] are left to the compositor which should be attended to by the mathematician”, he wrote this having a certain familiarity for, and ability to make generalizations about, printed mathematics. For instance, De Morgan's annotated bibliography Arithmetical Books (1847) displays his interest in and knowledge of a large number of mathematical books emanating from a variety of places and times (De Morgan 1847). When De Morgan died in 1871, he proved himself something of a book collector too, having amassed a private library of roughly three thousand volumes. While on the one hand De Morgan’s statement about the haphazard nature of mathematical printing is an offhand remark, on the other hand it is a meaningful comment from someone who published mathematics himself and who carefully observed printed mathematics in many forms.

The impression given in a variety of sources is that technical printing was a difficult undertaking for nineteenth century printers. William Francis, co-partner in the printing firm Taylor and

Francis and publisher of the science journal Philosophical Magazine, wrote to the physicist and mathematician George Gabriel Stokes in 1864, “I fear that the expense of printing Archdeacon Pratt's elaborate numerical calculations would prevent the Editors of the Philosophical Magazine from accepting the paper for insertion in their Journals”.8 Similarly, Francis’ publishing partner Richard Taylor explained that inclusion of mathematics in the Philosophical Magazine came with limitations:

It is not in [the editor’s] power to admit any very great quantity of pure mathematics. The majority of the readers of the Magazine are more interested in other sciences, and the Magazine would soon cease to exist if it were more than sparingly supplied with articles on lofty mathematical subjects… The papers of the Philosophical Transactions, of the Memoirs of the Royal Irish Academy, of the Cambridge Philosophical Society, of the Cambridge Mathematical Journal, &c, are much fitter vehicles for extensive mathematical discussion than those of the Philosophical Magazine (quoted in Brock and Meadows 1984: 100).

Although Taylor and Francis served as printers to most of London's scientific societies and were experienced printers of scientific work, Francis’ letter and Taylor’s sentiments suggest that even this firm had limits when it came to mathematical printing.

When the Cambridge Analytical Society took their Memoirs featuring new analytical expressions of the calculus to the Pitt Press at Cambridge University, William Whewell wrote that “the extraordinary complexity and symmetry of the symbolical combinations sorely puzzled the yet undisciplined compositors of that day” (quoted in Topham 2000a: 328). The irony in Whewell's statement is that the press at Cambridge was one of the best-equipped printers for mathematics in England at the time. Apprentice compositors received specific training in the composition of mathematics (McKitterick 2004b: 356). Despite this, John Smith, who was University Printer when the Memoirs was in progress, complained that he had “never put together such crabbed stuff in his life” (quoted in Enros 1983: 35). He had to order more type from out of town – small

8 William Francis to George Stokes, 21 April 1864, Taylor and Francis Papers, St. Bride Library, London UK. Other factors, such as Pratt’s residence outside England, may have contributed to Francis’ dismissive attitude. A chaplain for the East India Company, Pratt was appointed Archdeacon of Calcutta in 1850. From his geographical position in India Pratt attempted to carry forth his mathematical career and defend his professional interests and reputation in England, something that was not easy to do from such a distance (see Barrow-Green 2001: 200).

20 numerals and brackets – in order to complete the job. The Analytical’s new method for the calculus puzzled students using the fluxional and geometric approach required by the Tripos examination. Similarly their unfamiliar symbols challenged the printers at the Press. Once available in book form, the Memoirs were priced at a high cost of 15 shillings per volume.9 This reflected what the authors had paid the press to print it; each published the book at an individual loss of £9 6s. 4d. (Topham 2000a: 329). While the unfamiliar content of the Memoirs was likely the decisive factor in its lackluster reception among the Analytical’s contemporaries, another factor might have been the cost of the book.

The present study aims to answer questions arising from the suggestion that it was difficult to communicate mathematics through moveable type printing (for the text) and wood engraving (for the illustrations). Considering the few known examples of how mathematics was translated into print, was it really harder and more expensive to print mathematical matter over other printed matter? This chapter explores why technical manuscripts were in fact more tedious and expensive to produce than other printed materials.

Two consequences arose from the increased difficulty of printing mathematics, and these had specific effects on the communication of mathematics in print. First, the increased expense of composing mathematical matter resulted in a financial burden for the publisher, be that a scientific society, a publishing company, or the author. This exaggerated the cost-to-benefit ratio in the publication of mathematics. This had an oppressive effect on the publication of scholarly mathematics, but the opposite effect on mathematical textbooks. Because the cost to enter the market with a new book was higher than for other subjects, a successful mathematical textbook could become even more successful due to lack of competition. Secondly, the difficulties involved in printing higher mathematics resulted in certain printing houses doing most printing of mathematical works.10 In order to have mathematics printed in a professional manner, an

9 According to the National Archives currency converter, the Memoirs in 1813 cost approximately £30 or $50 in today’s money. 10 Or at least, the printing of difficult or unusual mathematical work was something that only certain printers were capable of, or willing, to do. The Analytical’s Memoirs, Frege’s Begriffsschrift, and Bertrand Russell and Alfred North Whitehead’s Principia Mathematica are examples of mathematical books that would have been non-trivial to produce. When University of Toronto professor John Charles Fields published his Theory of the Algebraic Functions of a Complex Variable with Mayer & Müller in Berlin and Almqvist & Wiksell in Sweden, proofs crossed

21 author or publisher would have required the cooperation of one of these firms in order to receive the most able preparation of the text.

When a manuscript was sent to the printer, how, if at all, was its presentation altered by the printing process? Did the cost of setting mathematics encourage authors to economize their symbolism or the requirement for illustrations? Did the limitations of type influence mathematicians in their choices of certain mathematical expressions over alternatives? How were common printing practices in nineteenth century England applied to printing mathematics? The printing of mathematics is contextualized within the history of technological changes that occurred within the nineteenth century printing industry, changes that inevitably affected the production of mathematical texts during this time.

In section (2) I offer a brief overview of nineteenth century printing technology, focusing on the processes of composition and wood engraving. (3) aims to answer the question, what were the specific issues that made printing mathematics difficult? Sections (4) through (7) survey nineteenth century English printers and the mathematical work they undertook, looking specifically at Cambridge University Press and Taylor and Francis, firms that have been identified as major printers of mathematics (Secord 2009: 466), as well as printing firms William Clowes, A&R Spottiswoode and Oxford University Press. In section (8) a short case study of the printing of Principia Mathematica (Bertrand Russell and Albert North Whitehead, 1910) is presented. While more a work of logic than of mathematics per se, the dense symbolism of this text certainly posed an unusual typographical challenge to Cambridge University Press. Section (9) examines the tradition of using wood engraving for mathematical illustration. In section (10), concerns and attitudes about the production of successful mathematical illustrations will be revealed through the case study of Isaac Todhunter's A Treatise on Plane Coordinate Geometry, published 1855 by Macmillan and Company. Plane Coordinate Geometry was a college level textbook printed at the Cambridge University Press. Through correspondence between the Macmillan publishing house and wood engravers William Dodd and William Dickes, details

the Atlantic several times and Fields made an overseas trip to supervise the printing (Riehm and Hoffman 2011: 63- 4).

22 about the production of illustrations for the book are revealed. Section (11) concludes by offering answers to questions raised in this introduction.

2. Printing in the nineteenth century

Until the beginning of the nineteenth century, the printer's art had not changed much since Gutenberg first practiced the craft in 1450.11 As one author put it, “printing historians agree that the period between 1500 and 1800 was technically stable. Despite some local variation, printers everywhere handled closely similar tools and materials in closely similar ways” (Dewalt 1995: 24).

The original tools of printing were, basically, the common press, or wooden press, paper, lead type, and ink. Sheets of paper were made by hand from a mix of pulverized linen rags and other scraps with water. The mixture was spread and left to dry in woven wire racks. Type was cast by hand, letter by letter, from reusable moulds. Ink was applied to the letterform by dabbers or pelt balls, and considerable skill was required to apply a uniform layer of ink over the surface of type. Books were typically sold in sheets, and traveled in large bales wrapped in heavy paper. Compared to textiles, their intrinsic value was slight, but shipping (by stagecoach or barge) was usually costly. As books initially traveled to their customers unbound, the paper was occasionally exposed to the elements and could be subject to damage during transit (Darnton 2002: 19). Bookbindings were arranged for separately and crafted according to taste and ability to pay.

The act of ‘composition’ is the assembly of pieces of spacing and type so as to prepare the manuscript in moveable type. Metal letterforms cast out of lead were stored in a type case such that an entire alphabet of type was sorted into compartments according to letter. In one hand, the printer or compositor held a composing stick made out of wood or metal. Lines of type were formed by assembling letters from the case in the correct order in the stick. Lines were separated by thin pieces of lead, called leading, to create appropriate spacing between lines of text. When

11 It should be noted that while Gutenberg is credited for the invention of printing from moveable type, it had been invented in China in the eleventh century (using wooden types), and in Korea (using bronze types) in the fourteenth century. Historians believe the invention of printing from moveable type in Europe to be independent of its discovery in Asia (Twyman 1998: 21).

23 the stick was full, the block of type was moved to a tray (also called a galley) for temporary storage. Once enough lines for a page were composed, they were fastened into a metal frame (a chase), using pieces of wood (furniture) and metal keys (coins) that, when tightened, applied pressure to the assembled type. This entire construction is called the printing forme (see figure 2). Held together by pressure and friction, the hundreds of separate pieces that make up the printing forme remain assembled when the forme is moved for printing from the composing stone to the press bed.

Figure 2 The printing forme

Wood engraving, a form of relief printing, was a commonly used technique for the reproduction of images in nineteenth century books. Using wood as a surface for relief printing is an ancient art, having been applied for the printing of block books in ninth century China. However, wood engraving (as opposed to wood cutting) was a method first popularized by Thomas Bewick in the late eighteenth century. Its expression in his book British Birds (1797-1804) started a trend in illustration that quickly spread into common use across Europe. Bewick's wood engraving technique used boxwood cut across the grain, and a burin replaced the knife and gouge as the principal tool of carving. The technique offered more detailed, refined images than were possible with traditional wood blocks cut with the grain (the artist Albrecht Dürer, for instance, is considered a master of the wood cutting method).

As engraved wood blocks could be made the same height as type, the innovation of wood engraving also made it possible to print refined pictures beside text printed with moveable type. The other advantage was that boxwood was a tough material, and images engraved on it could

24 withstand the wear and tear of long print runs, in some cases, up to one million impressions (Twyman 1998: 51). Wood engraving met the demands of the nineteenth century for detailed images capable of being reproduced quickly and in large volumes. Typically, an image drawn onto the block or separately by an artist was cut into wood by an engraver. In the 1830s and 40s engraving became an industrial trade in cities such as London or New York, where dedicated firms satisfied the high demand for large, detailed engravings by assigning many engravers to one image in an assembly-line manner. Each engraver worked a piece of the image according to his or her skill (outlines, parallel shading, backgrounds, etc.). It was not uncommon for certain engravers to acquire a specialty such that they would only do certain elements of the image, such as foliage, faces, or architecture.12

The first major invention in printing technology of the nineteenth century was the development of the iron press in 1800 (Clair 1965: 210). With an improved action it was quicker and took less effort to operate. Whereas the wooden or common press operated at about 30 sheets per hour, the upper limit on a Stanhope iron press was roughly 200 impressions per hour (Clair 1965: 211). The second major change to press design occurred when the cylinder was adapted to the press. Both inking the forme and pulling the impression were mechanized so that a series of touching cylinders accomplished these tasks. Eventually stereotype plates of the printing forme could be curved and bolted to a cylinder as well, making the entire printing process even more efficient. By the end of the century rotary presses were fed a continuous stream of paper from a spool, eliminating the need to feed the machine separate sheets of paper, and increasing printing speed again. When Frederick Koenig and Andreas Bauer built the first cylindrical perfecting machine in 1816 it was capable of 900 to 1,000 sheets per hour.13 The Applegath and Cooper machine installed by The Times of London in 1827 completed 4,200 sheets per hour. The rotary presses of the 1860s produced 12,000 perfected eight-page newspapers in one hour (Clair 1965: 217).

The skilled compositor could assemble just over 1,000 letters and spaces per hour. Around 1840 the first composing machine raised the speed of composition to over 6,000 letters and spaces an

12 An immense demand for wood engravings was created by the illustrated periodicals of the day, such as Charles Knight's Penny Magazine (f. 1823, London), the Illustrated London News (f. 1842) and Harper's New Monthly Magazine (f. 1850, New York). 13 The term ‘perfecting’ refers to the act of completing a printers' sheet by printing both sides of the paper.

25 hour. Composing machines went through various iterations and improvements in the next forty years. The problem with these machines initially was that while they hastened composition, no accelerated system had been implemented for distribution (putting the type back into the case for reuse). For this reason, the mechanization of typesetting was not widely adopted until the invention of typecasting machines in the 1880s. When the linotype machine was invented in 1886, it combined into one machine all the jobs involving type: casting, composing, justifying, and distributing. The linotype machine solved the problem of distributing by melting down old type and reusing the metal to make new type. Monotype machines also composed mechanically, but in this case a paper ribbon perforated by a keyboard was fed into a separate metal casting machine. The monotype system also reused material to cast new letters. The difference between the two systems was that the linotype produced a ‘slug’ – one complete line of type, whereas the monotype machine produced individually cast letters assembled in the correct order, approximating more closely the appearance of regular moveable type. It was the common use of these machines in newspaper printing offices that begat the widely used term “hot type” (Clair 1965: 226).

Although the basic idea to mould and copy the printing forme had been the subject of experiment throughout the eighteenth century, the stereotype was not fully realized until the nineteenth century. In the stereotype process a mould is made from the printing forme using either plaster of paris or papier mâché. A thin layer of metal is poured into the mould, producing a duplicate surface to the original forme. The advantage of stereotype copies was that once made, the original type was free for use in new jobs, while one retained the ability to reproduce the printing forme without having to re-compose it. In the case of books in high demand, this saved time and money. The plaster method was used in England until 1846 when the papier mâché method, common in France, was introduced (Clair 1965: 220). Electrotype was invented in 1839. In this case a wax mould was made from the printing forme and then an electroplating technique was used to create a metal printing plate. The average print-run for an electrotype was 100,000, compared to roughly 50,000 from stereos (Clair 1965: 226). Woodcuts were also reproduced using the stereo- and electrotype methods. Using stereo or electro copies, the same illustration could be printed on more than one machine, or used by more than one printer. If the original wood block was damaged during printing, there was an identical copy to take its place.

The advent of the papermaking machine (invented by Nicolas Louis Robert, in 1799) increased the output of papermakers by ten fold and had the effect of cheapening the price of paper considerably (Clair 1965: 208). The supply of rags couldn't match the demand for material created by machine papermaking, and so a variety of new sources for raw materials were considered. In 1840 ground wood pulp was introduced, and over the next decade chemicals were applied to break down the cellulose fibers, with paper being manufactured in this way. In 1865 esparto grass was introduced as a cheap and practical material out of which to make paper. The use of esparto grass drove a massive increase in the amount of printed matter. The introduction of this new material along with the reduction of long-standing taxes on paper and stamps (the so- called ‘taxes on knowledge’ were cut in 1836), made paper in all its forms cheaper and more accessible than ever. As a result, Britain quadrupled its paper production between 1865 and 1895 (McKitterick 2004b: 2).

By the end of the century, books were put “in boards” by the publisher rather than receiving custom bindings chosen by the book buyer. By the 1840s bookbinding, which at one time had been a separate trade, became a subsidiary business of the large printers and publishers, who folded and bound their own books in house. Standard issue books typically received a cardboard binding, usually wrapped in cloth. By 1900 all books received standard bindings issued by the publisher (Briggs 2008: 15; Potter 1997).

3. Difficulties of printing mathematics

Although nineteenth century book and printing history is a lively area of research, few sources exist on the history of printing science, and fewer still offer anything about printing mathematics specifically. In his survey of science publishing in the nineteenth century, James Secord mentions the difficult and expensive task it was to undertake the printing of mathematics (Secord 2009: 466). He references a student’s unpublished M.Phil paper on the subject, which book historian Jonathan Topham agrees is the best source he’s read on the matter.14 Amidst the published record, Robin Rider has provided the most engaging account of how mathematical

14 Jonathan Topham to J. E. Barrow-Green, personal e-mail correspondence, 6 April 2011. The paper to which they refer is Chitra Ramalingham, “The mathematician and the compositor”, unpublished MPhil essay, University of Cambridge, 2002.

27 knowledge was influenced by the practice of typography and the print medium (Rider 1993). However, Rider's article does not discuss the time period in question here, as it begins in the fifteenth century and ends with the eighteenth.

Despite the lack of historical writing about mathematical printing, we can isolate a few reasons why the printing of mathematics has been characterized as difficult or specialized. All the issues that made technical manuscripts difficult were incurred in the first step of the process, that is, in preparing the manuscript for printing. While many of the skills of the printing house could be applied equally to mathematical books as they were to other books, the setting of a mathematical book in type could be more difficult. It might require a highly skilled compositor for the text and a skilled wood engraver for the illustrations, and possibly specific fonts had to be specially cast for the job.

The difficulties encountered in composing mathematical matter for printing can be listed as follows: 1) it required time consuming justification, 2) the use of rules increased the difficulty of composition (rules, which are type-high pieces of lead, were required to create the printed lines required by fractions or square brackets, for instance), 3) it required skilled compositors to attend to the job, 4) special types were sometimes required and had to be specially cut and founded, 5) illustrations, where needed, had to be precise and labeled accurately. The qualities most sought in mathematical illustration, such as precision and the accurate labeling of vertices or other elements of the drawing, were not necessarily qualities required of other illustrations or of wood engravers working in other contexts (more on this in sections 9 and 10).

‘Justification’ is the process by which small pieces of non-printing metal spacing are fitted around assembled elements of type. This is required to build up a solid printing forme in which pressure holds everything together throughout the printing process. Justification was often more complex with mathematical works because the use of exponents and subscripts required the assembly of extra spacing in order to secure the printing forme. The addition of spacing below and around letterforms as well as between them made the setting of these expressions more difficult than setting a regular English sentence in type. The use of rules in mathematical printing also intensified the difficulty of justification. For example, if a fraction (with a division line, necessitating the use of a rule) is followed by an operator such as a ‘+’, ‘-’ or ‘=’, this is one of the mathematical forms that breaks the printers line, thereby causing difficult justification.

Brackets surrounding three or more lines of type also involved the use of rules, as they were bent to the necessary shape. Large brackets also broke the printers line of type.

In his chapter “Science, technology and mathematics” Secord cites an 1875 report of the British Association of the Advancement of Science (BAAS) as one source that indicates that mathematical printing was indeed tricky (Secord 2009). This report is worth examining in more depth. The report was filed from a subcommittee “appointed to study mathematical notation and printing”. On the committee were mathematicians William Spottiswoode, Arthur Cayley, George Stokes, William Clifford, and James W. L. Glaisher (Spottiswoode et al 1876). The report mainly addresses the first two difficulties of mathematical printing as identified above. Time- consuming justification and the need for rules are the two main problems cited. This BAAS report also includes a figure showing four examples of mathematical expressions as a way of illustrating why such forms were difficult to compose. It is reproduced here (figure 4).

In figure (4), A and B represent compound fractions, C depicts an integral expression with indices expressing the limits of the integral at the top and bottom of the integral sign, and D shows a base (the mathematical constant e) with a functional exponent. Each mathematical expression is depicted as an amalgamation of letterforms and spacing as it might appear in a printer's forme. The grey areas represent the non-printing bits of metal (i.e. spacing) and the white squares represent the letterforms, or bits of type. This diagram illustrates why composing mathematics for printing was different to setting, for instance, a novel, poem or other English work. English sentences (see figure 3) require much less spacing to be added than do compound fractions, integrals with indices or bases with complicated exponents. In figure (4) the letterforms and spacing pieces are various sizes whereas in figure (3) the spaces and type conform to one uniform font size. In figure (3) the structure of the printing forme is organized by lines of leading that separate each line of words from the next line of words. In figure (4) lines of leading do not structure the printing forme in this way.

Figure 3 A sentence set in type

Figure 4 Examples of difficult justification (Source: Spottiswoode et al 1876: 338)

Figure (4) illustrates both why mathematical typesetting required time-consuming justification and why division lines (i.e. rules) magnified this problem. The report states that because of the difficulties involved in justifying such forms, “the cost of composing mathematical matter may in general be estimated at three times that of ordinary or plain matter” (Spottiswoode et al 1875: 387). The function of the report is to suggest to mathematical authors that they take steps to replace certain expressions with equivalents that are easier and less expensive forms to typeset.

The authors recommend eliminating division lines (rules) where possible and suggest the use of specific mathematical expressions that do not break the printers line of type (see figure 5 for the list of recommended forms). Adopting the recommendations, they say, will maximize efforts of the compositor, thereby minimizing the extra costs involved in printing mathematics.

Figure 5 Mathematical expressions not involving justification (Source: Spottiswoode et al 1876: 339)

It makes sense that in their report, Spottiswoode et al would encourage mathematicians to standardize the forms in which they sent their mathematical language to the printer. One can imagine that the forms chosen to express certain ideas might have had a measurable impact on the speed and overall cost of composition, as expressions might be repeated numerous times in a book length work or technical paper of a certain size. This advice was still being offered seventy years later when G. H. Hardy was consulted about a mathematical manuscript intended for publication as part of the series Cambridge Tracts in Mathematics and Mathematical Physics. Hardy notes that the author “does not observe the rules for setting up formulae laid down by the

LMS [London Mathematical Society] ‘Notes for authors’ and the result is a good deal waste of space” (quoted in Todd 1994: 34). He further comments that

π π 1 The sort of thing that needs attention e.g. y < (instead of π , wasting a line), 2 (instead of π 2 2 ∫− 2

1 π 2 15 1 , wasting two lines). All these things add up to a serious amount. ∫− π 2 € € € Given the number of mathematical texts circulating in its day, it would be difficult to comment € on whether the 1875 BAAS report had any effect on the use of mathematical expressions by nineteenth century British mathematicians. However publications about the preparation of mathematical manuscripts continued to be issued in Britain well into the twentieth century. G. H. Hardy authored a short pamphlet on the preparation of mathematical manuscripts in 1932, published by the London Mathematical Society (Hardy refers to it in his comment above). In 1954, T. W. Chaundy, P. R. Barrett and Charles Beatty released a guide for authors, editors and compositors of mathematics at the Oxford University Press (Chaundy et al 1954). This replaced Hardy’s pamphlet as the standard guide for preparing mathematical manuscripts for printing. Ray Hitching’s 1964 publication The Mathematician and the Printer contains a description of typographical difficulties very similar to the difficulties described by the BAAS report of ninety years earlier. A base (the natural logarithm) with a fractional exponent presents a time- consuming justification problem for the compositor. In this case justification requires the assembly of seventeen small pieces of type (see “a” in figure 6). This example of difficult typesetting is quite similar to problems outlined by the BAAS report from the previous century (compare with figure 4 expression “D”). However the difference between the 1870s and the 1960s is reflected by Hitching’s depiction of an equivalent expression (see “b” in figure 6). In this case, the expression is composed entirely by Monotype machine. The adaptation of the Monotype machine to mathematical composition in the 1930s eliminated the human being having to pick out different sized fonts from various type cases, or assemble expressions by hand in a composing stick. A monotype operator sitting at a keyboard could compose a mathematical text by typing it; the machine would output the type. While originally machine composition had

15 Common fractions (such as ½) were available as single letterforms of type. Hardy suggested expressions that avoided the setting of a fraction by the compositor (a fraction requiring a “2” under a division line, would require the use of several separate letterforms). This would have saved space.

32 to be combined with a certain amount of make-ready, by the 1960s some mathematical manuscripts were entirely composed by machine (Hitchings 1965: 83).16

Figure 6 Two typographical forms expressing indicies; (a) showing an exponential function requiring justification and (b) showing an equivalent form composed by machine (Source: Hitchings 1965: 83)

In their 1954 guide, Chaundy et al noted that “the setting of mathematics is a rare and expensive skill not readily acquired. Existing facilities often have difficulty keeping pace with the rapidly growing output of mathematical writing. For this reason there may be a long and vexatious delay between the writing and the publication of a mathematical work” (Chaundy et al 1954: 21).17 In

16 Within the context of composition by machine, in some cases printers had to re-arrange certain bits of type by hand after machine composition but prior to the type forme being ready to print. This act is one of the tasks referred to by printers as make-ready. 17 In his essay about mathematical printing at the University of Toronto Press, Roy Gurney echoes this sentiment. The Press at UofT installed a monotype keyboard and caster in 1910 to aid in the composition of mathematical examination papers at the university. By 1950, the University of Toronto Press was a major printer of mathematics, with Gurney reflecting that “By 1950, the capabilities of the University Press in mathematical typesetting were being severely taxed. Only one of the machinist operators really possessed the requisite skill, and he was becoming advanced in years…There were two or three highly skilled hand compositors capable of making up the complicated formulae, but their available time was overloaded, and it was becoming very difficult to train apprentices in this difficult craft. To find Canadian craftsmen in the industry who had this skill was virtually impossible. Another problem was, of course, the increasingly high cost of the hand operations involved in the composition of technical

1930, G. H. Hardy, R. H. Fowler and the editors of the Quarterly Journal of Mathematics collaborated with Oxford University Press and the Monotype corporation to adapt machine composition to the setting of mathematics, but it was not an easy task: “much adaptation and recutting of type faces was necessary before the new system could come into use” (Chaundy et al 1954: v).

Whether the composition of mathematics was actually made more efficient by its adaptation to the Monotype machine is difficult to ascertain. Historian David McKitterick has noted that all compositors at the Cambridge University Press received specific training in the composition of mathematics. This practice of mathematically training compositors continued well into the twentieth century, even after the Press acquired Monotype machines and began relying heavily on them for composition (McKitterick 2004b: 356). For some mathematical work, type was still hand set at the Pitt Press well into the 1970s (McKitterick 2004b: 8). Even after computers could drive hot-metal casting machines in the 1960s, the press at Cambridge continued to rely on the established skills of an experienced compositor when it came to setting mathematical works. For most mathematical material “extremely skilled Monotype setting was combined with hand- composition, including filing down pieces of type so as to achieve better fit, or to create special sorts” (McKitterick 2004b: 12). Cambridge University Press was known to keep high standards for printing mathematics. McKitterick says that the Press “became for many the best for scientific and mathematical composition in Britain” in the 1950s and 1960s (McKitterick 2004b: 356). Until mathematicians themselves began to use computer programs for composition (TeX software was invented 1978), a highly skilled compositor using a combination of hand setting and Monotype machine remained the most efficient way to transform mathematical manuscripts into printable form in the twentieth century.

In a 1950s article in The Monotype Recorder, a trade publication of the Monotype Corporation, Arthur Phillips confirms the idea that skilled compositors with knowledge of mathematics are required for the job of composition. It is interesting to note that the requirement for a skilled

material. Labour cost had already become a major item in any printing job and this was reflected strongly in the cost sheets for mathematical works being produced” (Gurney 1961: 125).

34 compositor with mathematical literacy remained even after the advent of machine composition. Phillips describes the necessary ingredients for a successful job: “There are several requirements for successful mathematical setting. Both the ‘Monotype’ operator and the compositor need an elementary knowledge of mathematical notation. The author’s copy must be legible and without ambiguity. The printer must give some thought to the problem of mathematical setting before undertaking the work, for it is all too easy to underrate the extent of the planning and equipment required for mathematical composition” (Phillips 1956: 7).

Historically, compositors played a crucial role in the adaptation of any text for printing, mathematical or not. Until the twentieth century, the compositor was relied upon to make decisions about the visual presentation of a text, and to correct small mistakes in the manuscript. Graphic designers did not emerge as distinct professionals until after 1900 (Dewalt 1995: 46). In the nineteenth century it was the compositor’s job to devise the visual presentation of a book, possibly under the supervision of an author, editor, or publisher, depending on the circumstance. The compositor also frequently served as copy editor when setting English or Latin texts, routinely correcting spelling and punctuation errors in the original manuscript (Dewalt 1995: 46). Perhaps DeMorgan had this image of the compositor in mind when he stated that in mathematical printing, “many details are left to the compositor which should be attended to by the mathematician. Until some mathematician shall turn printer, or some printer mathematician, it is hardly to be hoped that this subject will be properly treated” (De Morgan 1842a: 444). Unless a compositor had a certain basic degree of mathematical literacy, decisions about line breaks, the organization of the material on the page, the prominence of headings or even the ability to interpret an author’s written symbol and chose the appropriate letter of type, would have been difficult.

Mathematics was a specialized art within the printing trade and only some printers undertook it. This was because of the extra expertise, time and tools required to do the job. However, bibliographies of mathematics show that mathematical books emanated from printers all over Britain, in cities and in smaller towns, not just in London, Cambridge, Oxford, Edinburgh and Dublin but also from Bristol, Birmingham, Newcastle, York, Whitehaven and Chipping Campden (Wallis and Wallis 1986). This seemingly presents a paradox and raises the question, how did printers outside major centers of learning overcome their lack of mathematical expertise when they printed a mathematical book? How can mathematical printing be a specialized art if in

35 fact mathematical books were printed in a variety of disparate places?

Robin Rider has conjectured an answer that is plausible and which is adopted by the present work. First of all, one might consider that not all entries in mathematical bibliographies represent first publications of original mathematics (Rider 1993: 111-112).18 In many cases smaller printers brought out their own versions of common guides or schoolbooks or subsequent editions of classic books on mathematical subjects. Peter and Ruth Wallis’ Biobibliography of British Mathematics and its Applications, for instance, also takes a broad definition of mathematics, including entries for books about astronomy, navigation, surveying, building, dialing and clockmaking, motive power, electricity, accounting and insurance (Wallis and Wallis 1986: v). Some of these books may not have required the kinds of specialized tools or specialized knowledge that producing other mathematical texts would have required.

For works of mathematics, Rider suggests that “typographical culture” took over from mathematical culture, for all subsequent editions beyond the first. While a book’s author often approved of the notation used in the first edition, for subsequent editions, Rider suggests printers copied the forms used in the first printing (Rider 1993: 111-113). She gives as her example Euler’s Elements of Algebra. First published in 1768 in Russian , numerous translations and editions appeared from various printers over the following four decades. In comparing these, Rider posits that the compositors always copied the formulae from earlier printed versions. While the house style (and language of the text) varied between editions, the similarities in the equation typography are, in her opinion, too similar to be the product of a new setting of the equations. Rider suggests that subsequent printers had on hand a previously printed copy of the text, and followed all the original decisions about how to present the symbols (regarding alignment, where to break a line, which sorts to use, etc.). Copying from previously printed mathematical symbolism created similarities in the typography of every edition, even if the text was translated into a different language (Rider 1993: 112). If this conjecture holds generally true, then most of the difficulty of composing mathematics was concentrated in the first printing, with

18 Bibliographies that come to mind are Peter and Ruth Wallis' Biobibliography of British Mathematics and its Applications, Part II, 1701-1760, Rider's A Bibliography of Early Modern Algebra, 1500-1800, and D. M. Sommerville's Bibliography of Non-Euclidean Geometry.

36 subsequent editions following conventions set by the first.19

These and other details arising from her close observation of early mathematical books lead Rider to conclude that “the practical problems of publishing mathematics [may have] had more influence on the simplification and standardization of mathematical expression than did any organized action by mathematicians” (Rider 1993: 113). The idea that printed forms begat similar printed forms of symbolic expression may have continued throughout the history of printed mathematics.

Rider observes, “The Book of Nature might be written in mathematical language, but it was printers who conveyed this language to the eyes of most students and scholars of early modern mathematics” (Rider 1993: 113). This statement holds for nineteenth century British mathematicians and their audiences even more so than it did in earlier times. By 1900 British mathematical books were in general, more affordable commodities available to ever-larger audiences domestically and around the world. This change occurred through the application of steam-power to printing, amplifying the number of available mathematical books, and the implementation of public education systems that, by the twentieth century, brought many students into to contact with mathematical textbooks.

4. British printers of mathematics

As has already been mentioned, Wallis’ Biobibliography of British Mathematics and Its Applications has demonstrated that in the eighteenth century, mathematical books were being produced not just from London, Cambridge, Oxford, Edinburgh and Dublin, but also outside major centers of learning in smaller towns and cities (Wallis and Wallis 1986). Given the expansion of the book trade in the nineteenth century, especially in the latter part of the century, both the number of mathematical books and the number of different printers of these books will be impossible to examine in entirety. That being said, we can look at some of the largest printing

19 To test how universal a practice this was, one might, for instance, examine some of Isaac Todhunter’s textbooks that were pirated and translated into local languages by Indian printers at the end of the nineteenth century (see Aggarwal 2007). If errors were present in the equations of the original edition, were these mistakes reproduced in the equations of the pirated editions? Were the syntactical breaks in the equations from the original book mimicked in pirated editions in Hindi, Bengali or Urdu? Copies of Indian printed mathematical books reside in the Oriental collections at the British Library. To date a comparison of these editions for typographic style has not been made.

37 houses and those already known as having a specialization in mathematical books, and examine their connections to the printing and publishing of these works. The following sections discuss some of the ways in which printers William Clowes, Andrew and Robert Spottiswoode, Oxford University Press, Cambridge University Press, and Taylor and Francis were involved with the printing of mathematical books, and how the conditions of each printing house would have shaped the material that was printed there.

5. Populist printers William Clowes and A&R Spottiswoode

William Clowes of London, the first printer in Britain to apply steam printing to book production, produced books and educational works for the masses. A&R Spottiswoode were also early adopters of steam-printing technology. Like Clowes, they had one of London's largest printing works in the 1830s. Clowes biggest client was the Society for the Diffusion of Useful Knowledge (or SDUK, founded in 1827), which developed materials for the edification of the working and middle classes, most notably the publications Penny Cyclopaedia and Cabinet Cyclopaedia. A number of mathematicians connected to the newly founded University College London (UCL) were associated with the SDUK, contributing materials about mathematical and scientific topics to its educational publications. Augustus De Morgan (UCL's first professor of mathematics) and Dionysius Lardner (UCL's first professor of natural philosophy and astronomy) both contributed materials to the Penny Cyclopaedia and Cabinet Cyclopaedia. These publications were printed by either Clowes or A&R Spottiswoode. Both printers had steam-printing machines as early as 1819, which facilitated the production of large quantities of books at low prices. These printing houses produced some of De Morgan’s most famous books. Clowes handled De Morgan’s The Differential and Integral Calculus (De Morgan 1842b). Released as part of the SDUK’s Library of Useful Knowledge series, De Morgan’s Calculus was sold for the low price of sixpence (Fischer 2004: 279).

Clowes was one of the first English printers to apply the invention of steam printing to make what had been essentially a craft product – the book – into an industrialized product. Clowes set up his printing shop with one press and one assistant in 1803. At this time his stock of type was so small, that Clowes was “under the necessity of working it from day to day like a banker’s gold” (Smiles 1885: 208). However, Clowes’ goal as a printer was to deliver a product with accuracy, speed and in large quantity. He made it his business to produce books in sufficient

38 amounts and affordable enough to be marketed to a large population. With these goals in mind, his business grew steadily, and in 1823 he purchased his first steam printing press from Applegath & Cowper in order to fill even larger orders for books. While steam-printing machines had been used for newspaper production, he was the first printer to make regular use of the steam press for books (Clair 1965: 228).20

In the course of a few years, Clowes acquired twenty steam powered printing machines. He kept them busy printing publications for the Society for the Diffusion of Useful Knowledge, including the Penny Magazine, edited by Charles Knight (which reached a circulation of 200,000 copies) and the Penny Cylopaedia. By 1839, Clowes expanded his business into type founding, a practice usually considered a trade unto itself and uncommonly undertaken by printers (Clair 1965: 225). Through this practice he reportedly supplied his compositors with 50,000 new sorts (bits of type) per day. He also undertook stereotyping on a large scale. In 1839 the Clowes premises held more than 1,600 formes of standing type, about 100 tons of free type, about 2,000 tons of weight in stereotype plates, and 50,000 woodcuts on hand from which stereotype casts were taken and sent to various printers across Europe (Clair 1965: 231, Smiles 1885: 214). He employed 500 people directly and many more indirectly (Smiles 1885: 214). Even in a time when industrialization was rapid, Clowes mid-nineteenth century printing establishment was gigantic, considered by some one of the largest in the world (Clair 1965: 228). Because of his association with the SDUK and his printing of many educational works aimed at the middle and working classes, the reformer and educational advocate Samuel Smiles wrote that “[William Clowes’] name is entitled to be permanently associated, not only with the industrial, but also with the intellectual development of our time” (Clair 1965: 229).

In 1819 when Andrew and Robert Spottiswoode succeeded their uncle Andrew Strahan in his London printing business, one of the first steps the brothers took was to install steam printing.21 Investments of this kind in the early days of the technology did not come cheaply: the steam

20 A Koenig machine, the first power driven cylindrical press, was used by The Times of London in 1814 (Twyman 1998: 70). 21 The mathematician and printer William Spottiswoode was related to the business (as Andrew Spottiswoode's son). In 1846 William took over the title of Queen's Printer and ran the government printing side of the family business.

39 engine itself cost £782, the Applegath perfecting machine £1200, the foundry £735. By 1832 Robert died and Andrew became the sole proprietor. In 1837 a fire consumed one of the Spottiswoode’s printing sites, and records of the fire document how large the operation was at that time. The quantity of destroyed books totaled an estimated value of twenty thousand pounds. Some of the lost works included spelling and other school-books for Longman’s and Co., various novels for Bentley, an edition of Shakespeare, various law-books, books commissioned by John Murray (including works by Lord Byron), the greater part of the forthcoming volume of Lardner's Cyclopaedia, and other works from a large variety of London's publishers (Austen- Leigh 1912: 39).

Both Clowes and A&R Spottiswoode were heavily capitalized in steam printing technology making it possible in the 1830s for each to produce large numbers of books at a lower price. This was not typical of all book printers at the time. Oxford applied steam printing in 1834 (eleven years after William Clowes), however these presses were used only for the production of Bibles. At the time, printers who applied steam technology to the production of regular trade books could produce many books at a lower unit cost than other book printers. This makes the application of steam printing a significant aspect of a book’s production history if it was printed this way in the early half of the nineteenth century. In general, print was becoming increasingly prolific during the nineteenth century (Eliot 1994). However, books were still considered a luxury, a fact particularly apparent in times of economic depression (Barnes 1985). Books in the Cabinet Cyclopaedia and Penny Cyclopaedia series were priced at three to six shillings. Books in the Library of Useful Knowledge series sold for sixpence. Through such series, large numbers of books were made available at cheap prices. Conceivably, such books could come into contact with a greatly expanded population.22

22 The average price of a new novel in the 1820s was 10s. 6d. Buying a book for this price was considered a luxury in 1818 (Barnes 1985: 211). In his extensive study of the nineteenth century book trade, Simon Eliot defines ‘cheap books’ as having a price of 3s. 6d. or less. The Society for the Diffusion of Useful Knowledge’s publications were on the leading edge of what would become a wave of cheap books. Eliot observes that in the late 1840s and throughout the 1850s, cheap books rose to dominance within the book trade. Eliot also notes that frequently a book’s low price correlated with longer and more frequent print runs, i.e. higher circulation (Eliot 1994: 24).

The author of numerous volumes on natural philosophy for the Cabinet Cyclopaedia series, Dionysius Lardner was deeply involved in broadening the audience for technical subjects during his day. When Lardner came to London from Dublin in 1827, he had already graduated from Trinity College Dublin (BA 1817, MA 1819) and received numerous prizes in logic, metaphysics and mathematics, including a gold medal for lectures on the steam engine (Peckham 1951: 39). By the time he took up the first professorship of natural philosophy and astronomy at the newly founded University College, he had already published a number of treatises on mathematical and technical subjects. During his time in London he continued his involvement in the writing and editing of books on mechanics, hydrostatics and mathematics for a popular audience.

Bibliographer Morse Peckham sees Larder's work in populist educational publishing as not strictly motivated by altruism but also a product of identifying a newly available market and capitalizing on it. Peckham particularly sees Lardner's involvement in the Cabinet Cyclopaedia series this way. The cheap and quick printing offered by steam-power suddenly opened up the middle and working classes as customers for books. This economic opportunity dovetailed with a political movement that viewed education as a benevolent and civilizing force for the lower classes. Peckham writes, “out of this situation of spreading literacy and agitation for political, social and educational reform came the Cabinet Cyclopaedia, edited by one of the men who saw the possibilities for simultaneously extending knowledge and making money, Dr. Dionysius Lardner” (Peckham 1951: 39).

The Cabinet Cyclopaedia series was comprised of sixty-one titles issued in 133 parts, published between 1829 and 1846. Dionysius Lardner was the series editor of this large project. Excluding unnamed authors, thirty-eight authors contributed to the series, and a number of them wrote books in the area of natural philosophy. Natural philosophy and natural history formed a large quantity of the material in the Cyclopaedia comprising 27 (nearly half) of the 61 titles published. The titles within the natural philosophy section included Augustus De Morgan’s book An Essay on Probabilities and on their Applications to Life Contingencies and Insurance Offices (1838). Dionysius Lardner’s contributions include separate volumes on heat, hydrostatics, and electricity, as well as Treatise on Arithmetic Practical and Theoretical (1834) and A Treatise on Geometry and its Application in the Arts (1840). Astronomer Sir John Herschel contributed Astronomy (1833) and A Preliminary Discourse on the Study of Natural Philosophy (1831).

David Brewster contributed Optics (1831). Henry Kater co-authored with Lardner a volume on Mechanics (1831).

Printed by A&R Spottiswoode, each volume of the Cabinet Cyclopaedia series sold for six shillings, a price that made it affordable for the middle class but slightly out of reach of the working class, the audience intended for the Penny Cyclopaedia. The Cabinet Cyclopaedia was popular enough that an American printer began pirating the work almost at once (Peckham 1951: 43). The series spawned many titles that continued to be in demand for years afterwards. Herschel’s books on natural philosophy and astronomy, De Morgan’s book on probabilities, and Lardner’s contributions, were reprinted many times. Though the dissemination of cheap books, particularly on subjects most often reserved for cultured or educated society, the Cabinet Cylcopaedia series played a role in nurturing popular interest in these subjects.

Thomas Peacock’s satirical novel of 1831, Crotchet Castle, gives some context for how the popularizing spirit was affecting the nation in the early nineteenth century. In the book, the main character Reverend Doctor Folliott (a learned, middle-aged clergyman) exclaims, “God bless my soul, sir! …I am out of all patience with this march of mind. Here has my house been nearly burned down, by my cook taking it into her head to study Hydrostatics, in a six-penny tract, published by the Steam Intellect Society…My cook must read his rubbish in bed; and as might naturally be expected, she [sic] dropped suddenly fast asleep, overturned the candle, and set the curtains in a blaze” (Peacock 1831: 19). Dr. Dionysius Lardner’s treatise on Hydrostatics and Pneumatics (published in April 1831, part of the Cabinet Cyclopaedia series) is the book being parodied here (Peckham 1951: 37). References to Lardner’s book in popular literature (despite, notably, the cook having been put asleep by reading it!) indicate that his books had a public impact in their day.

Lardner’s popular edition of Euclid for the use of schools, printed by Clowes in 1828, was also a successful publishing venture. The University of London opened for instruction in October of 1828, and Lardner’s book was ready to fill student demand. He self-published this version of Euclid and had it printed by Clowes, who by that time had on hand their twenty steam printing machines. The ability of these machines to print books cheaply may have meant that the price of Lardner’s Euclid undercut the price of other Euclids in the marketplace. Moreover, Clowes had the capability to stereotype the book and produce subsequent editions quickly and as needed.

June Barrow-Green in her survey of English Euclids notes that Lardner’s Euclid was very successful, being reprinted for the twelfth time by 1861 (Barrow-Green 2006: 13). While it may have been the presentation of the book that made it successful, qualities dictated by the circumstance of its printing, such as price, abundance, and timing, facilitated by Clowes intense capitalization in steam-powered printing technology, may have played a part in the success and longevity of the edition.

William Clowes and A&R Spottiswoode applied the power of steam printing to popular and educational works on technical subjects. This unique marriage paired content often considered specialized or particularly learned with a printer capable of producing the material in a large volume and at a price that facilitated a broad audience for these works. It is well known that the application of steam printing to book and newspaper production contributed to what Peacock referred to in Crotchet Castle as the “march of mind”. However, it is significant within the history of mathematics that mathematical subjects had some place within the diffusion-of- knowledge movement. Titles on technical subjects were written for the non-specialist audience and made affordable to middle class and working class audiences. That William Clowes and A&R Spottiswoode printed these materials in vast quantity was one way in which mathematical subjects achieved greater exposure in the early nineteenth century period.

According to Peckham, “the revolution of literacy, partly the result of the spread of liberal ideas by the French Revolution, partly of the desire to combat those ideas by teaching the poor to read the Bible and religious tracts, was to have an effect on modern society almost as profound as the industrial and agricultural revolutions” (Peckham 1951: 38). To what degree numeracy might have developed hand-in-hand with literacy during the same period is an open question worth considering. Possibly similar social forces brought about a wider familiarity with mathematics at the same time that public literacy was increasing. Before simple mathematics became a pillar of a public education system and before barriers to higher education were removed, these publishing ventures in the diffusion-of-knowledge movement were early attempts to make this material more broadly accessible.

6. Scholarly printers Oxford University Press and Cambridge University Press

As one of the two learned presses in England, Oxford University Press produced mathematical books since it was founded in the fifteenth century. A variety of editions of Euclid, for instance, were produced by the press in the late seventeenth and early eighteenth centuries (see Carter 1975, for a list). They published works by the Savilian Professors of Geometry and Astronomy, authors such as John Wallis, David Gregory, Edmund Halley, and Christian Huygens.

While Oxford University Press entered the nineteenth century a small to medium sized publishing house, it emerged in the twentieth century a publishing giant. In 1994 it was gauged as the largest university press in the world (Balter 1994). However, the Press’ development in the nineteenth century until very recently had remained opaque, as no comprehensive history of the press had yet been released. Fortunately, Oxford University Press just received comprehensive historical treatment, as a multivolume history edited by Simon Eliot was published in the fall of 2013.23

One crucial factor that shaped both Cambridge University Press and Oxford University Press over the course of the nineteenth century was their involvement in the printing of Bibles. This fact played an important role their development as scholarly printers. The Bible movement, which began in England in 1804 with the founding of the British and Foreign Bible Society, was a cultural force that transformed both Cambridge University Press and Oxford University Press as printers. By 1816, the Bible society had 236 auxiliaries and 305 active branches spread out over the United Kingdom (Clair 1965: 250). The society was one of the printing industry’s largest clients in the first half of the nineteenth century. It commissioned the printing of millions of Bibles, and because of an ancient law regulating the printing of these so-called ‘privileged books’, Oxford University Press, Cambridge University Press, and the Queens Printers shared the exclusive right to print the Bible and associated religious texts of the Church of England. The Bible society’s mission to make available cheap religious books reorganized and transformed the

23 With sincere thanks to Jonathan Topham, I have had advance access to his contribution to the second volume (Topham 2013). His chapter “Science, Medicine, and Mathematics” will appear in History of Oxford University Press, vol. 2, 1780-1896, edited by Simon Eliot, forthcoming from Oxford’s Clarendon Press in November 2013.

British printing trade, and particularly the presses at Oxford and Cambridge, who reorganized themselves in the early nineteenth century to serve the demands of this powerful client.

Historian Leslie Howsam has characterized the effect of the Bible movement on the printing industry this way: “That nineteenth century Britain was deeply attached to its Bible as the source-book of Protestant Christianity is well known; the text did not, however, enter the minds and hearts of its readers without the mediation of publishers and printers” (Howsam 1991: xiii). The British and Foreign Bible Society was such a ubiquitous presence within early Victorian culture that its organizing effects were completely taken for granted (Howsam 1991: xv).24

When the British and Foreign Bible Society began purchasing Bibles in 1804, the extraordinary numbers in which they demanded books, combined with Oxford and Cambridge’s exclusive ability to fill this need, placed extraordinary demands on each university press. The development of stereotype, machine printing and papermaking were developed for and then perfected by the work each did on the mass production of Bibles. In the process of working for the Bible societies both presses at Oxford and Cambridge developed the technology and supply-chain necessary to mass-produce books. The Bible having primed the pump, these printers went on to apply the same industrial capacity for the projects of other clients, and other markets, later in the century. In this way, the Bible movement had an important organizing force on these two academic publishing houses, making both uniquely equipped to serve as printers on other large and complicated printing projects.

In the case of Cambridge University Press, their involvement with the Bible trade had specific beneficial effects on their printing of scholarly work. Their presses were kept in good condition and up to date. They invested in their stock of type; when it became worn they replaced it. The demand for Bibles brought about their early application of stereotyping, a process that the Pitt

24 When Charles Babbage and Michael Slegg founded the Analytical Society at Cambridge, they took as inspiration the activities of the British and Foreign Bible Society. Babbage conceived of the Analyticals as purveyors of the French math text Traité élémentaire by Silvestre Lacroix. In jest he modeled their mathematical agenda to parody the controversy over the British and Foreign Bible Society’s policy on whether or not the Bible should be distributed with commentary. Babbage set out the Analyticals’ agenda: “that we should have periodical meetings for the propagation of d’s; and [consign] to perdition all who support the heresy of dots” (d’s and dots being symbolic of the rival notations for the calculus bring used on the continent versus in Britain). It maintained that the work of Lacroix was “so perfect that any comment was unnecessary” (Babbage, quoted in Enros 1983: 27, 44 f.n.2).

Press began using in the very earliest days of its development as a technique (McKitterick 2004a: 32). For an extremely large work like the Bible, which contains nearly 800,000 words, every page of an octavo edition required some 5,000 pieces of metal to compose it. Despite the vigilance of proofreaders, the possibility of errors due to the mixing up of letters was very great. Because of the way in which stereotyped plates could be corrected, printers learned to apply this technology to reproduce an accurate text through multiple editions. Because of the skills and technologies Cambridge University Press had acquired from the printing of Bibles, it had become by mid-century a highly skilled and well-equipped printing house. These investments benefited all clients who subsequently commissioned work from the Press (for example, Macmillan and Company, who used Cambridge University Press as their printer for almost all their mathematical books). The skills of a highly trained printing house were especially beneficial for the production of scholarly works that demanded precision and an unusual attention to detail in the composition and printing process. Mathematics was one such subject that benefitted from the experience of Cambridge University Press staff. Trained by the demands of the Bible trade, the Press could apply its learning and experience to the preparation of other complicated texts, for instance, mathematics.25

Oxford University Press also benefited from their involvement with Bible work. In 1834 Oxford installed their first steam-powered presses, which vastly expanded their output of Bible work. At Oxford, close to half a million Bibles were printed between 1808 and 1815. After the installation of the steam-printing machines, roughly two and a half million Bibles were printed in the same number of years after that (Barker 1978: 44). This is an astonishingly large number of books to have been produced by a printer at this time. In 1822 Oxford had for sale nineteen different editions of the Bible, nine editions of the New Testament, and twenty-one different prayer books, ranging in price from over five pounds for a royal folio Bible to eight pence for a small pocket- sized prayer book. In 1895, Oxford University Press had seventy-eight different editions of the Bible available.

25 McKitterick notes that the standards for proof reading at Cambridge were high, because readers accustomed to proofing the Bible and Prayer Book developed rigorous skills. This fact was appreciated by clients such as Macmillan, who themselves had high standards for printing (McKitterick 2004b: 66).

However, because Oxford's “Bible press” and “Learned press” operated separately until 1882, the benefits of investment arising from the Bible business did not cross over to benefit the printing of scholarly books in the same way that it did at Cambridge. Only when Oxford’s press began losing lucrative contracts to print the Bible did it decide to venture more seriously into the business of publishing, at the same time reinvesting in its learned press. In May 1863 Alexander Macmillan (the head of London publisher Macmillan and Co.) was appointed publisher to Oxford University. The publishing arm of the Oxford University Press was called the Clarendon Press. During the nineteenth century Oxford published about one hundred and fifty titles within the subjects of mathematics, science and medicine, as well as printing on commission other books for Oxford authors and booksellers. Some of the significant titles they produced include William Thomson and Peter Guthrie Tait’s Treatise on Natural Philosophy (1867), James Clerk Maxwell's A Treatise on Electricity and Magnetism (1872), the Index Kewensis (1893–5), and translations of German physiological and botanical works including August Weismann’s Essays on Heredity (1889) (Topham 2013).

Because the height of the type used by Oxford's Bible press and height of type used by Oxford's learned press was not equal, none of the type maintained for the Bible press could be assimilated for use in the learned press, or vice versa.26 In 1882 Oxford amalgamated their learned and Bible presses, which had previously run as two independent businesses using separate sets of equipment. At that time, the learned press was relying on then-antiquated machinery (Barker 1978: 50). Horace Hart, formerly of William Clowes and Sons (the London printing works) became printer to Oxford in 1883. He subsequently bought new presses and purchased new fonts of type for learned works (mainly from Germany). To go along with the reorganization, Hart published his Rules for Compositors and Readers, in 1893.

At Cambridge, Bible work had benefits beyond just the rejuvenation of physical infrastructure. For the first half of the nineteenth century, Bible work was the bread and butter business from

26 In 1688 Oxford had set up a ‘Bible press’ as a special department, separating this from the ‘Learned’ or Classical Press (Clair 1965: 250). There was not a standard height of type in England until 1905, when the American point system became general (Clair 1965: 271). Why the typefounders of England spurned standardization is unknown, although Clair suggests that perhaps it was to prevent the lending of sorts among printers (Clair 1965: 269). France’s typefounders Fournier and Didot made the first efforts to set standards for type size, and the system was generally adopted in France in 1801 and in Germany shortly thereafter. By 1890, most American type founders had adopted an American point system.

47 which they could pay for unprofitable ventures in the expensive realm of scholarly publishing. McKitterick notes, “their privilege, permitted them to print the Bible and prayer book; and in the second half of the eighteenth century these two books became the economic rocks on which it was possible to build a structure of publications many of which required subsidy such as this assured income could provide” (McKitterick 2004a: 40). The profitability of Bible printing lasted until the mid-nineteenth century. For nearly a century the Bible business was a major source of income from which Cambridge could finance its scholarly publishing program.

Until the mid-nineteenth century, Cambridge University Press’s business was oriented more towards printing-for-hire (job printing for external clients) than its own publishing program. In the 1850s, Cambridge offered a narrow list of books for sale, which appealed only to a small audience, even among the academic population. By 1900, the Press’ printed catalogue spread to 164 pages, signaling how much the publishing side of the business had grown (McKitterick 2004b: 108). Much of the growth came when Cambridge University Press began publishing textbooks and schoolbooks in the 1880s. The profits that flowed from sales of educational titles became a new source from which scholarly books could be funded. Through the many transitions the Press weathered as a printer-for-hire, it continued its commitment to scholarly publishing, where in general titles moved slowly and some projects never recouped expense or would only after many years.27 McKitterick notes that the press carried on with scholarly projects with little effort directed towards discovering the true cost of this part of their business (McKitterick 2004b: 110).

Among the collected works they undertook were G. G. Stokes Mathematical and Physical Papers (5 volumes, 1880-1905) and the Mathematical and Physical Papers of Sir William Thomson (6 volumes, 1882-1911).28 These were multivolume works that required subsidy to

27 At the end of 1891 the press still held 1,144 sets of Isaac Barrow’s collected works in nine volumes, which had been published in 1859. In eight years, only thirty-two sets had been sold or given away. During the same time the stock of Whewell’s edition of Barrow's Mathematical Works (1860) had reduced by forty-two copies, from 367 to 325 (McKitterick 2004b: 112). 28 William Thomson acquired the title of Lord Kelvin in 1892. However, during the majority of his activities discussed in this thesis, for instance in his role as editor of the Cambridge and Dublin Mathematical Journal (see chapter three), he was still known as William Thomson. For the sake of consistency, he will be referred to as such throughout this work.

48 produce. Sometimes a series such as these would not sell out for decades, which meant that Cambridge University Press waited many years to recoup its investment. In particular, one volume of Stokes’ mathematical papers produced at the end of 1884 required the allocation of a portion of the Government Annuity Fund, a sum of £500 per annum, to fund its completion (McKitterick 2004b: 92). The Government Annuity Fund was designed to support scholarly publishing work that could not be expected to return a surplus. Subsidy of Stokes’ Mathematical and Physical Papers signals that the Press deemed the work important but not profitable.29

In the nineteenth century, Cambridge also published many single volume books (or monographs) by prominent men of science. As either graduates, tutors, professors, or students, many of these authors were in some way connected with Cambridge’s institutional focus on mathematics. Some of the books on mathematical topics that the press released include J. Gow’s History of Greek Mathematics (1884), A. R. Forsyth's Theory of Functions of a Complex Variable (1900), and S. L. Loney’s Treatise on Elementary Dynamics with Solutions (1889-92). On physical topics they produced A. Freeman’s translation of Fourier’s Analytical Theory of Heat (1878), and Maxwell's edition of Henry Cavendish's electrical research. The Press also bought titles that had been originally published or considered for publication elsewhere. For instance William Thomson and P. G. Tait’s Treatise on Natural Philosophy and Elements of Natural Philosophy as well as Tait’s Elementary Treatise on Quaternions, had originally been Oxford books (McKitterick 2004b: 103).

Cambridge also printed college level mathematical textbooks. R. T. Glazebrook, who was appointed one of the first of the university’s mathematical lecturers in 1883, wrote a number of such books for the Press. When a revision of the university’s statutes brought about reforms to undergraduate education, one result was demand for suitable textbooks. For Cambridge University Press, Glazebrook authored such texts as Mechanics and Hydrostatics (1895), Electricity and Magnetism (1903), and Heat and Light (1894). Horace Lamb was also a major author of textbooks for the press. He wrote A Treatise on the Motion of Fluids (1879), later

29 While mathematical books were often among the more carefully prepared and expensive books Cambridge University Press produced, they were not always the most expensive. There were some extreme outlier projects in terms of expense, for instance C. M Doughty's two-volume Arabia Deserta, costing £700 to produce 1000 copies in 1885 (McKitterick 2004b: 93).

49 revised and released as Hydrodynamics (1895), as well as Statics (1912) and Dynamics (1914). Many of these were highly successful textbooks going into six or more editions (McKitterick 2004b: 103).

In the 1880s Cambridge entered the market in schoolbooks. Perhaps due to Cambridge’s institutional concentration in mathematics, The Pitt Press’ school book series in mathematics were aimed at a higher level than some others publisher’s school math books, and were pitched higher than titles in other subjects in their general educational series. Titles from the Pitt Press’ mathematical series include H. M. Taylor’s Euclid (1893) and S. L. Loney’s Elements of Statics and Dynamics (1891). Both of these texts were specifically aimed at school-aged students taking examinations, a process that had been initiated by the 1870 Education Act (McKitterick 2004b: 78). By 1903 the Pitt Press series had 300 titles, including many in science and mathematics.

The Cambridge name had a connection to excellence in mathematics. In the 1870s publisher Bell and Sons issued a “Cambridge Mathematical Series”, although it lacked any connection to Cambridge (McKitterick 2004b: 80). The Press at Cambridge didn’t defend their ownership over the title until later. It was only in the late nineteenth century that Cambridge developed a sense of itself as a publisher, developing at the same time a more proprietary attitude toward its name and connection to excellence in mathematics.

In the 1870s and 1880s University Printer C. J. Clay established a hierarchy of format for all Cambridge University Press books. This hierarchy used the physical form of the book to confer status on certain authors and projects. James Clerk Maxwell’s collected papers, for instance, were printed in the largest size, royal quarto (for an explanation of book sizes, see footnote 38). This was slightly larger than the collected works of John Couch Adams and Arthur Cayley (which were printed in demy quarto size). Smaller still were the volumes of William Thomson, in the demy octavo size. On the shelf, Maxwell’s books would be the largest; thus a value judgment about the work was subtly stated by the work itself. By the early years of the twentieth century, many mathematical books were printed in blue binding in the demy octavo size. More ordinary textbooks were treated to the crown octavo size (McKitterick 2004b: 110). The collected papers of G. H. Darwin, William Thomson (Lord Kelvin), Lord Rayleigh, G. G. Stokes and the thirteen volumes of Arthur Cayley’s collected papers in mathematics were among the so-

50 called “big blue books” the press produced in the late nineteenth century period. These books remained a staple of the Press’ back catalogue for years to come.

7. Journal printers Taylor and Francis

Richard Taylor and William Francis’ firm Taylor and Francis have been identified previously as a major nineteenth century printer of mathematics (Secord 2009: 466). As a printer, Taylor and Francis served many of London's scientific societies, and for some time were the printers of the Royal Society’s Philosophical Transactions, in which many mathematical papers appeared. They also published the physical and natural science oriented Philosophical Magazine. While they printed books, Taylor and Francis were most preoccupied with the printing and publishing of journals. Many of these journals, newly founded in the nineteenth century, reflect a growing community of practitioners concerned with scientific topics.30

In the 1830s, Richard Taylor attended meetings of many of London's scientific societies. Starting in 1827 Taylor began printing “Taylor’s calendar of the meetings of the scientific bodies of London”. A single-sided broadsheet tightly packed with information, this document at one glance speaks remarkably to the breadth of activity among London’s knowledgeable class. Comparing Taylor’s calendar over some of the years it was issued, one can gather the appearance and disappearance of specific groups amidst the overall growth of scientific activity in general.31

Taylor’s activities brought him into contact with many members of Britain's scientific elite. One of the firms’ bestselling books was Michael Faraday’s Experimental Researches in Electricity of 1839, which was composed of Faraday's articles from the Philosophical Magazine. Because of the way that Faraday had cross-referenced papers, a volume presenting the collected papers

30 Taylor and Francis’ publishing projects the 1840s and 50s reflect their connection to scientific London. These publications include the Journal of the Geological Society, Transactions of the Linnean Society, The Annals and Magazine of Natural History, The Chemical Gazette, The Journal of Entomology, The Ibis: A Magazine of General Ornithology, Transactions of the Zoological Society, and the Journal of the Photographic Society. Other learned clients of the press included the Royal Society (for their Philosophical Transactions), The British Museum (for catalogues), the British Meteorological Society, the Royal College of Surgeons of England, and the Royal Botanic Society (See listings in Check Book, 1845-1860, Taylor and Francis Papers, St. Bride Printing Library, London UK). 31 The British Library has a collection of Taylor’s calendars for years 1854/55 through 1907/08. See Taylor’s Calendar of the meetings of the Scientific Bodies of London, British Library, London UK.

51 proved to be a desirable commodity. Other best selling titles included a popular manual of the barometer and a work of natural theology (Brock and Meadows 2003: 44). Of the scientific books Taylor and Francis published, it was often through Taylor’s personal connection to the scientific societies, or editorship of the Philosophical Magazine, that introductions to authors and their respective publishing projects came about.

Taylor generally employed between twenty and thirty compositors (Brock and Meadows 2003: 38, 45). A list of the typical weekly jobs in 1832 shows that a great majority of their work was devoted to composing learned materials of one sort or another, with a large portion devoted to subjects within natural history and science (Brock and Meadows 2003: 45). A scan of Taylor and Francis’ costing book for the years 1854-60, shows that they set mathematics for experts and students alike, composing mathematical papers for the Philosophical Transactions and setting examinations papers for Woolwich’s Royal Military Academy and the East India Company. Other projects from these years include Richard Potter’s Physical Optics (1856), Useful Information for Engineers by William Fairbairn (1856), A New View of Electrical Action by Richard Laming (1858) and Rev. W. Foster’s Examples in Arithmetic (1856).

At Taylor and Francis, an experienced printer of scientific materials, the composition of mathematics incurred higher costs than the composition of more routine jobs. Taylor’s detailed records and costing books show extra changes routinely applied to the composition of mathematical pages. In the case of Arthur Cayley’s “An Introductory Memoir upon Quantics”, a paper from volume 144 of the Philosophical Transactions, its eight pages of text incurred an extra 16 shillings levy. Cayley’s paper, while not too symbol laden, does use some unusual sorts. Of the 143 pages in volume 144 of the Transactions, published in 1854, Taylor charged an extra £15 for all the mathematics.32 In general, the company’s record books confirm that mathematical composition incurred additional charges that were added to regular charges for composing. The suggestion by Spottiswoode et al that mathematics cost one-third more to compose than regular English text is confirmed by Taylor and Francis’ checkbook records.

32 Check Book 1845-1860, p. 10, Taylor and Francis Papers, St. Bride Printing Library, London UK.

James Secord’s observations that printing science often required special techniques, in the form of precise illustrations or unusual symbolism, is certainly observed in the history of Taylor and Francis. In the early years, Taylor made his reputation as a specialized printer when he undertook the printing of Flora Graeca by the Oxford botanist John Sibthrop. Taylor printed the first of ten folio volumes in 1806. The entire series included 966 coloured plates (Brock and Meadows 2003: 28). Some of these books were costly and the specialized work proved troublesome, such as when George Grave’s Flora Londonensis (1818-1834) was plagued by the cost of engravers’ bills (Brock and Meadows 2003: 43). But by the 1840s, records indicate that the firm was careful to enumerate extra costs relating to both mathematical composition and any engravings needed to produce the illustrations required. For instance, Taylor’s records indicate the one hundred and one figures in Richard Potter’s Physical Optics, added approximately £3 to the cost of production.33

Taylor and Francis’ development as printers and publishers reflects a growing awareness of how to manage the costs associated with publishing scientific materials. They placed limits on the number of illustrations appearing in some of their periodicals, and levied extra per-page changes for the composition of mathematics (Brock and Meadows 2003: 125).

8. Mathematical typesetting at Cambridge, Principia Mathematica (1910)

Bertrand Russell and Alfred North Whitehead's three-volume logical work Principia Mathematica provides an interesting case study in the difficulty of mathematical typesetting. It confirms some of the factors that made technical printing difficult. It was time consuming to compose, it required a skilled compositor to do the job, and the book required typefaces to be newly founded. As such it is a good example of how some specialized mathematical printing could be difficult. The manuscript required a printer experienced in specialist works and it was extremely expensive to produce.

Principia Mathematica was an unusually complex and massive work, intellectually and physically. Its manuscript was enormous at an estimated five to six thousand hand-written leaves

33 Check Book 1845-1860, p. 71, Taylor and Francis Papers, St. Bride Printing Library, London UK.

53 of paper (Linsky and Blackwell 2005: 143). The manuscript was so large and the symbols it employed so unusual that it was never typed or even copied. In October of 1909, Russell packed the first 4000 leaves of original handwritten manuscript into two large crates, and in this manner he transported it by rail from London to Cambridge.34

Russell described the notation used in Principia as party invented, partly based on the logical notation of George Boole, Ernst Schröder and Giuseppe Peano (Grattan-Guinness 1975: 97). Although many of the symbols it uses can be found in other Cambridge books, there is some evidence suggesting that in fact special types were specifically cast for the job of printing this book.35

There is also evidence that only one compositor at the Cambridge University Press set the manuscript in type. In 1910, while the manuscript was in press, Russell informed a correspondent “there is only one compositor who can read our queer symbols”.36 Whitehead’s biographer Victor Lowe also suggested this, describing the printing process as slow going since only one compositor could manage it (Lowe 1985: 289). The few existing manuscript leaves have the name “Rackham” penciled in and circled in the margin above the instruction for the next printers’ sheet. Comparing these marks to similar ones on other manuscripts of Russell had printed at Cambridge, Kenneth Blackwell surmises that Rackham is the name of the compositor to whom the manuscript of Principia Mathematica was assigned (Linsky and Blackwell 2005: 153).

If, in fact, Principia Mathematica was composed by Mr. Rackham alone, this would have been a highly unusual way for a book to have been composed. As was standard practice at most printing houses, at Cambridge compositors traditionally worked in ships (teams), dividing up the text of a manuscript and composing different sections in parallel so as to maximize efficiency

34 Letter from Bertrand Russell to Lucy Donnelly, 18 October 1909, RAI 710.049473; Bertrand Russell Archives, McMaster University, Hamilton, Canada. Also see (Grattan-Guinness 1975; Linsky and Blackwell 2005). 35 Letter from R.W. David to Bertrand Russell, 10 May 1956, REC. ACQ. 25. Bertrand Russell Archives, McMaster University, Hamilton, Canada. Also see (Linsky and Blackwell 2005: 154 f.n.22). 36 Letter from Bertrand Russell to Ralph Barton Perry, April 1910, quotation taken from (Linsky and Blackwell 2005: 152, f.n.17).

(McKitterick 2004b: 135). While all compositors at the Cambridge University Press received special training in mathematics, one can imagine that Principia Mathematica, a work that pushed many intellectual boundaries and in the process defined its own unique language, would have challenged the most experienced compositors of mathematical work. If in fact only one compositor could handle setting its text, then this remarkable book was equally remarkable for how challenging it was to typeset.

There is also evidence that suggests this manuscript was set directly into pages, and that Russell and Whitehead did not see galley proofs. Likely someone at the press (perhaps Mr. Rackham) made the decision about how to break the manuscript into printed pages of formula, after which Russell received printer’s sheets for correction and proofreading (Linsky and Blackwell 2005: 142).

When comparing the few pages of extant manuscript and the printed book, it is possible to observe certain compositional decisions, for instance the choice of where to make line-breaks and appropriate spacing between symbols. As Blackwell noted, “the lines of formulae were laid out, sometimes realigned under major operators, and broken according to professional standards, although the positioning of references was not changed; a period was inserted after theorem numbers and the heading “Dem” to accord with Cambridge house-style; and—important for readability—the relative spacing of the symbols now reflected syntactic elements. No instructions for the manuscript’s passage into print were marked on the extant leaves, yet the whole attained an austere typographical beauty” (Linsky and Blackwell 2005: 152).

The three volumes of Principia Mathematica were printed in 750, 500 and 500 copies respectively. Somewhat predictably for the nature of the book, the first edition was neither stereotyped nor electrotyped, suggesting the publisher did not expected a second printing.37 Each printer’s sheet, once corrections were final, were printed off in the required number without waiting for the entire volume to be completed in type. Blackwell surmises that from each printer’s sheet the type was distributed “otherwise a stock of many thousands of unusual types

37 There is no record of plates having been made in the press book “Catalogue of electrotype and stereotype plates and moulds, 1878-1949”, CUP 33/11, Archives of the Cambridge University Press, Cambridge University, Cambridge, UK.

55 would have been necessary” (Linsky and Blackwell 2005: 154). By the time Cambridge University Press reprinted the book in 1926, the type was not standing.

In 1909 the Syndics of the press consented to publish the book, but balked at absorbing the entire cost of such an expensive project. They were willing to take a loss of £600, not the full £920 loss that was estimated. The Royal Society’s relief fund agreed to chip in £200 towards its publication, and Russell and Whitehead agreed to split the remaining £100. This lead Russell to later quip that both authors had thus “earned minus £50 each for ten years work” (see Grattan- Guinness 1975: 102).

9. Mathematical illustrations in print

Prior to 1800, copperplate engraving offered an alternative to woodcuts when mathematical illustrations were required (recall descriptions of the woodcut and wood engraving methods in section 2 of this chapter). With an engraver of average skill, fairly complicated and detailed diagrams could be achieved using an intaglio method on copperplate. Intaglio is a process in which details to be printed are scratched, engraved, or otherwise etched into a flat metal surface. Ink is wiped or pushed into these indentations and the plate is polished with muslin or light fabric, wicking away ink from the highest surfaces, leaving ink in the recesses or troughs. The impression is taken with the pressure of a rolling press on a piece of dampened paper.

In 1800 the intaglio process had two main drawbacks as a method of book illustration. Copper, as a softer metal, lost certain engraved details after the force of a few hundred impressions. Also, printing intaglio plates was more laborious than printing a wood cut. The intaglio process required a different press altogether than that for moveable type printing or relief wood blocks, and often printers specialized in one method or the other, but not both.

In practice, the use of copperplate as an illustration technique meant that detailed images could not be integrated within the textual pages of a book. Most books that included copperplate illustrations had foldout pages in which all the figures were presented together, most likely bound into the back of the book. Intaglio printed frontispieces were common, as these could be added fairly easily onto the front of the first signature of a book. They either would have had a

56 stub that wrapped around the first gathering of pages or would have been tipped in (i.e., glued to the leaf it was facing).38

Amassing all the figures for a technical work into a few pages at the back of a book often had the effect of removing what might have been a helpful visual referent from the text to which it was associated. Robin Rider in her study of early modern algebra has even suggested a connection between the use of copperplate technology as a dominant form for printed illustrations and the disappearance of visual materials in works about algebra during this time (Rider 1982). She writes that the printer’s necessity of separating illustrations from the relevant text reinforced a trend within mathematics itself: “over the course of the 17th and 18th centuries, analysis of mathematical relationships as expressed in the formalism of algebraic language grew even more distant from geometric context as depicted in diagrams, just as all diagrams were relegated to the back of the book” (Rider 1993: 99).

Henry Kater and Dionysius Lardner's Treatise on Mechanics (1831), which was part of the Cabinet Cyclopaedia series, has 21 pages of intaglio illustrations at the back of the book, containing 224 figures. I would imagine this arrangement would not have been ideal, as it requires the reader to continually turn pages to refer to diagrams. Likely the figures were deemed too detailed for wood engraving, and thus were printed intaglio, a process that could capture more detail. Although wood engraving became a popular illustration method in the nineteenth century, mathematical books continued to be illustrated using intaglio printed figures, for example John Henry Pratt’s Mathematical Principles of Mechanical Philosophy (1845). Pratt’s book was an early co-publication of the Macmillan brothers, and was printed at the Cambridge University Press. Like Kater and Lardner’s Treatise on Mechanics, Pratt’s book also uses intaglio printed illustrations, the effect being that the figures are collected in pages at the back of the book (see figure 9).

38 A “signature” or a “gathering” is the term used to describe the packet of pages created by folding a printer’s sheet. A printer’s sheet is one large piece of paper printed on both sides. If a printer’s sheet is folded once to make a signature, it is referred to as folio size (producing two leaves, or four pages). When a printer’s sheet is folded twice it makes the quarto size (with four leaves, eight pages), folded three times it makes an octavo (with eight leaves, sixteen pages), folded four times makes the duodecimo or twelvemo size (with twelve leaves, twenty-four pages), folding five times forms the sextodecimo or sixteenmo size (with sixteen leaves, or thirty-two pages).

Prior to 1800, woodcutting was the other method in which illustrations could be produced for a book. Woodcuts could be placed next to moveable type; thus this method allowed for images to be integrated with text. However, fine detail was more difficult to achieve in a woodcut. Woodcuts were also prone to splintering. If a line was broken or a label on a diagram was obscured because a piece of wood had chipped off in the printing process, the diagram could be rendered inaccurate or a certain crucial meaning of the diagram lost.

An example of the woodcut technique as used in a mathematical text can be found in Robert Simson's Euclid of 1762. In it woodcuts are used throughout the text. The letters identifying vertices are cut from the wood and appear rather large (see figure 7). As the book progresses the diagrams become more complicated. In these later diagrams it is evident that only so much complexity could be achieved using the woodcutting method (see examples on pages 50, 218, and 225 of Simson’s Euclid).

Because of the different limitations posed by both the woodcutting and copperplate techniques, wood engraving coming into greater use after 1800 must have been a boon to mathematical authors – or at least those who felt that visual representations assisted with the comprehension of their work.39 As mentioned, wood engraving meant that more detailed diagrams could be placed within the body text and were less subject to wear or damage through extensive use in printing. In Richard Potter’s An Elementary Treatise on Mechanics (1846), the detail in the line suggests that its illustrations were produced using the wood engraving technique (see figure 8).40 The incredibly small and precise letters used to identify vertices may have been created by drilling holes in the wood block so that actual pieces of cast type could be used in the place of engraved letters. A level of delicacy and detail are achieved in the illustrations in Potter’s book that sets these in contrast to the wood cut diagrams in Simson’s Euclid.

39 In the preface to his Mécanique Analytique, Lagrange proudly wrote that “On ne trouvera point de Figurés dans cet Ouvrage. Les methods que j'y expose ne demandent ni constructions, ni raisonnemens géométriques ou mécaniques, mais seulement des operations algébriques” (Lagrange 1815: i). 40 Richard Potter was a professor of natural philosophy and astronomy at University College London. Potter’s biography describes him as having been an incompetent teacher, whose views on optics (as a proponent of the corpuscular theory), were ridiculed by his contemporaries who embraced the wave theory of light. Apparently Potter had some difficulty keeping up with the increasing mathematization of physics. The conclusion of the ODNB article about him is that Potter “made no significant contributions to science” (Cantor 2004).

Figure 7 Woodcut illustrations from Robert Simson’s Euclid (1762); the figure on the left is from Book I, proposition 2; the figure on the right is from Book II, proposition 25 (Source: Simson 1762: 7, 218)

Figure 8 Wood engravings from Richard Potter’s An Elementary Treatise on Mechanics (1846); the figure on the left illustrates the addition of moments of force; the figure on the right illustrates finding the center of gravity of a pyramid whose base is a polygon (Source: Potter 1846: 13, 47)

Figure 9 Illustrations printed intaglio from John Henry Pratt’s The Mathematical Principles of Mechanical Philosophy (1845) (Source: Pratt 1845: figures 10, 56, 75)

Copperplate engraving was generally too easily worn to produce high-quality illustrations in cheap mass-produced books. Pratt’s Mathematical Principles shows what can happen when an intaglio illustration starts to become worn. In diagram number 56, from figure 9, the black lines describing the architectural figure are beginning to dissolve into broken rather than solid lines. This is a sign of wearing of the copperplate, or possibly, the result of a careless printer.

As of 1823 steel engraving offered an alternative to copperplate, using a similar printing process yet resisting the wear of thousands of impressions on the press. Steel engraved plates were expensive to commission. However, it could be a good investment if the images produced from such plates could be sold many times, or if the plates themselves could be sold to another publisher for further use after the initial printing.41 Taylor and Francis had some illustrations

41 The practice of re-using illustrations was common practice. As Elizabeth Eisenstein points out, it was common for early newspapers to use the same woodcut to represent several different cities, or the same portrait to represent several individuals (Eisenstein 1979: vol. 1, 65). Engraved plates were valuable commodities bought and sold between printers, and re-used for different purposes. Works of mathematics display evidence of this as well. The lushly illustrated frontispiece for Henry Billingsley’s Euclid (1570) was originally commissioned for William Cunningham’s The Cosmographical Glasse (1559), which explains why the frontispiece contains symbols of geography rather than mathematics. William Whiston’s 1714 Euclid includes a ‘portrait’ of Euclid, as does

60 engraved on steel, for instance, for their journal Annals of Natural History (Brock and Meadows 2003: 125).

As technology changed rapidly, very many different printing techniques were in use at any given time during the century. This multiplicity of printing techniques used in the printing trade lead to experiments in which novel techniques were applied to mathematics. One fine example of this, and a highly original use of colour in mathematical illustration, can been seen in Oliver Byrne's The First Six Books of the Elements of Euclid published in London by William Pickering in 1847, and printed at the Chiswick press.

In his introduction, Byrne states “this work has a greater aim than mere illustration; we do not introduce colours for the purpose of entertainment, or to amuse by certain combinations of tint and form, but to assist the mind in its researches after truth, to increase the facilities of instruction, and to diffuse permanent knowledge” (Byrne 1847: vii). His introduction attempts to explain the existence of this most unusual book. Byrne defends the book’s aims as far more serious than merely aesthetic. According to Byrne, the special diagrams make the process of reasoning itself more precise, and the student’s attainment of mathematical reasoning “more expeditious”. In fact, he claims that by using his book, the student of Euclid will acquire the subject in less than a third the usual time devoted to studying it. Additional benefits include a long-lasting retention of the material: “these facts have been ascertained by numerous experiments made by the inventor [i.e. Byrne], and several others who have adopted his plans” (Byrne 1847: ix).

In Byrne’s book, colours and shapes are used as the primary identifying characteristics of the diagrams, instead of letterform labels. This provides an unusual alternative to the convention of naming diagrams with letters that are used to connect the diagram to the written proof. In more conventional books the letterforms ∆ABC are used to refer to a diagram of a triangle with

Sawbridge’s edition of Leeke and Serle’s 1661 Euclid (Barrow-Green 2006: 6, 9, 11). Since nothing is known about the life of Euclid, these ‘portraits’ of him are spurious at best. In the nineteenth century, Charles Dodson re-used the same engravings for his edition of Euclid in 1882 that had been created and used for Isaac Todhunter’s 1862 Euclid (Barrow-Green 2006: 15). Although publishing and printing are commonly assumed to confer standardization and accuracy to a text, this was not always the case (Eisenstein 1979: vol. 1, 65).

61 vertices labeled A, B, and C. In Byrnes book a tiny picture of a triangle, colour-coordinated with its larger presentation as a full-blown figure, is how a diagram’s parts are identified and referred to within a demonstration (see Figure 10, showing Proposition 6 in Book I).

Figure 10 Proposition 6, Book I from Oliver Byrne’s The First Six Books of the Elements of Euclid (1847) (Source: Byrne 1847: 6)

While certainly a clever and visually interesting way to apprehend the connection between the proofs of geometry and the constructions that accompany these proofs, it does not present as radical a technique for comprehending geometry as Byrne had first claimed. It remains, however, interesting that Byrne held this belief about the enlightening benefits of visual representation in mathematics. Equally interesting is how a specialized printing technique was applied in this case to create such unique mathematical illustrations. Byrne’s edition of Euclid is a beautiful piece of

62 fine printing, and must be one of the most aesthetically pleasing Euclids that exist. However, the cost to produce a book such as this, in which every page is printed with four different colours, must have been extremely high. The book was featured as an example of fine printing at the Great Exhibition of 1851. Unfortunately, William Pickering’s expensive tastes put him into bankruptcy in 1853 (Warrington 1990).

Prior to the nineteenth century, early printers of mathematics also experimented with unusual printing and illustration techniques as a way to illustrate mathematical concepts. Rider points out how in some eighteenth century books, movable cut out diagrams (called ‘volvelles’) depicted the function of an astrolabe or guided the observation of comets. In this case, concentric paper circles were attached to the page in the center such that their rotation could actually display the position or rotation to be apprehended. Billingsley's Euclid (the first English edition, 1570) included pop-up diagrams to illustrate concepts of modern geometry. The figures, made of paper, were pasted into the book so that they could be opened up to create three-dimensional models of the solid figures they represented (Barrow-Green 2006: 6). Sometimes these three-dimensional “illustrations” remained only potentially illustrative if they had never been cut out and assembled from the original bound-in printers sheet (Rider 1993: 102).

Outstanding books like Byrne's Euclid exemplify the kinds of elaborate illustration techniques capable in craft book printing. These books belong to a tradition of experimental printing in which new methods are employed to facilitating the teaching and learning of mathematics. In contrast, books such as Todhunter's Plane Co-ordinate Geometry (see section 10 below) and many other school math books of the period exemplify how nineteenth century printing technology was harnessed for different effect, that is, to reproduce math books into the hundreds of thousands of copies. The multiplicity of these books wielded a different sort of intellectual influence on mathematics, as they were used by many generations of students. Even in earlier centuries, books varied greatly according to the audience they were seeking and the cost paid to produce them: Tartaglia's 16th-century Italian edition of Euclid was “aimed at the low end of the market” while Commandino's Latin edition of 1572 was “a scholar's edition de luxe” (Rider 1993: 99). Similarly in the nineteenth century a variety of mathematical books continued to be produced with different production values, aimed at different audiences, and serving different purposes.

In her book The Printing Revolution in Early Modern Europe, Elizabeth Eisenstein claims that the print medium itself shaped the evolution of science in ways that would not have been explored or considered if it had remained in manuscript form. Her vision for the change printing brought to science applies to mathematics as well. In particular, she notes how printing changed the visual presentation of information, which in turn affected its comprehension. She writes, “mathematical tables, for example, were also transformed. For scholars concerned with scientific change, what happened to numbers and equations [during the printing revolution] is surely just as significant as what happened to either images or words. Furthermore, many of the more important pictorial statements produced during the first century of printing employed various devices…to relate images to texts. To treat the visual aid as a discrete unit is to lose sight of the connected links which were especially important for technical literature because they expressed the relationship between words and things” (Eisenstein 1979: vol. 1, 26).

10. Engraved diagrams for Todhunter's Plane Co-ordinate Geometry (1855)

Isaac Todhunter (1820-1884), who has retained some fame as the author of many textbooks, was a Cambridge graduate and a mathematical lecturer. By some accounts he was an able mathematician who wasted his talent on textbook authorship over the pursuit of highly original mathematics. When Todhunter married he left his position as college fellow and took up work as a private tutor, examiner and author.

Todhunter’s book A Treatise on Plane Co-ordinate Geometry, As Applied to the Straight Line and the Conic Sections, With Numerous Examples was a beginner’s textbook published by what then was a burgeoning new publisher, Macmillan and Company, in 1855. At 299 pages in length, 1250 copies were originally printed at Cambridge University Press and sold for 10 shillings and 6 pence. The book proved to be a success and went into several re-printings. A total of 27,750 copies were printed, the last edition being printed in 1888.42 The book was distributed and sold in London, Oxford, Edinbugh, Dublin, Cambridge, and possibly elsewhere.

42 Macmillan's first Editions Book, p. 511, Macmillan Archive, British Library, London UK.

For our purposes we will examine the production of the illustrations for this book, which contained 63 wood engraved diagrams. Macmillan commissioned work from two engravers, William Dodd and William Dickes, to fabricate Todhunter’s diagrams into engraved figures for the book. Dodd’s illustrations appear on pages 133-163, with Dickes’ figures on the remaining pages.43

Two things are interesting about the correspondence between Macmillan and Todhunter, and Macmillan and Dickes, regarding the composition of images for this book. As we discuss below, Dodd was an experienced technical engraver, while Dickes was not. In doing engravings for Todhunter’s book, Dickes received a kind of informal training, or on the job training, for the technical illustrations he produced. Todhunter’s Plane Coordinate Geometry was the first book Dickes illustrated for Macmillan, and it may have been his first experience producing technical illustrations (Dickes set up business as an engraver in 1846).

Secondly, we can infer from these letters certain values that Macmillan and Todhunter (via Macmillan’s intermediary letters) felt were important to successful mathematical illustration. Successful mathematical illustrations are uniform, symmetrical, with identifying letters appearing close to the proper parts. When a letter indicates an intersection it must be placed close to this point in the corresponding angle. The appearance of pinched up corners (when lines meet in vertices) detracts from the beauty and readability of the image. A bold style in the identifying letters makes the diagram easier to read. When Dickes illustrations did not conform to these qualities, they were sent back for revision.

Dickes’ informal education on how to do technical illustrations begins with Macmillan instructing him to study Dodd’s work. In a letter to Todhunter, Daniel Macmillan writes: “Many thanks for the trouble you have taken in writing about the woodcuts. I wrote to Mr. Dickes on Saturday night and enclosed a sheet of Phear’s to show him how Dodd had done the thing. The enclosed is his answer. Our fear is that no one but Mr. Dodd has mastered the woodcutting of

43 Daniel Macmillan to William Dickes, 1 July 1855, 55377 General Letter Book 1855, Macmillan Papers, British Library, London UK. Hereafter references to the British Library’s Macmillan Papers collection will be abbreviated with the letters MP, followed by the relevant accession number.

65 mathematical diagrams”.44 However, as Macmillan goes on to explain, Mr. Dodd is very slow to produce, which is why Macmillan has sought another engraver to do the work.

It appears that Todhunter was not too pleased with Dickes’ first efforts. The proofs of four engravings were returned to Dickes with Todhunter’s corrections marked in pencil. Macmillan cites “a want of uniformity” and work “done by some extremely timid hand” as the problem with Dickes’ approach.45 After Dickes sends a second round of proofs just two days later, Macmillan relays that Todhunter’s estimate of these is actually worse: “We enclose you a specimen of the woodcuts that we have been used to and we hoped for something better [from you]. But our author thinks they are much worse and that they indicate a weak female hand. It is not impossible that he may be too severe a critic. We shall be glad if those which you have still to send come up to his standard”.46

Macmillan again instructs Dickes to study carefully Dodd’s work. Macmillan sends him to a nearby bookshop to borrow a copy of Goodwin’s Mathematical Course, telling him that in this book, “you will see the kind of woodcuts we want”.47

A few days later, Dickes produced something pleasing Macmillan. He writes to Dickes, “Nothing could be better than these… They are all right except one – (which Mr. Todhunter has corrected in pencil) the letters are beautiful but for the sake of uniformity they must be drilled out to match the others”.48 However within a few weeks time, Todhunter was again displeased to

44 Daniel Macmillan to Isaac Todhunter, 20 February 1855, MP 55376 General Letter Book 1854-55. Macmillan’s reference to “Phear’s” is probably to J. B. Phear’s Elementary Mechanics, published by Macmillan in 1850. 45 Daniel Macmillan to William Dickes, 15 February 15 1855, MP 55376. 46 Daniel Macmillan To William Dickes, 17 February 1855, MP 55376. It’s hard to know if Todhunter’s charge of “a weak female hand” was brought about by specific knowledge or whether by this accusation he meant to emphasize the inferiority of the engravings. Women may have worked as assistants in engraving houses. To my knowledge, however, it was rare for a woman to be recognized as the engraver when such a name was signed to an engraving. 47 Daniel Macmillan To William Dickes, 20 February 1855, MP 55376. In the letter, Macmillan identifies the woodcuts in Goodwin’s Mathematical Course as being the work of Mr. Dodd (i.e., Harvey Goodwin’s An Elementary Course of Mathematics, J. & J.J. Deighton, 1846). 48 Daniel Macmillan To William Dickes, 23 February 1855, MP 55376. The replacement of wood engraved letters by drilling and fitting in their place precisely cast lead letters, was a technique apparently used to achieve greater

66 the point where entire diagrams had to be re-cut. Todhunter was, apparently, an author that demanded high production values from his published work.49 Macmillan writes to Dickes, “I will call on you tomorrow…to talk about those woodcuts. We find that nothing will satisfy Mr. Todhunter but having them recut, and with good letters. And he now wishes them upright like those you sent down last. We hope under the circumstances you will do them justice or at any rate make some … compromise. We cannot make him pay for these [revisions] and should very much grudge to pay for them ourselves”.50

A month later, trouble continued over accurate labeling of the diagrams. An unhappy Macmillan wrote, “I shall remark that you people still do not seem to be fully impressed with the importance of placing the letters close to the proper parts. In all cases where the letter is to refer to an intersection it ought to be placed quite close to the angle. On looking carefully at Mr. Todhunter’s drawings, it seems to me that an intelligent man … need find no difficulty in reproducing his drawings from what has been sent. I must say I do not think proper care has been taken”.51

Even after Todhunter’s Plane Coordinate Geometry was in press, Macmillan continued to express his feeling that in comparison to Dodd’s work, Dickes’ engravings lacked uniformity and symmetry.52 However, Macmillan felt that Dickes was trainable and that, in time, his skills for this kind of work would equal the standards to which he was accustomed. Dickes had been occupied by Todhunter’s book from early February until the end of May. By July, Todhunter’s Plane Coordinate Geometry had been printed and its pages were at the binder. Macmillan

uniformity in the labeling of mathematical diagrams. Macmillan also mentions this in a letter to Dodd (Daniel Macmillan to William Dodd, 23 February 1855, MP 55376). 49 Barrow-Green mentions this in (Barrow-Green 2001: 189). Apparently clarity was an issue to which Todhunter attached great importance. In correspondence with the editor of his last two textbooks in 1877, Todhunter apparently picked over publication details, on one occasion discussing the merits of having woodcuts printed in Paris as opposed to London. 50 Daniel Macmillan To William Dickes, 7 March 1855, MP 55377. 51 Daniel Macmillan To William Dickes, 13 April 1855, MP 55377. 52 Daniel Macmillan To William Dickes, 1 July 1855, MP 55377.

67 instructed Dickes to go take a look at the pages and compare his engravings to those that Dodd produced. Macmillan notes that “Dodd’s diagrams …have a uniformity and symmetry yours entirely want. We should very much like you to see the book and …to make diagrams … as like Dodd’s as possible”.53 Plane Coordinate Geometry was officially released on August 6, 1855.54

Figure 11 Wood engravings from Todhunter’s Plane Coordinate Geometry (1855); William Dodd’s engraving (left); William Dickes’ engraving (right) (Source: Todhunter 1855: 146, 282)

Macmillan continued to employ Dickes on his next projects. Dickes engraved the diagrams for Stephen Parkinson’s Mechanics (Macmillan, published on November 7, 1855) and Peter Guthrie Tait and William John Steele’s A Treatise on the Dynamics of a Particle (Macmillan, published on January 26, 1856).55 With respect to his contributions to these works, Macmillan seems to judge that Dickes’ style is improving, and that he has understood what is aesthetically required

53 Daniel Macmillan to William Dickes, 1 July 1855, MP 55377. 54 August 6, 1855 is the publication date listed for Todhunter’s Plane Coordinate Geometry in Macmillan’s editions book. Macmillan's first Editions Book, p. 511, Macmillan Archive, British Library, London UK. 55 See letters from Daniel Macmillan To William Dickes, 16 and 22 August 1855, MP 55377.

68 for good mathematical illustration. In August, Macmillan writes “as far as we can judge from the proofs the cuts are very good in all respects except that the corners have a pinched up look which detracts both from their beauty and readability”.56 In September, a minor criticism is levied: “as far as we can gauge these you have sent [for Parkinson’s Mechanics] are very good except that a little bolder style of letter would be better”.57

By the end of September, Dickes is still completing new engravings and doing revisions on the diagrams for these books. However, by early November Dickes moved on to his next assignment. Macmillan had him do the engravings for Charles Kingsley’s book Heroes, or, Greek fairy tales for my children (Macmillan, published on December 22, 1855). His instructions were that all the engravings were to be finished so the book could be released in time for Christmas. Macmillan promises that, “If you get ready in time we fancy we shall not disagree about the price”.58

Dickes’ work on Kingsley’s book is a departure from the technical style to which he had be apprenticing from February to November. As a trade engraver Dickes is best known for his colour printing, using wood engraving and lithography (Buchanan-Brown 1982: 48). Technical illustration was not his only business. He illustrated natural history works for Charles Kingsley’s books and also engraved many portraits. An 1890 edition of Glaucus contains interesting examples of Dickes’ full colour renderings of undersea life using the chromolithography technique. The frontispiece to Glaucus shows what kind of lush and aesthetically pleasing lines, shades and tones Dickes was capable of as an engraver, when he worked in a completely different genre from the mathematical one (see Figure 12).

56 Daniel Macmillan to William Dickes, 29 August 1855, MP 55377. 57 Daniel Macmillan to William Dickes, 6 September 1855, MP 55377. 58 See letters from Daniel Macmillan to William Dickes, 27 November and 13 December 1855, MP 55379.

Figure 12 Frontispiece from Charles Kingsley’s Glaucus, or, Wonders of the Shore (1856); William Dickes signature is visible in the bottom right hand corner of the engraving (Source: Kingsley 1856: iv)

Technical illustration comprised part of Dickes’ overall business enterprise. However, one would never know that Dickes worked as an engraver for mathematical diagrams. Unlike his work in other genres, he is not acknowledged in Todunter’s book. This anonymity separates Dickes’ mathematical engraving from his other work, as it was common for engravers to initial or sign illustrations. In portraits, landscapes, or children’s book illustrations, engravings were most often considered a collaboration between artist and engraver. The artist and engraver were often both

70 credited on the image. Unacknowledged in the technical engravings he completed, Dickes’ contribution to Todhunter’s book is invisible. Dickes and similar artists who engraved mathematical illustrations are forgotten and their role in rendering these images for the print process is overlooked.

11. Conclusion

In conclusion, twentieth century style guides point to problems with mathematical typesetting similar to those outlined in the 1875 British Association for the Advancement of Science report. This suggests that the problems that made composing mathematics difficult and expensive remained so despite most of the nineteenth century’s technological changes. Moreover, the more contemporary guides offer similar recommendations to mathematical authors (i.e. use equivalent expressions that ease composition) offered in Spottiswoode’s 1875 report. Given this, it seems likely that familiarity with mathematical expressions that eased typographical concerns must have arisen slowly over time, and that no immediate shift followed directly from printed guides relating to mathematical typography. All these documents reinforce the impression that typesetting mathematics was a subject of ongoing concern, in the nineteenth century and after the application of the Monotype machine to aid mathematical composition in the 1930s.

While the difficulty of composing mathematics in type was not eliminated by improved technology, other nineteenth century printing efficiencies – such as improved press speed, cheaper paper and electro and stereotype methods – were easily applied to the printing of mathematics. Efficiencies of the press came in particularly handy when school textbooks were demanded in larger and larger numbers towards the century’s end. It was common for the publisher Macmillan to order their best-selling mathematical texts in batches of twenty or thirty 59 thousand copies, printed from electrotype plates. On the other hand stereos or electros were rarely made for “high” books of mathematics that, in some cases, were not expected to sell out the first printing of 500 copies.

While the printing of mathematics was expensive and technically challenging, it was one of many printing tasks that challenged the technical capabilities of the British printing trade. Music,

59 Macmillan's first Editions Book, p. 477, 506, Macmillan Archive, British Library, London UK.

71 oriental and other foreign languages, as well as other works of science required specialized techniques, special sorts of type, or precise illustrations. Mathematics was difficult to compose for the printing press. But other unique symbolisms such as music, and even uncommonly printed languages outside major printing centers, were adapted for moveable type and the printing press, even when these symbolisms served similarly restricted audiences.60 In effect, while the printing of mathematics was a specialized art within the printing trade, it was not as special or difficult a printing task as one might, at first, assume.

In his chapter “Science, technology and mathematics” in The Cambridge History of the Book in Britain, James Secord observes that scientific publishing encouraged a close integration between authors, publishers and printers, and challenged standard printing techniques in a variety of ways. The publication of technical works placed extraordinary demands on the typesetters, illustrators, and printers through whose hands scientific manuscripts passed. Technical terminology, lists of species names and mathematical symbols all lead to a greater expense and labour in the typesetting room. The requirements for details and specific forms of illustration pushed the boundaries of image making in print media and forged new techniques (Secord 2009: 465).

Factors governing the British printing trade as a whole also had an effect on the printing of mathematics. Market forces organized the printing industry such that only some printing establishments became involved with printing mathematics. Pragmatic business decisions made higher mathematics a specialized art within the printing trade. Only some printing houses invested in the equipment and human resources needed to print difficult mathematical symbolism well. James Secord observes, “although the major printing firms had capabilities for setting simple geometry and algebra, more advanced mathematical works presented challenges not covered in the standard printers’ manuals. Much of the work was done at Taylor and Francis and

60 On the development of music printing, see (Poole 1965, 1966; Twyman 1998: 45). Prior to the twentieth century, the Cambridge University Press, for instance, had been equipped to print many languages, including Arabic, Hebrew, Armenian, Coptic, Ethiopic, Bengali, Sanskrit, Syriac, Nestorian Syriac, Estrangelo Syriac, and Egyptian hieroglyphic type (McKitterick 2004: 119). Even in remote parts of Canada, ingenuity overcame difficulty when applied to the printer’s art. In 1841 a missionary devised an entirely homemade system for printing the Cree language, complete with homemade movable type, printer’s ink from lampblack and using a common fur press to make the impression. Using these tools in 1842, in a remote outpost in what is now Manitoba, he printed a sixteen- page booklet containing hymns and Bible passages in Cree (Dewalt 1995: 15, Gundy 1972: 68, 70).

72 later, at the University Press in Cambridge, where mathematical typesetting became part of every apprentice’s training” (Secord 2009: 466). Printing houses that were large enough or specialized enough to take on mathematical work were made so by economic and market forces that were largely external to and had little to do with mathematics. Partly the larger profitable markets served by these printers enabled them to apply their honed skills to the printing of difficult mathematics, which was often achieved with an excellence of skill (but executed at little financial gain) by these firms.

Chapter 3 Referees, Publisher’s Readers and the Image of Mathematics in Journals and Books

1. Introduction

Although the relationship between publisher and literary author has been a subject of study since at least the 1970s, the relationship between publisher and scientific author has been less frequently attended (MacLeod 1980: 63). The relationship between mathematical author and book publisher has been explored even less. In the few cases where it has been acknowledged that mathematical authors had relationships with book publishers, it has often been bibliographers or book historians who have taken notice (Wallis and Wallis 1986; Rider 1993, 1982; Topham 2000a).

In the nineteenth century, there was a considerable expansion in the number of mathematicians for whom publication was increasingly important. As Roy MacLeod has described in Development of Science Publishing in Europe, mathematical practitioners, like scientists in the nineteenth century, increasingly depended on establishing peer recognition in an academic hierarchy. Within this structure, publication in journals or books began to take on a new significance.

With regards to publication in journals, Tony Crilly has argued that journals were instrumental in launching mathematical careers. In particular Crilly demonstrates how the Cambridge Mathematical Journal provided networking opportunities for its editors, first publications for its authors, and an outlet for non-university affiliated mathematicians to become known and recognized within the largely Cambridge-connected mathematical community (Crilly 2004: 487). While mathematical prowess had often been equated with standing in the Tripos exam, the Cambridge Mathematical Journal challenged traditional systems of achievement, as publication on its pages provided an alternative standard for measuring accomplishment (Crilly 2004: 492). New journals also helped change educational standards, as these materials were adapted and used in teaching and in setting examinations (Crilly 2004: 467).

In their power over what to publish, book publishers, like journal editors, were instrumental in advancing careers and in forming the reputations of their authors, including mathematical authors. Book publishers were also nodes around which communities of intellectuals and culture makers organized. Publishers like Alexander Macmillan consulted their personal networks in order to solicit materials for publication. Macmillan also relied on the opinions of his friends and advisors to make decisions about what to publish. As such, both the publisher and his advisors influenced a larger community of authors who submitted books to the publishing house. This influence extended over the readers as well who interacted with the texts that were the product.

The reach of the printed text expanded in the nineteenth century. Increasingly literate populations expanded the potential market for books, and new technologies and infrastructures facilitated the movement of texts to geographically diverse locations. Mathematical authors sought to publish books for the peer and public recognition publication might bring. Particularly with textbooks or books that could be used in an educational or practical context, the prospect of financial gain was also motivation to publish. Publishers acquired mathematical work when they valued being associated with the author’s scholarly achievement, or if they expected a profitable sale of the book, which most often coincided with the prospective sales of schoolbooks or manuals. While book publishers relied on an informal network of advisors to make decisions about what mathematical books to publish, publisher’s readers also played a role in the selection of mathematical texts, as the case study of Macmillan and Company demonstrates.

In section (2) of this chapter the role of authorship is briefly explored. While most of what we know about authorship comes from historical studies of literary works, some observations about how authorship was perceived and the motivations for it provide helpful background to this study. Following this, section (3) investigates what is known about mathematical refereeing in the nineteenth century. The role of refereeing in nineteenth century mathematical journals is examined by looking at how it was done at the Cambridge Mathematical Journal and Acta Mathematica. Additionally the refereeing of mathematical papers at general science journals, such as the Royal Society of London’s Philosophical Transactions, is discussed.

In the realm of book publishing, many large publishing houses hired publisher’s readers to help them decide which manuscripts to publish. The publisher’s reader read unsolicited manuscripts and provided advice to the publisher about which ones were worthy of publication. Publisher’s

75 readers read manuscripts on a variety of topics. While most of the known examples of publisher’s readers were literary in influence, this chapter demonstrates that the publisher’s reader also influenced decisions about the publication of manuscripts on scientific and mathematical topics. Section (4) explores what is known about the publisher’s reader.

Section (5) gives a history of Macmillan and Company and demonstrates their importance as publishers of science and mathematics. Macmillan received many unsolicited manuscripts on mathematical topics (as demonstrated in Appendix A). Section (6) looks at what mathematical manuscripts were considered for publication by the company, and which ones were accepted or declined during the 1850s, 60s and 70s. Isaac Todhunter is identified as one of Macmillan’s most important advisors on mathematics during this time. Section (7) looks at Donald MacAlister specifically as Macmillan’s reader of mathematics in the 1880s and 90s.

Decision-making about publishing mathematics was different at book publishers compared to how it was done at mathematical journals or general science journals. The values that were applied to the decision-making process were unique in each case. In my conclusion, I contend that the values applied to decision-making ultimately affected the image of mathematics cultivated within each print medium.

2. Emergence of mathematical authors

Francis Galton once estimated that there were only three hundred scientists of any repute in 1870s Britain. Of these, perhaps forty or fifty had achieved public recognition (Meadows 2004: 1). In his look at the developing profession of science in Victorian times, Jack Meadows estimates the pace of change in the scientific community was greatest from the 1850s to the 1870s. Increased activity was due in part to the many technological changes that facilitated greater communication between people, for instance a reliable postal system, an extended railway network, and the telegraph.

Technological change also arrived in the world of printing, leading to an increase in printed matter (recall section 2 of the first chapter). There was a concurrent growth in literacy and in the publication of materials for public consumption and for use in education. Given that the practice of mathematics and the standards of professionalism in this subject were also in flux during the nineteenth century, we might wonder whether an increase in publishing influenced the course of

76 mathematical knowledge in any way. Presumably there was an increase in the printed culture of mathematics, as print culture in general, expanded. If so, who were the mathematical authors who contributed materials to this expanded printed culture of mathematics? Furthermore, what were the motivations for authors to produce content? What was in it for the publishers? In order to answer some of these questions, we consider first what is known about authorship at this time.

Dustin Griffin’s article “The rise of the professional author?” proposes that since the dawn of printing there had existed a class of learned men for whom authorship was a pastime pursued for either pleasure or for fame. Griffin terms the members of this group the “gentleman authors”. To this class of writers, Griffin suggests the eighteenth century added a second distinct group, the “author by profession”. Opportunities for authors by profession grew as booksellers increasingly looked for material to keep their presses and printers busy. However, the author by profession was not seen as a respectable occupation, and was associated with base and foolish work. By some estimates, the author by profession was little more than the printer’s boy, a fellow who does menial jobs at the printing house (Griffin 2009: 140). To be writing for a living was not particularly distinguished, and at the time it was remarked upon that this work required no skill at all, as anyone could be a writer (Griffin 2009: 142). Some literature characterized the author who wrote for a living as occupying a gutter profession, comparing the work to a type of prostitution (Griffin 2009: 143).

Robin Myers concurs with this early portrayal of men and women who wrote for a living. Myers writes that prejudice against working authors remained into the nineteenth century. She writes, “It was not yet the thing for a real gentleman to write for a living… Gladstone… considered it the proper thing to live on his private income and to donate the liberal fruits of his pen to charity, rather than take the bread from the mouths of those who depended on income earned from writing” (Myers 1983: 119).61

61 In her article about writing for the booksellers, Robin Myers describes the middling work typically undertaken by these little-known men (and increasingly, women) who wrote for a living. Myers described Joseph Timothy Haydn’s work and career as fairly typical of the literary hack. Haydn worked as a political journalist in Ireland before moving to London where he worked for a publisher, writing and revising editions of typographical dictionaries. Haydn’s name appears nowhere in any of these volumes, and for the years of work he contributed to their production he received a modest income and acquired no credit. Later in life he revised books of chronological tables and contributed research that lead to a modernization of a political index. Later in life Haydn’s family narrowly escaped penury when a stroke rendered him unable to work. Haydn’s story exemplifies how this type of work lacked reward and respect in the late eighteenth and early nineteenth century (Myers 1983).

Peter and Ruth Wallis’s Biobibliography of British Mathematics and Its Applications identifies over one thousand different mathematical authors who published mathematical work in the period between 1701 and 1760. In the introduction to this volume the Wallis’ comment that one result of their research is that “the widespread, popular nature of mathematical culture is demonstrated” (Wallis and Wallis 1986: v). For authors who wrote manuals about bookkeeping or business arithmetic, how-to guides for building or surveying, textbooks of accounting or insurance, it is conceivable that such authors may have been motivated by some financial gain from publication as well as possibly having in mind the greater good that sharing such knowledge could achieve. It is possible that some of the many unknown writers whose various mathematical publications are listed in bibliographies such as the Wallis’ may have been, in some way, authors by profession.

On the other hand, we can easily identify a group of mathematical authors whose qualities align with Griffin’s description of the gentleman author. The ancient presses at the University of Oxford, for instance, published mathematical books written by learned men and gentlemen scholars throughout the eighteenth century (see Carter 1975, for a list). The press at Oxford put out a variety of editions of Euclid, for instance, in the late seventeenth and early eighteenth centuries, as well as works by the Savilian Professors of Geometry and the Savilian Professors Astronomy, for instance John Wallis, David Gregory and Edmund Halley. These men may have had things in common with Griffin’s description of the gentleman author, upon whose work a high degree of cultural value is bestowed. Some mathematical books transcended the subject, serving as symbols of nationalism and cultural achievement.62

By the end of the nineteenth century, there was less of a divide between the author by profession and the gentleman author. The schism that Griffin outlined narrowed over the course of the nineteenth century. Simon Nowell-Smith, in writing about Macmillan’s authors in the latter century period, argues that authors had matured somewhat in both their relationship to publishers, and in their public image:

62 I would put Newton’s Principia for example, in this category, and I might also include some of the English Euclids surveyed in (Barrow-Green 2006).

It is in the nature of the author-publisher relationship that certain themes should be recurrent. Certain attitudes of mind have coloured that relationship since long before Macmillans entered the trade. In the eighteenth century there were roughly speaking two principal types of author: on one side the nobleman, gentleman or well-found scholar who cared little for the financial rewards of writing, and on the other the poor scholar and the Grub Street hack to whom reward was anything but immaterial. The nineteenth century, in the middle of which the firm of Macmillan was founded, witnessed a leveling process – and not only in authorship – in which the scholar and creative writer became of necessity, if he was to succeed, his own man of business (Nowell-Smith 1967: 13).

As books and journals were increasingly produced and consumed within culture at large, gentleman authors were forced to become savvy to the business of publishing. No matter what their background, late nineteenth century authors had to navigate the publishing industry to get published and ultimately to get ahead. Large publishers had developed sophisticated distribution and advertising capabilities. It was in the author’s interest to align this power behind their work.

At the same time that authorship and publication were taking place in a more commercial environment, scientific authors adopted practices that distinguished themselves. Historians Bertrum MacDonald and Jennifer Connor note that in the nineteenth century, scientific authors frequently undersigned their names in publications with their academic credentials, including degrees earned, professional affiliations (alma mater, Royal Society Fellowship), current employer and position. They note that associating professional qualifications with authorship “reflected the desire of authors to stamp their work with authoritative, scientific credibility” (MacDonald and Connor 2007: 181). This practice was common for research reports and other types of original scientific articles and books, including monographs and textbooks. This may have reflected a desire to continue to present oneself as part of the tradition of gentleman authors in what was an increasingly commercial environment.

3. Refereeing at mathematical journals

In his brief article about the archives of mathematical journals, Jeremy Gray wrote “It should be mentioned that the highly structured refereeing system in operation today often had no counterpart in years gone by. Much of the refereeing was done by word of mouth, on an informal basis” (Gray 1975: 202). Gray wrote this in 1975, and a considerable amount of writing has since

79 taken place about the founding of mathematical journals and their role in the internationalization of mathematics. In general this work has confirmed Gray’s statement about the lack of a highly structured refereeing process within the organization of nineteenth century mathematical journals.

In June Barrow-Green’s history of Acta Mathematica, we learn how Gösta Mittag-Leffler, with financial sponsorship from the King of Sweden and the help of his fellow Scandinavian mathematicians, was able to found and maintain what would become a highly successful international journal of mathematics (Barrow-Green 2002). The journal was begun with an editorial board of fourteen (originally including Hugo Gyldén, Sophus Lie, Johan Malmsten, and Hieronymus Zeuthen) and Mittag-Leffler acting as editor. However, Barrow-Green makes it clear in whose hands control of the journal rested:

At all events, it is clear that, once publication began, Mittag-Leffler became the driving force, and [Sophus] Lie effectively dropped out of the picture. And Lie was not the only member of the editorial board not to play an active part in the journal’s early years. Of the fourteen original members of the editorial board, only Malmsten and Zeuthen made any significant contribution. It was Mittag-Leffler who shouldered the responsibilities and Mittag-Leffler who ensured the journal’s survival (Barrow-Green 2002: 147-8).

Fortunately the journal was able to attract submissions from some of the mathematical community’s most talented members due to Mittag-Leffler’s many personal contacts. As well, the portrait of Norwegian mathematician Niels Henrik Abel on its frontispiece provided a standard to which the journal sought to have its submissions aspire (Barrow-Green 2002: 140, 146). Mittag-Leffler had the ultimate say on what was published in Acta. As editor, Mittag- Leffler was the gatekeeper who ensured the high quality of articles in his journal.

In his dealings with German mathematician Georg Cantor, we can find an example of how Mittag-Leffler as editor, took responsibility for the content that was published. While Cantor’s challenging ideas about set theory had generated controversy elsewhere, Mittag-Leffler decided to publish Cantor’s papers on set theory in Acta thinking it would be beneficial for the journal and good for Cantor (Barrow-Green 2002: 150). While Mittag-Leffler’s support for Cantor was sincere, he also felt some discomfort surrounding the philosophical aspects of Cantor’s mathematics (Barrow-Green 2002: 150). In 1884, when Cantor received a letter from Mittag-

Leffler requesting that he withdraw a paper on the theory of ordered sets from the journal, this decision did not come from a reviewer or the editorial board, but from Mittag-Leffler himself. The decision to publish or not to publish was made between Cantor the author, and Mittag-Leffer the editor. Ultimately the decision not to publish the article lead to a break between Cantor and Acta Mathematica (Cantor did not publish any further papers in Acta), and put a strain on the personal relationship between Cantor and Mittag-Leffler, (Barrow-Green 2002: 153).

As the editor of a mathematical journal, Mittag-Leffler held a great degree of control over what was published, although he likely consulted, on an informal basis, his network of mathematicians. As editor of the Cambridge Mathematical Journal, William Thomson undertook a similarly centralized and fluid approach to decision making over what to publish. Under his editorship informal consultations with colleagues constituted the refereeing process.

Duncan Gregory, Archibald Smith and Samuel Greatheed founded the Cambridge Mathematical Journal at Trinity College Cambridge in November of 1837. The aim of the journal was to publish short articles of mathematics, including abstracts of important articles from foreign journals as well as original contributions. Gregory, Smith and Greatheed frequently contributed work anonymously in early issues of the journal, partly to give the impression that contributions were coming from a greater number of authors. In the early stages of many scientific journals unattributed articles written by the editors helped fill space (MacDonald and Connor 2007: 178).

Under William Thomson’s editorship, the journal evolved into what one might recognize today as a nascent scholarly journal. After its first decade, the Cambridge Mathematical Journal found a larger audience and a substantial body of contributors. Some issues sold better than expected, and the journal became a forum for many previously unpublished authors to gain a reputation through publishing (Crilly 2004).63 It also was a vehicle through which Thomson exerted influence over the community for which the journal had become a hub: “Thomson recognized the value of the journal for the mathematical community, but the fact that it was a useful channel

63 The first number of the first volume went out of print, and in 1845, the Cambridge Mathematical Journal’s London publisher/distributor, Macmillan and Co., wrote to Thomson asking for more copies for the issues printed in 1844 and 1845 (Crilly 2004: 467, 470).

81 for maintaining a wide range of contacts in the academic community would not have escaped his notice” (Crilly 2004: 480).

After Thomson became editor he put in place a series of reforms.64 As part of these reforms, Thomson began a refereeing system for articles (Crilly 2004: 480). While one might assume a refereeing process implies the existence of criteria for the acceptance of material, in practice Thomson did not specify criteria and there were no formal guidelines for referees. However, some attitudes involved in the decision-making process are revealed in individual cases (Crilly 2004: 481).

In one case, then lawyer and mathematician Arthur Cayley recommended against publishing an article on analytic geometry by Stephen Fenwick.65 The reasons he gave against it were a lack of originality (“almost all, if not the whole of it is known”) as well as a disorganization of the material, which, Cayley said, lacked both an overall composition and references to generally known geometrical theorems (Crilly 2004: 481). Crilly’s take on Cayley’s intentions as a referee are that, as an ambitious young mathematician himself, he took his role as a gatekeeper seriously. As such, Cayley did not hesitate to exclude inferior work from the printed record.66

George Boole, who also refereed articles for the journal, was less forceful in his outlook.67 While commenting that a differential equations paper by Brice Bronwin did not contain anything useful, he still recommended it for publication, giving the reason that “it is desirable to have

64 These reforms included a name change (to the Cambridge and Dublin Mathematical Journal), the requirement that every article be signed by the author’s name (eliminating pseudonyms and anonymity), an affiliation with a new publisher (Macmillan and Co.), and an expressed wish to expand the body of authors and readers beyond any specific academic affiliation. 65 Stephen Fenwick was a mathematical master at the Royal Military Academy at Woolwich, and an editor at The Mathematician, another mathematical journal that operated from 1843-1850. 66 For more about Arthur Cayley and his role in the development of British mathematics, see (Crilly 2006). 67 George Boole was largely self-taught as a mathematician, something that distinguished him from the majority of English mathematicians, who were graduates of the universities at Cambridge, Oxford, Dublin or London (see Table 2, Crilly 2004: 491). After a decade of contributions to mathematics, Boole became the first professor of mathematics at Queens College, Cork in 1849.

82 records of our own progress even in directions in which nothing is to be hoped for” (George Boole quoted in Crilly 2004: 481).68

In the case of both Acta Mathematica and the Cambridge Mathematical Journal, the editor held a great degree of control over the publication of content. However, Mittag-Leffler and Thomson were both accomplished mathematicians themselves, and also were accountable to the mathematical community they served, as editorship of a journal was a public role. The refereeing process, when it was practiced, consisted in the informal consultation of colleagues.

Refereeing systems were also enacted at general science journals at this time. The Royal Society of London’s Philosophical Transactions and Taylor and Francis’ Philosophical Magazine were general science journals that published occasional articles of mathematics. Both journals relied on reviews by referees. The Royal Society established a formal refereeing system for Philosophical Transactions in 1832. The system required that the Committee of Papers solicit reports from Society Fellows for recommendations regarding the publication of articles.69 The surviving record of reports includes correspondence about mathematical articles considered for publication.

Sloan Despeaux’s article about mathematical contributions to the Philosophical Transactions demonstrates that unlike at specialized mathematical journals, the editors assumed less responsibility for which submissions would be published (Despeaux 2011). Decisions were based on whether a vote of support for an article came from the majority of referees consulted.70 Sometimes mathematical articles were valued differently at general science journals than they were at mathematics-only journals. As Despeaux observes, ‘good’ articles of mathematics were

68 Bronwin was a curate in the parish of Denby Dale in Yorkshire who wrote many papers in pure mathematics and astronomy (Crilly 2004: 472). 69 The Committee of Papers was a subgroup of the Council, who managed the selection, editing, and publication of papers in the Philosophical Transactions and later in the Proceedings of the Royal Society. 70 In the first decades of refereeing at the Philosophical Transactions, well-known figures of the British mathematical community frequently served as referees. George Peacock, Arthur Cayley, Henry J. S. Smith, George Boole, William Spottiswoode and Archibald Smith were some of these. Initially the pool of mathematical referees for Royal Society publications was restricted to the Fellowship (and as Despeaux notes, this was a small number; in 1830 only 48 Fellows identified as mathematicians, astronomers or physicists). By 1891 it had become common practice to also use referees who were not necessarily members of the Royal Society (Despeaux 2011).

83 occasionally passed over because they were deemed too specialized for the audience, whereas ‘bad’ papers were occasionally published because rejection might offend a powerful author.71 Despeaux also notes that at general science journals, committees tasked with evaluating mathematical submissions were not always capable of recognizing outstanding contributions to mathematics.72 Occasionally, the editors of general science journals limited the amount of pure mathematics they were willing to print, because of concerns over cost or because the esoteric nature of the subject was perceived as alienating the majority of their readers.73

Extending some of the questions arising from these examples into the domain of mathematical books, we might wonder, how did book publishers decide what mathematical manuscripts to publish? Book publishers, like editors at general science journals, might not have been knowledgeable enough to judge a book manuscript in mathematics. Also, the volume of manuscripts being received by a publishing house may have been large. As examples in the following sections demonstrate, both of these factors contributed to the employment of publisher’s readers to help make decisions about which mathematical books to publish at some nineteenth century publishing houses.

4. Origin of the publisher’s reader

As the volume of overall publications increased after the 1850s, it was common for British publishers to employ publisher’s readers. The role of the publisher’s reader and the relationship these readers formed with both the authors they reviewed and the publishers they worked for is largely unknown. Identifying the frequently anonymous publisher’s reader has been a difficult

71 Despeaux gives two examples. Authur Cayley submitted some highly technical work that was not published in the Philosophical Transactions because its content surpassed even the understanding of his referees, let alone the average Royal Society Fellow. On the other hand, rejection was handled with care when the paper originated from Sir Frederick Pollock, parliamentarian, Attorney General and Chief Baron of the Exchequer (Despeaux 2011: 236, 239). 72 Despeaux’s example is the Royal Irish Academy’s rejection of William Rowan Hamilton’s 1824 submission ‘On Caustics’. Hamilton resubmitted an enlarged version of the article two years later as ‘Theory of Systems of Rays’. This paper expressed fundamental ideas that contributed to Hamilton’s later fame as a mathematician (Despeaux 2011: 245-46). 73 For example, William Francis and Richard Taylor, publishers of the Philosophical Magazine, limited the amount of mathematics included in their journal for reasons of both expense and limited readership. See the letter from William Francis to George Stokes and the quotation from Richard Taylor in chapter two, p. 19, of the present work.

84 task. It was often the case that only the publisher-employer knew a readers’ identity. Few readers have been identified by name in the history of publishing and bookselling (Fritschner 1980: 46).

In 1833 R. H. Horne announced the existence of publisher’s readers in his book Exposition of the False Medium and Barriers Excluding Men of Genius From the Public (Horne 1833). Horne’s book portrayed the publisher’s reader as a pernicious force in publishing, blaming them for holding back works of true originality while rewarding mediocrity with publication (Horne 1833; Fritschner 1980: 45).74

The job of the publisher’s reader was multifaceted. The publisher’s reader had to understand the book trade and be acquainted with the current literature. He or she had to have a familiarity with the work of living authors, and know to what degree they were esteemed. The publisher’s reader frequently had to assess a manuscript against the current state of the book market, providing advice for whether the market was in need of a particular kind of book. Ultimately their job was to recommend acceptance or rejection of a manuscript, but over time some played a role in the development of author’s careers and the shaping of work prior to publication (Fritschner 1980: 46).

To assess the impact of publisher’s readers on the publication record is difficult, as the British publishing industry was large and diverse. Not all publishers relied on the advice of publisher’s readers. Additionally, since publisher’s readers have on the whole remained obscure to history, it leaves historians, like Linda Fritschner, to speculate on their relative importance: “…reports suggest that even the unimportant readers have left an indelible imprint on literature, authors, publishers, and the public” (Frischer 1980: 94).

As for what role publisher’s readers may have played in the publication of scientific books, monographs or textbooks, little has been written. At Cambridge University Press, where many mathematical and scientific books were published, it was up to the Syndics of the Press to decide

74 In this passage Horne describes the reader as something like the publisher’s secret weapon: “there is a barrier between an Author’s heart and the Public, be his work of what merit soever, which nothing but an accidental contingency, of wealth, rank, interest, &c., can surmount…There is a regular, common-place turnpike to the first step on the high road of Fame, the only toll for which is mediocrity. There is a “Secret in all trades”—a “Skeleton in every house”— and every publisher has—his Reader! Invisible behind his employer’s arras, the author’s unknown, unsuspected enemy, works to the sure discomfiture of all original ability” (Horne 1833: 134-5).

85 what material would be published.75 After the 1870s, Cambridge University Press, like the Macmillan Company, employed publisher’s readers whose reports supplemented the knowledge and opinions of the Syndics (McKitterick 2004b: 87).

5. Macmillan & Co. as publishers of science and mathematics

Two brothers, Daniel and Alexander Macmillan, published the first Macmillan title from a bookshop on Aldersgate Street, Cambridge in 1843. These two brothers, whose biographer describes as having “descended from peasants”, grew their company from inauspicious beginnings into one of the greatest nineteenth century publishing houses in London (Morgan 1943: 1). By the 1870s Macmillan equaled Longmans or Rivington in terms of production, backlist, status and influence, despite these venerable publishing houses having been established an entire century earlier (Eliot 2002: 11). It is remarkable that Daniel and Alexander were able to steward a similar growth in their own company in just forty years.

In his biography of Macmillan, Charles Morgan describes the conundrum that is publishing, before explaining how the Macmillan brothers successfully navigated it. He writes,

There are two principal aspects of publishing, the idealistic and the commercial, and the character of a firm must largely depend on its reconciliation of them. You may put out books because you believe someone will buy them, or you may put out books because you believe it right that they should be available to the public, or you may put out books for both of these reasons (Morgan 1943: 5).

The Macmillan brothers reconciled the poles of the publishing business rather well. Morgan observes that they never operated as publishers of a particular party or sect. Although they did support the Broad Church movement, “their interest and sympathies extended beyond it” (Morgan 1943: 5). Daniel and Alexander were conscientious young men who were also “deeply interested in education, having lacked it themselves” (Morgan 1943: 2). This characteristic both shaped their publishing program and was one factor leading to its eventual success. In general,

75 The Syndics of Cambridge University Press were a committee drawn from senior members of the Cambridge University community. With regards to how the Syndics decided on what books to publish, some insight might be found in the minutes of the Press Syndicate, for which a fairly continuous set exists from 1696-1900 (Leedham- Green 1973: 17).

86 the brothers’ resourcefulness, reliability and intellectual curiosity lead them to maintain a fruitful balance between the pursuit of idealism and commercial success in publishing.

Daniel brought to the business knowledge and experience in the book trade, having been apprenticed to booksellers in London and Cambridge from the age of ten. However, Daniel was often limited in his abilities due to bad health. After Daniel died in 1857, Alexander took over leadership (and lived until 1896), expanding the business in England and in other English- speaking countries. One of Macmillan’s characteristics as a publisher is that they offered books in more markets than any other British publisher in the period. In the 1870s and 80s they began operating in Canada, America, and India (James 2002: xix). They sold books into Cape Town, Glasgow, Dublin, Leipzig, New York, Melbourne, Sydney, Adelaide, Hobart, and Philadelphia (McKitterick 2004a: 397-8). From the 1850s onwards, there was a constant exchange of books between Britain and America in particular, and one of Alexander’s major preoccupations became sales in the US and the lack of copyright protection for British books in other countries (Cunliffe 1998: 3).

As the business massively expanded during the last half of the nineteenth century, Daniel and Alexander’s children rose to partnership in the company. Frederick Macmillan helped establish the company in New York (where an office opened in 1869), India (the first books for Indian schools were produced in 1875, and by World War One they had offices in Calcutta, Bombay, and Madras), Canada (established 1905) and Australia (James 2002: 9). Maurice Macmillan became partner in 1883. Malcolm and George Macmillan worked for the firm their entire lives and by the 1880s, the third generation began to play a role in the company.76

Macmillan’s first bestseller was Charles Kingsley’s Westward Ho! (1855). Macmillan published works by famous literary figures, for example Henry James, Matthew Arnold, Alfred Tennyson and William Butler Yeats. Macmillan’s New York office selected Gone with the Wind from their slush pile. They published the children’s stories of Lewis Carroll (Charles Dodgson). Macmillan had a strong presence in children's books, religious titles, science, academic publishing and textbooks.

76 See “Macmillan Biographies, 1843-1965” prepared by John Handford (James 2002: xxi-xxiv); also, the frontispiece featuring the Macmillan family tree in (Nowell-Smith 1967).

In 1859 Macmillan started their own review magazine, Macmillan’s Magazine, which helped to promote their other publishing activities. Macmillan’s Magazine as well as the scientific journal Nature (f. 1869), were founded under Alexander’s leadership. In 1886 they launched the Colonial Library, a collection of standard works and popular fiction intended for publication in the colonies and in India. The Colonial Library became one of the most successful publisher’s series at the time, of which there were many (see Howsam 2000).

The Macmillans were also important industry leaders, helping to found the Net Book Agreement, which sought to regulate the sale price of books. Macmillan bought out Richard Bentley in 1898, and the consolidation of the Bentley publishing company into Macmillan brought valuable stock and copyright to the business, including steel and copper plates engraved by noted nineteenth century artists and illustrators. Macmillan is still in business today. Renamed Palgrave- Macmillan the company focuses on academic publishing for higher education all over the world.

While Macmillan and Company’s nineteenth century business records were made publicly available roughly fifty years ago, the vast majority of historical interest in Macmillan has been focused on its literary publishing program and the publisher’s relationship with its attendant fiction authors. The scientific side of their publishing program has received comparatively little attention.77 Macmillan had a strong presence in science, as well as in academic publishing and textbooks (Eliot 2002: 24). As well as founding the general science journal Nature (f. 1869) they also began the publication of several medical journals, such as Brain: A Journal of Neurology (f. 1878), Journal of Physiology (f. 1878), Practitioner: A Monthly Journal of Therapeutics (f. 1868) and The Journal of Anatomy and Physiology (f. 1866). Melinda Baldwin has recently shed light on the founding and development of the journal Nature into one of the most important vehicles for scientific communication in Britain (Baldwin 2012, 2013). Prior to that, almost nothing had been written about Macmillan as a publisher of scientific work. Nowell-Smith’s scrapbook about Macmillan contained nothing from Macmillan’s scientific authors. He noted the omission thusly: “Some authors of great significance in the history of Macmillans find no place here: the scientists, doctors and musicians…. ‘Hall and Knight’ of algebra fame, and many more.

77 Elizabeth James notes that Macmillan's scientific publishing program, as well as their industry leadership (i.e. their role in the formation of the Net Book Agreement), has yet to be studied (James 2002: xix). For a history of how the Macmillan Papers were acquired by the British Library and the University of Reading, see (Fredeman 1970).

Either their letters are of no interest or the stories they have to tell do not fall into the pattern of a scrapbook” (Nowell-Smith 1967: 13).

It was during the early period of the Macmillan business that Daniel and Alexander met and came to know many of their most successful authors of science and mathematics. In the 1840s and 1850s the brothers operated a bookshop out of number seventeen Trinity Street, Cambridge. Daniel was in poor health and the brothers were heavily in debt, but during their bookstore days they built relationships with some of their most successful authors, many who were Cambridge educated men or Cambridge connected men. Patrons of the bookstore grew to become Daniel and Alexander’s guests, personal friends, and then, in many cases, the authors that they published. Isaac Todhunter and Barnard Smith were two acquaintances the brothers met at this time, with whom the Macmillans developed long-standing publishing relationships (Morgan 1943: 30, 37). Todhunter and Smith were both Cambridge graduates who authored successful mathematical textbooks for Macmillan.78

The climate of teaching and learning at Cambridge University during the nineteenth century has been a subject frequently commented upon by historians (Crilly 1999; Rothblatt 1967; Warwick 2003; Barrow-Green and Gray 2006). Many professors had little reason to be in direct contact with their students in the Cambridge of the 1840s and 50s. In that climate, the Macmillan’s bookshop served as common ground, a space that both professors and students frequented. Morgan calls the Macmillan bookshop a “little college in itself” and explains how the store served as the locus for an entire social scene:

The old principle of bookselling and publishing had one of its last great exemplars in them, and the men who came into the shop to buy books stayed in the publishing house to write them. Thus they drew on the whole resources of the University and an upper room in Number One [Trinity street] became a common-room where young men and old men assembled to discuss books or God or social reform – but chiefly, it would appear, God – before going into four o’clock hall (Morgan 1943: 30, 34).79

78 Macmillan printed more than 597,500 copies of Barnard Smith's Arithmetic for Schools between 1854 and 1920, and 693,000 copies of Isaac Todhunter’s Algebra for Beginners during the period 1863-1917. See Macmillan’s first Editions Book, p. 472, 594, Macmillan Archive, British Library, London UK. 79 The upper room in Number One Trinity Street was Daniel and Alexander’s lodging.

During their Cambridge bookshop days, Macmillan’s first publications in the 1840s included mathematical textbooks that had been previously published and which had proven consistent sales. This was a calculated investment on their part, as the right to print standard works of instruction had long been recognized as a valuable asset to booksellers and publishers (Topham 2000a: 318-19). The earliest mathematical books published under the Macmillan imprint were new editions of established textbooks used in the Cambridge context. These included The Elements of Mechanics by J. C. Snowball and The Cambridge Course of Elementary Natural Philosophy, Snowball’s compilation of a text by Thomas Lund. Both of these texts had a proven track record of sales and had been previously published elsewhere. As a mathematical author Thomas Lund was well known to the students of Cambridge having revised and enlarged James Wood’s ubiquitous Elements of Algebra in some of its later editions (the fifteenth edition of Wood’s Algebra was printed in 1857).

These mathematical textbooks were consulted by students studying for the Tripos examinations at Cambridge, and as such were part of the Cambridge education system that presented students with a normative image of mathematics.80 On the title page of Harvey Goodwin’s Elementary Course of Mathematics, Designed Principally for Students of the University of Cambridge, the chosen quote by Francis Bacon captures something of the spirit in which Cambridge students were introduced to mathematics. The quote reads:

As Tennis is a game of no use in itself, but of great use in respect it maketh a quick eye, and a body ready to put itself into all postures; so in the Mathematics, that use which is 81 collateral and intervenient is no less worthy than that which is principal and intended.

When the Analytical Society attempted to alter the mathematical atmosphere at Cambridge by introducing continental methods of analysis via their Memoirs, Charles Babbage wrote to Edward Bromhead regarding the reception of the new mathematics by the average Cambridge

80 Joan Richards, in her book Mathematical Visions, develops the idea that the English viewed mathematics as an empirically flawless body of knowledge. They did not, in general, regard mathematics, and in particular geometry, as capable of growth, failure, or change. As such, mathematics held special cultural value in English culture and society, for its ability to provide an exemplar, or norm, for truth. Richards argues that this image of mathematics was particularly expressed in England’s educational structures, and shaped the approach to teaching mathematics at the University of Cambridge (Richards 1988a). 81 Excerpt from Bacon’s Advancement of Learning, as quoted on the title page of (Goodwin 1849).

90 man. He wrote: “Of course much nonsense is talked about them here [the Memoirs]; but I have not heard criticism yet ventured beyond the second line of the first Memoir: of which men ask ‘is it to be found in Jemmy Wood’ [i.e. James Wood’s The Elements of Algebra] and if not they divide by x and are lost in the clouds of [Greek letter psi]’s which follow” (quoted in Topham 2000a: 329). This off-handed quote from Babbage is a reminder of how committed Cambridge students were to their mathematics textbooks (such as Wood’s Algebra), and the image of mathematics these contained. With their first mathematical publications, Macmillan chose conservatively, following an already hewn path.

As Cambridge University Press historian David McKitterick reflected, “In continuing assured markets in mathematics….[Daniel and Alexander Macmillan] were conservative” (McKitterick 2004a: 390). After beginning their career as mathematical publishers with republications of already successful textbook authors, they later established a new group of mathematical textbook authors, some of whom became associated with the firm of Macmillan in particular. As the business became more successful in the 1860s, 70s and 80s, Macmillan expanded their publications to include scholarly texts in addition to school and college textbooks. Macmillan’s authors in mathematics and mathematical physics grew to include Isaac Todhunter, Barnard Smith, George Boole, John Venn, W. W. Rouse Ball, Joseph Wolstenholme, A. George Greenhill, William Kingdon Clifford, Peter Guthrie Tait, John Strutt (Lord Rayleigh), George Gabriel Stokes, William Thomson (Lord Kelvin), Silvanus Phillips Thompson, James Clerk Maxwell, William Spottiswoode and George Biddell Airy.82

After Daniel died in 1857, Alexander expanded their Cambridge-based publishing business, establishing an office at 23 Henrietta Street, in the Covent Garden area of London, in 1858. Five years later Alexander would move from Cambridge to London, establishing the business headquarters there. But for the five years between the creation of the London office and while Cambridge remained the base, Alexander travelled to the city every Thursday for the night. Alexander’s weekly visits to London became an occasion to gather socially with the intellectuals, authors and scientists who mingled in Macmillan’s growing sphere. In the words of Robert Bowes, Alexander’s nephew who operated their London premises, these get-togethers in the

82 For a complete list of Macmillan’s publications between 1843 and 1889, see (Foster 1891).

Henrietta Street offices were “at home to all and sundry, when tea and stronger fluids, with occasional tobacco, were going on” (Robert Bowes, quoted in Morgan 1943: 50).

These occasions became known as the “Tobacco Parliaments”, and were somewhat legendary gatherings attracting both men of science, artists and writers of fiction. Some of the regular attendees included the painter Holman Hunt, the sculptors Thomas Woolner and Alexander Munro, and the writers Lord Tennyson, Thomas Hughes and Charles Kingsley. Among the scientific guests were T. H. Huxley, William Sharpey, and Herbert Spencer (Morgan 1943: 50- 51). The talk revolved around “Darwin and conundrums with general jollity pleasantly intermixed” (Morgan 1943: 52). At Hughes’ suggestion, a round table was made and the signatures of some of the Tobacco Parliament attendees were engraved around its edge.83

While Macmillan’s clout as a publisher increased with the move into London’s intellectual circles, they continued to rely on the base that Cambridge had provided. One of the Cambridge connections they continued to exploit was their patronage of the printing facilities at Cambridge University Press. From the very beginning of their publishing business Macmillan had their books handled by various printers including Richard Clay (London), Eyre and Spottiswoode (London), and Constable (Edinburgh). Macmillan also worked closely with Richard Clay’s son, C. J. Clay, who was employed as University Printer at the Cambridge University Press from 1854 to 1882.

Many of Macmillan’s regular orders at Cambridge University Press were either new books in mathematics or repeated printings of successful mathematical textbooks. Barnard Smith’s Arithmetic for Schools (1854) was ordered up almost yearly in increments of several thousand copies at a time (McKitterick 2004a: 390).84 Isaac Todhunter’s books Treatise on the Differential Calculus (1852), Algebra for the Use of Colleges and Schools (1858), and Elements of Euclid (1862) also became staples at the Cambridge press where these books were printed and

83 Alysoun Sanders, archivist for Macmillan Publishers Ltd., “Macmillan’s ‘Tobacco Parliament’ History (1858- 1880s)” (unpublished notes). The round table may still exist as well as a guest-book recording attendance at these events. According to Sanders, no further research has been carried out about these gatherings, other than what Charles Morgan has written about in his biography of the firm. Alysoun Sanders to Sylvia Nickerson, personal e- mail correspondence, 31 July 2012. 84 Macmillan’s first Editions Book, p. 472, Macmillan Archive, British Library, London UK.

92 reprinted. In general Macmillan had a steady account at Cambridge. Their annual printing expenses ranged from three to four thousand pounds per year during the 1860s (McKitterick 2004a: 396).

The Macmillan list was strong in theology and in mathematics. Even after Macmillan moved their headquarters to London, they maintained connections to Cambridge University through their authors, and to the press at Cambridge where they continued to print Macmillan’s books, catalogues and prospectuses. As David McKitterick has reflected in his history of Cambridge University Press from the 1850s to the 1880s, it was actually Macmillan that was, in effect, acting as the university publisher for Cambridge. While the Syndics continued with their traditional management of the press that included a small publications program, they largely failed to evolve in response to the changing times. McKitterick observes, “The Macmillan list was remarkable for authors from Oxford and London, from Manchester and from the Public Schools…the firm’s future was established during these years as what would now be called an academic publisher, a university press in all but name and organization” (McKitterick 2004a: 397).

It was the Macmillan brothers and also John Deighton – both Cambridge bookseller-publishers of the nineteenth century – who forged new frontiers in many aspects of science publishing in response to the changing educational needs and interests of nineteenth century Britain (McKitterick 2004a: 32). Macmillan’s publication history demonstrates their engagement with the growing importance of science in culture, and the way in which scientific inquiry was increasingly pursued, shared and published (McKitterick 2004a: 32). Charles Morgan also acknowledged Alexander Macmillan’s openness towards science and his recognition of its increasingly important role in society: “Through [the Darwinian controversies] Alexander held a steadfast conviction that religion and science were allies, not foes, in the interpretation and achievement of human destiny, and the firm’s policy reflects his view” (Morgan 1943: 71). Cambridge University Press, by contrast, continued to be lead by the Syndics whose university traditions may have insulated them from the ways in which the cultural winds were changing.

The result was that Macmillan effectively poached much of the talent that had been trained and molded by Cambridge away from publication with the University. Macmillan may have paid Cambridge significant sums for their printing bills, but ultimately the printing work Cambridge

University Press undertook for Macmillan lead to the growth of Macmillan as publishers, leaving the Syndics’ list of Cambridge published books atrophied by comparison. McKitterick’s assessment of the Syndics management of the press is fairly biting in this regard:

Long before the mid-nineteenth century, the University was taking no formal responsibility for all that it printed, save in the most indirect way. It appointed a University Printer; it required him to print certain books agreed by the Syndics and such administrative papers as were necessary each year for the smooth running of an increasingly paper-dependent organization; but it left him free to use the University’s equipment as he would, for most of his time. Such an arrangement, folly at best but actually the result of culpable neglect, potentially left University Printers in personally very profitable positions. Much more importantly, it permitted an active, imaginative and well-informed publisher, Macmillan, to profit at the University’s expense, and to lay the foundations of a list that became ever stronger as the University Press’ own meager list became ever more disabled (McKitterick 2004a: 31).

Macmillan was also innovative on the frontier that was the introduction of science into elementary education. Charles Morgan writes about how Alexander Macmillan noticed the influence of James Maurice Wilson on the introduction of science into the public schools (Morgan 1943: 71). Wilson, who worked as a mathematics master at the Rugby School and then headmaster at Clifton, served on a committee with T. H. Huxley and John Tyndall at the British Association for the Advancement of Science to study the development of science education for the country (Mayor 2004). Wilson encouraged the introduction of botany, geology and chemistry into the school curriculum. In response to Wilson’s activism on this front, Macmillan began to publish elementary school books in these areas. For his authors Macmillan sought out the most recognized masters in every subject. Morgan notes that Daniel and Alexander’s practice of seeking out the best names to write school-level textbooks was an expression of a deeply felt philosophy about education (Morgan 1943: 71). Alexander once summarized his approach to educational texts this way, “I conceive of three classes of reader. 1. A general public to be moved by broad, strong representations of the truth. 2. A thoughtful class who demand some striking originality, or 3. A learned class who want the pabulum suited to their special digestion” (Alexander Macmillan quoted in Morgan 1943: 55). According to his vision, Macmillan pursued the publication of elementary science textbooks authored by men he considered first-rate experts

94 in their fields, for instance, Balfour Stewart, Henry Roscoe, W. Stanley Jevons, Norman Lockyer and T. H. Huxley.

In an 1854 letter to Thomas Lund, Macmillan expressed value in having the best minds write elementary textbooks, in this particular case, elementary mathematics textbooks. In his letter to Lund, Daniel Macmillan responds to reticence Lund had about Isaac Todhunter authoring mathematical textbooks. Lund feared that Todhunter had plagiarized his textbook for material, and that because Todhunter’s textbooks were also to be published by Macmillan, they would be in direct competition with his own. In reply, Macmillan both dismissed Lund’s fears and inadvertently confirmed them:

There is doubt that there is room enough for several first rate school books on such subjects as algebra. We are largely sure that Mr. Todhunter will steal from no one – so your property is safe. It is same and good for the educational prospects of England that first rate Cambridge Mathematicians should strive to produce the best elementary works. This field has been too long in the hands of quacks.85

Whether or not Macmillan intended to insult Lund in this letter is hard to say for sure. Macmillan is stating that he would prefer to publish elementary textbooks by first rate Cambridge mathematicians, simultaneously implying that either Lund was second-rate or that he would be correct in assuming that Todhunter’s book would be in competition with Lund’s own. Macmillan’s statement that the job of writing textbooks had been “too long in the hands of quacks” may be an expression of the vestigial prejudice that authorship itself brought a person no special ennoblement. Thomas Lund was a rector at Morton, Derbyshire. He was known as an editor of Wood’s Algebra, and had been a Fellow and Sadlerian lecturer at St. John’s College. Todhunter was Senior Wrangler and first Smith’s Prizeman in 1848 (Barrow-Green 1999: 286 f.n. 80). Senior Wrangler and Smith’s Prize were titles of mathematical accomplishment to which Lund could not lay claim. By 1854 Todhunter had already published two books with Macmillan, and would go on to publish many more, while Lund’s last publication with

85 Daniel Macmillan to Thomas Lund, 28 October 1854, 55376 General Letter Book, 1854-1855, Macmillan

Archive, British Library, London UK.

Macmillan was in 1852. Daniel and Alexander placed priority on gathering authors for educational works who were already recognized as authoritative and important in their field. By securing the two most important titles of mathematical accomplishment at Cambridge, Todhunter had been recognized as authoritative and important.

Macmillan wanted to publish elementary works authored by esteemed specialists, and in these efforts Macmillan followed in the footsteps of the educational reform movement embodied earlier in the century by the Society for the Diffusion of Useful Knowledge. Recall that Dionysius Lardner, in his role as series editor of the Society’s Cabinet Cyclopaedia series, had compiled several books on scientific subjects intended to ennoble the working and middle- classes (see section 5 in chapter two). Sir John Herschel, Henry Kater, Augustus De Morgan, David Brewster and Lardner himself wrote volumes on natural philosophy and mathematical topics in the Cabinet Cyclopaedia series. Offering books on scientific and mathematical subjects ranging from as little as sixpence to a few shillings, the Society for the Diffusion of Useful Knowledge offered some of the first mass-produced publications through which academic knowledge about science was made available to a broad audience through books. Following the example set by the Society and its educational publications, Macmillan similarly encouraged “first rate” men to develop introductory and elementary works in their areas of expertise.

In touch with the changing needs of education, interested in engagement with science, and proximate to the center of English mathematical activity at the time, Macmillan became one of the most important publishers of science in nineteenth century England. From 1843 to the turn of the century, Macmillan demonstrated what an academic and educational publisher might do. McKitterick reflects, “Their success, while the Syndics of Cambridge University Press slept, had repercussions for a century” (McKitterick 2004a: 401). What they discovered and then drew out of Cambridge was “a mine hitherto almost unworked, of the best book-producing power of the nation, especially for educational works. There was a great want of these, and in every generation of undergraduates were men specially fitted for writing or editing them” (McKitterick 2004a: 387).

6. Manuscripts on scientific and mathematical topics from Macmillan’s “slush pile”

The publishing records of Macmillan demonstrate a large number of authors writing about scientific and mathematical topics who were, in their contact with Macmillan, attempting to establish a publication record. Macmillan and their publisher’s readers held a certain sway over these authors. It was the publisher’s job to form an opinion on the quality of the work submitted, and ultimately decide whether or not to invest capital in printing and promoting these texts. Macmillan and their readers reviewed mathematical and scientific manuscripts to decide what to publish. From the 1860s to the turn of the century, a new position in the chain of scientific communication was created. Macmillan and their publisher’s readers became engaged in choosing which scientific and mathematical books, textbooks and monographs, to publish.

Most of the manuscripts Macmillan considered for publication were written by men (and a few women) who are now unknown or forgotten. Appendix A contains a list of the mathematical manuscripts received by Macmillan and considered for publication in the period between 1867 and 1896. This list shows that Macmillan considered a number of elementary arithmetic textbooks submitted by little known authors.

Another frequent subject of the unknown or lesser-known authors were popularizations of science. In most cases these popularizations by unknown writers – to the eyes of the publisher’s reader at least – offered nothing, perhaps less, compared with the writings of the men who had proposed the theories themselves. Some of these popularizations had titles such as “Modern science”, “Science explained in plain English”, “Gems of science”, “Harmonic Laws of the Universe”, “Science and religion”, and “The invisible powers of nature”. None of these manuscripts were ultimately published.86 While Macmillan also rejected many of the arithmetic

86 See 56016, Records of Manuscripts Received, 1866-1883, Macmillan Papers, British Library, London UK. Hereafter references to this collection will be given by the abbreviation MP followed by the accession number. An anonymous reviewer wrote of one such popularization, entitled The Science of Method submitted by J. O. Connell: “It is deplorable to think of the time which must have been spent in producing this laborious farrago – three parts of the sentences in which are absolutely meaningless. I went over one test chapter with a thoroughly learned man in this special subject, and he agreed with me that it was pure rubbish – not because its meaning is wrong, but because it has no meaning. It would be a discredit to publish it” (MP 55933, Readers Reports 1871-1877, p. 5).

97 textbooks that were submitted, it was more likely that a mathematics book, rather than a scientific popularization, rose to publication from the “slush pile”.

In contrast to the unknown authors whose names appear frequently in the records of manuscripts, there are also many names of prominent men of nineteenth century science. These men were frequently authors for Macmillan and also consulted as reviewers on book manuscripts written by others. Appendix B gives a list of some of Macmillan’s readers on scientific subjects. Some of the people Macmillan sought out for opinions were Mary Boole (widow of George Boole), Thomas Henry Huxley, astronomer Norman Lockyer, logician William Stanley Jevons, Scottish physicians T. Laudner Brunton and Sir David Ferrier, and Scottish physicist Balfour Stewart. Mathematicians Joseph Wolstenholme and Isaac Todhunter were consulted about mathematics. In 1881 Charles Darwin and Alexander Dickson were consulted regarding the possibility of translating Ferdinand von Müller’s German botanical text Befruchtung der Blumen into English.87

Macmillan also turned to these figures when soliciting new material. While corresponding in November of 1854 about acquiring Abel’s Oeuvres for George Stokes, Daniel Macmillan invited Stokes to consider publishing his lectures on physics with Macmillan.88 While presented by Macmillan as a casual suggestion in passing, it was no doubt a serious offer. In 1854 Macmillan was still a burgeoning publisher, and Stokes already held an impressive list of scientific titles.89 This is one of several examples in which Macmillan directly solicited material from favoured authors.90 The record of readers’ reports also shows that Macmillan considered commissioning

87 MP 55935, Readers Reports, 1880-1883, p. 92. Some of the foreign mathematical books considered for translation (but not ultimately adopted) were a popular German mathematical textbook by Heiss on algebraic problems (MP 55939, Readers Reports 1885-1886, p. 73), and an arithmetic text by an unknown author from Hong Kong (MP 55939, p. 129). 88 MP 55376 General Letter Book, 1854-1855, p. 70. 89 Stokes, besides being Senior Wrangler and first Smith’s Prizeman at Cambridge in 1837, was appointed to the Cambridge Lucasian professorship of mathematics in 1849, and served as a secretary for the Royal Society from 1854 until he became president in 1885. In 1877 Stokes published some lectures with Macmillan. This was several decades after their initial attempt to woo Stokes as an author. 90 Alexander Macmillan pursued George Biddell Airy in 1861: “I should have great pleasure and feel much honour, if at any time you had a book of a popular character like your Lectures on Astronomy to publish to take risk and divide profits with you” (Macmillan 1908: 75).

98 books on particular topics. Macmillan’s circle of trusted consultants acted as referees, and in some cases, the font from which Macmillan could source material for publication. Many of Macmillan’s regular contributors and closest confidents were also frequent attendees at Macmillan’s Tobacco Parliaments.

In the early days of the Macmillan business, there is evidence Todhunter served in an informal role as Daniel and Alexander’s consulting expert on mathematics. Letters from Macmillan to their mathematical authors in the 1850s contain oblique references that suggest Todhunter was advising on a variety of topics with regards to the presentation, quality and form of mathematical manuscripts for the press.91 Todhunter’s influence over the mathematical books Macmillan published at this time lead to Macmillan replacing some of the well-trod mathematical textbooks they had been publishing with books by new authors. When John Hymers wrote to Macmillan requesting they take up a new edition of his textbook on differential equations, for example, Macmillan discouraged the idea, having undertaken, at Todhunter’s suggestion, Boole’s book on the same subject.92 There is little direct record of Todhunter’s opinions on these matters, except in the passages of Macmillan’s correspondence that refer to him. Likely advice was given in person, as the Macmillan brothers and Todhunter lived in Cambridge in the 1850s.93

After Daniel’s death and Alexander’s decision to move the headquarters from Cambridge to London, Macmillan’s expanding organization established a system in which potential book manuscripts were numbered, dated and recorded as received, with a note as to whether they were reviewed by a reader, and ultimately whether they were accepted for publication or declined. In these records one can observe that mathematical manuscripts were sent to the press with

91 In 1855, Daniel wrote to George Boole about his differential equations manuscript, commenting, “The title you suggest to us seems very good and Mr. Todhunter to whom I showed it liked it too”. Daniel Macmillan to George Boole, 12 September 1855, MP 55377 General Letter Book 1855. 92 See Daniel Macmillan to George Boole, 12 September 1855, MP 55377 General Letter Book 1855, and Daniel Macmillan to John Hymers, September 16 1855, MP 55377. It was a new edition of Hymer’s A Treatise on Differential Equations, and on the Calculus of Finite Differences (1839), originally published by Deighton in Cambridge and Rivington in London, that Macmillan presumably turned down. 93 See MP 55376, 55377 and 55379 General Letter Books from 1855-1856. One might observe that in their publication catalogue, Hymers is listed as being a Fellow and Tutor at St. John’s College, Cambridge. George Boole by comparison is listed as having more prestigious titles, such as Fellow of the Royal Society, Professor of Mathematics at Queens University, Ireland and Honourary Member of the Cambridge Philosophical Society (see Foster 1891: 55).

99 surprising frequency. Manuscripts on mathematical subjects (including topics in mixed mathematics and mathematical physics) were more frequent submissions to the press than manuscripts on any other topic in science. Next to the mathematical genre, the second most popular science subject was chemistry, followed by botany and the life sciences, including medicine and its related sub-disciplines such as anatomy, pathology, and surgery.94

More work would have to be done to identify Alexander Macmillan’s closest advisor on mathematical manuscripts in the 1860s and 1870s. Todhunter may have remained a source of informal advice during this time. In the records of manuscripts, there is only one note of a review by him. In 1873 he reviewed a manuscript on Differential Coefficients by John Newton Lyle.95 In the 1870s, Norman Lockyer (who published Elementary Lessons in Astronomy with Macmillan, in 1868) became Alexander Macmillan’s “consulting physician in regard to scientific books and schemes” (Alexander Macmillan as quoted in Graves 1910: 262). However whether Macmillan relied on him for mathematical expertise as well is uncertain.

The 1860s and 70s were a time of expansion by the company, and during these decades many mathematical manuscripts were accepted for publication, although no formal review, by a publisher’s reader or confidant (like Todhunter), is recorded in the records of manuscripts. During this period of time books by eminent men of science were rarely turned away from the press and in fact were seemingly expedited when they were received. Manuscripts from reputable scientists were often accepted immediately (without a noted review) and sent to the printer in short order. Perhaps this reflects Macmillan’s eagerness to publish what Daniel described as first rate men of science.

Henry Roscoe’s manuscript of his lectures on Spectrum Analysis (1869) was received, accepted and sent to the printer all on one day in April of 1869.96 Similarly, other manuscripts seem to have been fast-forwarded through the process of receipt, review, and response, which normally

94 MP 56016-56018, Records of Manuscripts Received, 1866-1899. 95 John Newton Lyle was a mathematics professor from Westminster College in Fulton, Missouri USA. The manuscript was returned to the author. Presumably, Todhunter did not recommend its publication (MP 56016, p. 31). 96 MP 56016, p. 9.

100 took a week or two. Lectures by T. H. Huxley, First Book of Indian Botany by Prof. Daniel Oliver of Kew and London’s University College, and Principles of Reason, Elementary Logic and Theory of Political Economy by Prof. Stanley Jevons from Manchester are all marked in the records of received manuscripts with a squiggly line running through the column were reviews are normally recorded.97 Each of these manuscripts was received and accepted by the publisher on the same day, and sent to the printer right away. Thomas Clifford Allbutt’s manuscript on the opthalmoscope was accepted on the day it was received in November 1870.98 Lord Rayleigh sent the second chapter of his book on sound to Macmillan on May 2, 1876, when it was accepted without any note of a review.99 Other authors who had manuscripts received without review include physician J. Milner Fothergill.100

During this period of time, mathematical manuscripts were also being accepted or declined. Macmillan received the first part of W. K. Clifford’s Elements of Dynamic on September 20, 1877, on the same day it was accepted without a noted review.101 The Elements of Descriptive Geometry, by J. B. Millar, was accepted without review in 1876.102 Millar was a civil engineer and assistant lecturer in engineering at Owens College in Manchester (Foster 1891: 343). Mathematical Problems (1878) by Joseph Wolstenholme, A Treatise of the Theory of Determinants (1882) by Thomas Muir and Examples in Arithmetic (1879) by S. Pedley, were all accepted without review.103 These authors were all math teachers: Wolstenholme a professor of mathematics at the Royal Indian Engineering College (and late fellow and tutor of Christ’s

97 MP 56016, p. 11, 16, 20. 98 MP 56016, p. 18. 99 MP 56016, p. 42. This record indicates that the second chapter of volume one (not the text of the second volume) was sent at this time. Note that Macmillan published volume one of Rayleigh’s Theory of Sound in 1877, while volume two appeared in 1878. 100 MP 56016, p. 41. 101 MP 56016, p. 49. 102 MP 56016, p. 45. One wonders whether Alexander Macmillan may have turned to his network of informal advisors on these occasions. For instance William Stanley Jevons, a man within Macmillan’s circle, may have known Millar from his time working at Owens College. 103 MP 56016, p. 51, 53, 57.

101

College), Muir a mathematical master in the high school of Glasgow, and Pedley a teacher from the Tamworth Grammar school (outside Birmingham).

In some cases immediate acceptance took place because Macmillan had acquired rights to print the second edition of an already published work. For instance Wolstenholme’s Mathematical Problems had been first published by Macmillan in 1867 (containing 1,628 problems), and published for a second time by Macmillan in 1878 (containing 2,815 problems).104 When George John Romanes’ manuscript on the Scientific Evidences of Organic Evolution was accepted immediately in May of 1882, it was a second edition.105

Macmillan received a manuscript from unknown author A. Mault, of 66 Blenheim Crescent Kensington W, for the book Natural Geometry: An Introduction to the Logical Study of Mathematics (1877) on October 12 of 1876. It was accepted a few weeks later on December 6.106 While no record of its review exists, I suspect Macmillan might have sought an opinion on it, due to the obscurity of the author and the time lapse between the receipt of the manuscript and the date recorded when a decision was made to publish it. This unusual book was published in 1877, along with a companion product, a box of models to be used by students working with Mault’s geometry (Foster 1891: 324).

Other mathematical manuscripts from this time were declined without a noted review. “Mathematical Formulae” by R. M. Milburn and “Arithmetic and Answers” by John Flint of Glasgow were returned in 1878.107 “Elementary Plane Trigonometry” by Joseph McKinn and “Geometrical Conic Sections” by H. G. Wills were returned in 1879.108 “Rules and examples in

104 See (Foster 1891: 165). I am grateful to June-Barrow-Green for pointing this out. 105 MP 56016, p. 83. 106 MP 56016, 44. 107 MP 56016, p. 58, 60. Milburn’s Mathematical Formulae was published by Longman’s in 1880. Flint was the author of a previously published textbook in Glasgow. 108 MP 56016, p. 64, 65.

102 algebra” by W. Henry Bond and “Matriculation mathematics” by E. H. Matthews were declined in 1880.109

The year 1880 witnessed a change in how Macmillan handled their received manuscripts. In the 1880s the records of readers’ reports exhibit greater regularity. It was also during this time that Macmillan began to employ a publisher’s reader to review manuscripts about topics in mathematics and science.110 Donald MacAlister began reviewing manuscripts for Macmillan in 1880.111 From 1880 to 1896 most if not all of the manuscripts in mathematics, physics and general science topics received a review by Donald MacAlister.112

7. Macmillan’s reader of mathematics Donald MacAlister

Sir Donald MacAlister (1854-1934) was born in 1854 in Earls Dykes East, Perth. Given MacAlister’s later involvement in the publishing world, it is notable that Donald’s father diverged from traditional family work (farming and fishing) to become a publishers’ agent for Blackie & Son. This career change initiated the family’s to move to Liverpool, where Donald grew up and attended school.

As a youth MacAlister showed early academic promise, winning the Royal Geographical Society gold medal while attending the Liverpool Institute. MacAlister entered St. John’s College, Cambridge, on scholarship. He took mathematics, graduating Senior Wrangler and winner of Smith’s Prize in 1877. He was elected a fellow of St. John’s College and taught for a term at Harrow while contemplating his career. As winner of the Royal Geographical Society medal, MacAlister had come to the attention of Francis Galton. Galton acted as a mentor to MacAlister, encouraging his pursuit of mathematics, specifically. Under Galton’s patronage, MacAlister published a paper on the mathematical distribution of the geometric mean in the Proceedings of

109 MP 56016, p. 69, 70. W. Henry Bond is identified as headmaster of Barrow School, Borden, Kent. 110 Other publisher’s readers were employed by Macmillan at this time. The reader’s reports of Thomas E. Page (active 1893-1899), Henry Stuart Jones (1895-1904), and Frederic Relton (1879-1925) are held within the Macmillan Papers, British Library. 111 The first report attributed to MacAlister occurs in November of 1880 (MP 56016, p. 73). 112 While most of MacAlister’s reports are identified by the initials DM, DMA or DMcA, his full name appears in (MP 55935, p. 47).

103 the Royal Society (Crilly 2004; MacAlister 1879). However, this would be MacAlister’s only publication in mathematics, as he decided against mathematics and pursued medicine as his occupation.

MacAlister got degrees in medicine from Cambridge, studied at St. Bartholomew’s Hospital in London and studied abroad in Leipzig. In 1881 McAlister returned to Cambridge where he was appointed Linacre lecturer and worked under the Regius Professor of Physic, Sir George Paget. He graduated MD in 1884, and became a consulting physician at Addenbrooke’s Hospital. He was recognized in 1886 with election to the Royal College of Physicians.

During the 1880s and 1890s when McAlister was active as a publisher’s reader for Macmillan, he was also an integral part of Cambridge University and its college and university life. He served on the council of the University Senate. From 1893 to 1904 he was a senior tutor at St. John’s College. In 1889 MacAlister’s life was transformed when a surprising election resulted in his representation of Cambridge on the General Medical Council, defeating the Downing professor of medicine in the process. This position began a chapter in MacAlister’s life for which he is now most frequently remembered: as a longstanding and successful administrator. MacAlister remained a member of the General Medical Council for forty-four years, serving as its president from 1904-1931, and by all accounts ruling the council “with a rod of iron” (Crilly 2004). In 1907 he was elected principal of Glasgow University, a position he held until 1929, when he became chancellor of the University. By the time MacAlister died in 1934, he had been recognized with thirteen honourary doctorates and made a baronet.

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Plate 1 Sir Donald MacAlister, first baronet (1854-1934); photograph by Olive Edis; picture credit © National Portrait Gallery, London

While the circumstances under which MacAlister became a publisher’s reader for Macmillan are not entirely clear, it is possible that Todhunter recommended him to the job.113 As familiar to the Cambridge community as he was, MacAlister probably knew many of the authors whose work he reviewed. But MacAlister worked for Macmillan as an anonymous reviewer, as was the custom of publisher’s readers (recall Hone’s description of the publisher’s reader as secret and “invisible behind his employers arras”).

Following this custom, MacAlister too was circumspect about his work for Macmillan. His biography, written posthumously by his wife, does not mention this role (MacAlister 1935). In

113 MacAlister and Todhunter were “old friends” according to MacAlister (MP 55940, p. 137).

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MacAlister’s reports for Macmillan he explains how he took steps to conceal his identity as Macmillan’s reader when he consulted colleagues for their opinions about a manuscript.114

As a reviewer, MacAlister was academically qualified to judge the relevance and originality of elementary to college level presentations of mathematical subjects. He was also attuned to the qualities of a manuscript that would be of concern to a publisher. Was there a book on Macmillan’s backlist that already covered the subject matter? Was there a rival book already published in the market? MacAlister’s reports attended to these questions. His reports often identify the prospective audience for a manuscript, recommending the work as destined for mathematicians, students, practical men or engineers. Often he declares it rubbish and therefore not fit for any audience, in his opinion.

MacAlister’s reviews comment on the social connections or peer recognition of the author, and he associates the author’s reputation and identity with his estimation of the book’s financial success.115 His judgments of authors range from descriptions like a “good man”, “a clever and rising man of the second-rank”, “self-taught school master”, “intelligent working man”, to the statement: “there are numerous signs that the writer though he may be a good arithmetician is not a fully educated man”.116 About a manuscript on light and heat, MacAlister writes that “the author’s knowledge is book knowledge only”, furthermore recommending that due to an unfortunate similarity between the author’s name and the author of another already well known book “which was an atrocious piece of bungling, and is tabooed by all good teachers”, Macmillan would do well to decline the work with thanks.117

MacAlister also provides opinions as to whether the manuscript he is evaluating would be useful to students or if he expects it to have a remunerative sale. Even if the work is deemed to be

114 MacAlister writes in one review, about the difficulty of consulting a Cambridge colleague for his opinion, as this person also knew the prospective author: “If I ask him he would at once connect me directly with you, and I shall be freer in the future if the connection is not so public” (MP 55935, p. 171).

115 MP 55935, p. 26; MP 55931 Readers Reports 1886-1871, p. 174. 116 MP 55939, p. 129. 117 MP 55940, p. 135.

106 neither of these, MacAlister sometimes recommends a highly accomplished work as a “credit to publish”, implying that it would be advantageous for Macmillan to be associated with a highly accomplished work or a prestigious author, even if the publication resulted in little financial gain to the company.118

About the manuscripts he did not favour, MacAlister describes these texts as in turn ill arranged, imperfect, a boiling down, containing blunders, having a foreign style, too antiquarian, flighty, crude, clumsy, repetitive, a book of rough notes, half-brained, made-up, or full of misunderstandings. About a manuscript entitled “Arithmetical papers”, MacAlister recommends declining the book as it offers little more than cramming tips.119 MacAlister calls C. Pendlebury’s book on arithmetic too verbose.120 A proposal for spherical trigonometry by N. M. McClelland is charged with bad style, a mere collection of problems set in examinations, with meager notes, and at that not even ready for press.121

In some cases, a book is seen to be too costly to produce. About a book “On Light” aimed at working men and amateurs, MacAlister recommends cutting costs by skimping on engravings, since a book for this market can be successfully sold, in his opinion, for at maximum a cost of four shillings.122

MacAlister’s reports also contain advice for how the form and style of material should be presented. In many cases he discourages the “lecture-style” in which manuscripts are initially presented, noting that publishing mathematics in the lecture style is passé.123 He advocates for a

118 “Elliptic Functions” by W. A. Greenhill [A. G. Greenhill], H. B. Halstead’s “Elements of Geometry”, and a book on the Calculus of Variations were recommended for publication on this basis (MP 55939, p. 54; MP 55936, Readers Reports 1883-1884, p. 164; MP 55937, Readers Reports, 1883-1885, p. 73). Note that although the manuscript for “Elliptic Functions” is noted in the papers as being written by W. A. Greenhill, the author was probably A. G. Greenhill, who published several mathematical titles with Macmillan. 119 MP 55939, p. 16. 120 MP 55939, p. 17. 121 MP 55939, p. 17. 122 MP 55935, p. 63. 123 MP 55935, p. 32.

107 regrouping of the material according to natural divisions of the subject, under numbered sections and chapter headings.124 He suggests that large and small type be used, with propositions and proofs printed larger than the body text, and boldface used to create emphatic words.125 He also insists upon continuously numbered examples. Particularly with textbooks, the inclusion of problems and solutions is deemed important.126 Alternatively references to solutions published elsewhere, or references to standard texts, is encouraged.127 With respect to diagrams, he recommends that lines be made bold and varied with thick, thin, dotted or plain lines with arrowheads as appropriate, and that solid figures be drawn in perspective. In general, his guidance is to make mathematical illustrations “artistic rather than merely geometrical”.128

The organization, presentation, and usability of mathematical texts seem to take priority for MacAlister over the incorporation of new mathematical methods in the content. On one occasion, MacAlister notes that presenting the differential and integral calculus side by side is a “fresh idea”, and observes that the author A. G. Greenhill introduces “from the beginning [of the book] the newer developments” in the subject, revealing from the start “the bigger vistas of what great things [the student] is entering upon”.129 This observation is made with the tone of moderate praise. In fact MacAlister estimates this book as unlikely to have any great success. Because so many books are published on calculus, he explains, the only room to distinguish a new book from the others is in refining the style of presentation, rather than in the way in which the subject itself is treated.130

MacAlister discourages what he calls the “Euclidizing” method within elementary algebra. He also criticizes certain math textbooks as “quite unsuited to English needs”, without explaining

124 MP 55937, p. 46. 125 MP 55940, p. 16. 126 MP 55935, p. 96. 127 MP 55935, p. 32, 63. 128 MP 55940, p. 16; MP 55937, p. 46. 129 MP 55937, p. 53. 130 MP 55937, p. 53.

108 further what, in his view, the English needs are.131 More than once a textbook is deemed unsuitable because it is too foreign or too French.132 MacAlister was aware of contemporary controversies about how geometry ought to be taught, and saw in this a renewed interest in the subject, and possibly a reason for new books in this area. About one manuscript on geometry he wrote: “Geometrical teaching is in so transitional a state just now that any attempt to reconcile old and new will at least gain some hearing”.133

MacAlister never elaborated on what he meant when he said that a mathematics textbook was “too French”. One wonders whether being “too French” was MacAlister’s shorthand for the analytical approach that was more commonly used in continental mathematics during the nineteenth century. It has been observed that methods and theories of mathematical analysis being developed in continental Europe were not generally integrated into the mathematical culture of England, or at least not into the Cambridge culture of mathematics, which largely taught mixed mathematics (“water, gas and electricity” subjects), using synthetic methods (Warwick 2003: 434). The influence of the Analytical Society, the publication of its Memoirs in 1813, and mathematical journals like the Cambridge Mathematical Journal encouraged some cross-fertilization between Continental and British mathematical cultures. Nevertheless, when Bertrand Russell reflected on his mathematical training at Cambridge in the 1890s, he noted that while studying mathematics there he had never been introduced to the work of Karl Weierstrass, Richard Dedekind, Georg Cantor, Gottlob Frege or Giuseppe Peano (Russell 1959: 39). These mathematicians, as well as their French counterparts, may have been emblematic of the kind of mathematics MacAlister deemed unsuitable for what he described as “English needs”. Unfortunately, this attitude kept English students from being exposed to important new ideas in nineteenth century mathematics. Cambridge experienced a precipitous decline in the number of mathematics students towards the end of the nineteenth century (Griffin and Lewis 1990: 57). A declining interest in mathematical study at Cambridge has been linked to a culture there that

131 MP 55937, p. 26. 132 MP 55936, p. 81; MP 55932, Readers Reports, 1867-1882, p. 25. 133 MP 55935, p. 26. About another geometry manuscript, he mentions: “Euclid and elementary geometry are being much shaken up just now, but there are several much more promising books in the field than this” (MP 55938, Readers Reports 1884-1885, p. 22).

109 generally did not include new results in mathematical research in the curriculum (Griffin and Lewis 1990: 57).

In the realm of science, MacAlister’s readers’ reports display how a learned man of this era was still assumed to have adequate knowledge to make contributions to – or judgments about – many areas of science. In the 1880s and 90s, MacAlister reviewed manuscripts on subjects including chemistry, trigonometry, micro-botany, mushrooms, light and heat, conic sections, orthographic projection, the diseases of field crops and heredity. Only on a few occasions did he seek the opinion of someone more expert than himself to judge the quality of the work.

Over the years surveyed here, MacAlister held significant sway over Macmillan’s scientific and mathematical publishing program, although his power as a publisher’s reader was not absolute. Macmillan did not always solicit MacAlister’s opinion, nor did Macmillan’s decision about what to publish always align with MacAlister’s recommendation (although usually, it did). During his time working for MacMillan, manuscripts by what Macmillan may have considered as first-rate men still circumvented the review process. A manuscript on the “Scientific Evidences of Organic Evolution”, written by Darwin’s protégé George Romanes, was immediately accepted without review in 1882.134 When a manuscript arrived from John Fiske of Harvard University – “Excursions of an Evolutionist” communicated by the literary agent A. P. Watt in 1883 – it was accepted promptly without MacAlister having reviewed it.135

Although it is not known what remuneration MacAlister received for working as a reader with Macmillan, MacAlister did not undertake this work for notoriety, as his role as a publisher’s reader was not public. Since he was asked to read many manuscripts of which he disapproved or was critical, one assumes he did not undertake the role solely for its pleasures. As the eldest son in a large family with middling means, MacAlister provided for his own education, and into adulthood he continued supporting his family, providing living and educational expenses for his younger brothers and sisters. Perhaps financial reward was his motivation to do the work if Macmillan was offering him reasonable compensation for it.

134 MP 56016, p. 83. 135 MP 56017, p. 3.

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8. Conclusion

During the second half of the nineteenth century, Macmillan and Co. was actively reshaping the public image of science, particularly during the height of its powers as a popular and educational publisher from the 1880s onwards. Within Macmillan’s organization and its attendant channels of procurement, production and distribution that encompassed its publishing empire, only a few people at the top played a role in deciding what scientific and mathematical content would be supported by the power that a press the likes of Macmillan could command. This model of book publishing put the responsibility for decision-making in the hands of just a few people.

Some of Macmillan’s mathematical textbooks were astonishingly successful, with the most widely produced ones rivaling Macmillan’s best-selling fiction titles in their circulation.136 These books made their way all around the world, to Canada, Australia, India, the United States and to other places with English-speaking populations. Macmillan’s textbooks presented an English image of mathematics and promoted the authors of these texts, men associated with English institutions (mainly Cambridge) all over the world.

Many of Todhunter’s mathematics textbooks, and those of J. Hamblin Smith, ended up in Canada, where they were prescribed at the University of Toronto and at the Hamilton, Ontario high school where Canada’s first notable research mathematician, John Charles Fields, was taught. After he left Canada for doctoral and post-doctoral study abroad, Fields always testified to the quality of education he had received in Canada, although he did note that his grounding in Calculus had been “irremediably and fundamentally [false]” (Riehm and Hoffman 2011: 22). This fallacious grounding was likely connected to the English mathematical textbooks that were so widely used, and the fact that these originated from a culture that had for nationalistic and

136 Some 525,000 copies of Todhunter’s edition of The Elements of Euclid were produced between 1862 and 1903. In comparison, 577,250 copies of the firm's top-selling fiction title (Charles Kingsley’s Westward Ho!) were printed during the same period. Even at a time when classic math texts were being eclipsed by modern demonstrations, Euclid’s Elements rivaled a literary work for the distinction of best-selling title for its publisher. This evidence was retrieved from the first Editions Book, Macmillan Papers, British Library, London, UK.

111 pedagogical reasons, failed to update the representation of mathematics in their educational curriculum.137

What this example might confirm for us is that within each genre of the print medium that served to express mathematical knowledge, there were separate cultures each with their own acceptable standards. Mathematical journals were run by editors who were themselves developers of new mathematics, and who maintained their own standards depending on what kinds of contributors they could attract (also, frequently, the benefactor on which they depended for the maintenance of their periodical was also an influential factor in a journal’s operations). In his dealings with one of the most visionary mathematicians of the nineteenth century, Gösta Mittag-Leffler recognized the importance of Cantor’s work. Mittag-Leffler, however, was sensitive about what would appear on the public record in his journal (as were Boole and Cayley, in their reviews for the Cambridge and Dublin Mathematical Journal). In the case of Cantor’s work on ordered sets, Mittag-Leffler may have declined to publish Cantor’s paper because he expected it to be controversial with Acta Mathematica’s readership, perhaps even undermining his credibility as editor.138

As Sloan Despeaux has pointed out, the situation at general science journals was slightly different. The culture of mathematics developed there was often more aligned with mathematics in the service of other sciences. Articles that explored the higher echelons of mathematical theory were not always welcome. Editors of general science journals had to consider their readers, many of whom did not have the skills or the inclination to read articles of mathematics. Mathematics that was too specialized could be regarded negatively, and further, the referees who were assigned to give advice were not always the best at identifying what new mathematics would later become important.

At book publishers, if we take Macmillan as our only example, the situation was once again, unique. Macmillan’s publishing program included mathematics, and developed materials for

137 About the English image of mathematics, see Joan Richards’s book Mathematical Visions (Richards 1988a), as explained in footnote 80, page 89 of this work. 138 Cantor’s mathematics was controversial. Several of his contemporaries considered Cantor’s work illegitimate (Dauben 1977: 89-91).

112 broad educational purposes on mathematical topics. Mathematical textbooks, especially on the scale in which Macmillan produced them, had greater reach than most other printed sources in mathematics, and formed first impressions upon many students. However, the values that influenced the image of mathematics presented here were closely tied to national traditions and cultural values. As such, material that proceeded to publication frequently reinforced established ideas. In the case of Macmillan’s mathematical books and the culture of English mathematics that they reflected, some of these established ideas had already been proven incorrect, as both Russell and Fields later noted.

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Chapter 4 Mathematics for the World: The Business of Publishing Mathematics at Macmillan and Company

1. Introduction

Between the 1840s and 1890s, Macmillan grew from a small business into a mature and powerful publisher of both mathematical works and educational works in mathematics. Because comprehensive records of Macmillan’s publishing activities remain, it is possible to draw both a qualitative and a quantitative picture of its activities during this period. The previous chapter provides qualitative descriptions of Macmillan’s relationship to mathematical publishing, including descriptions of the community from which Macmillan drew their authors, a look at some of Macmillan’s received manuscripts about mathematics that were either accepted or declined, and the reader’s reports that were relied upon to help manage decision-making about these mathematical publications. The present chapter takes a quantitative measure of Macmillan’s mathematical publishing program, examining how numerous their mathematical books may have been, and how profitable they were for both their publisher and author.

Macmillan is just one example of a publishing company that printed and sold mathematical books. However, from this example we can learn about how mathematical authors interacted with the book publishing industry. For instance, we may wonder if mathematical authors profited from the successful sale of their books. Did authors who wrote school books for Macmillan also use the publishing house to publish their more academic titles, or vice versa? If so, what was the rationale for the author and publisher behind the publication of each type of work? Through printing, distributing and making public the work of its authors, did Macmillan’s publishing activities act to extend the influence of these men? Did Macmillan develop a new business model for publishing during this period, becoming what we might describe today as an academic publisher? This chapter casts light on quantitative and commercial aspects of publishing mathematics in book form, as it was applied at Macmillan and Company in the late nineteenth century.

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The evidence presented in this chapter challenges several assumptions about scientific publishing. It has been suggested that in general, scientific publishing was not highly lucrative for either authors or publishers.139 This chapter shows this was not in all cases true. Some of Macmillan’s titles in science and in science education (specifically, mathematics education) were their most successful, and financially lucrative, books. Science as a subject was commercially favourable in late nineteenth century England, and this has already been signaled (if not recognized) by the observation that most science publishing carried out at this time was done by commercial, not academic, publishers.140

It has also been suggested that scientific authors were motivated by the desire to advance knowledge rather than by more worldly motives, such as vanity or profit.141 This chapter shows that altruism was not the only motive behind publication. Some of Macmillan’s educational books in mathematics earned as much for their authors as Macmillan’s best-selling fiction titles did for their literary ones. From records of Macmillan’s contracts with authors we can gage what income authors and publishers earned from these books.

Further, it will be shown that the commercialization of mathematics in book form had an effect on the growth of mathematical knowledge. The wide dissemination of certain versions of the subject through the mass-production of educational textbooks may have influenced cultural values placed upon mathematical knowledge.142 Particularly as Macmillan was ambitious not

139 David McKitterick’s book about Cambridge University Press includes extensive sections about Macmillan. One of McKitterick’s suggestions about Macmillan is that their fiction writers were more lucrative earners for the firm than their authors who wrote school and university texts. He writes, “As general publishers, [Macmillan’s publication] list included fiction, travel and poetry as well as school and university studies. …Lewis Carroll, Charles Kingsley, Thomas Hughes, Charlotte Mary Yonge and Mrs. Craik (her husband was a partner in the firm) were all major authors – and financially usually more important than their university counterparts” (McKitterick 2004b: 58). 140 Both David McKitterick and Jonathan Topham have found that the bulk of scientific publications in the nineteenth century were not emanating from the university presses but rather from London publishers such as Longmans, Macmillan or Taylor and Francis (McKitterick 2004a, 2004b; Topham 2013). 141 Bertrum MacDonald and Jennifer Connor write in History of the Book in Canada, “Few authors of scientific, technical and medical texts were motivated by the possibility of financial benefit for their efforts. Most were primarily interested in informing readers or producing texts that could be used for educational purposes” (MacDonald and Connor 2007: 184). 142 In her essay about printed mathematics in early modern Europe, Robin Rider reflects, “The company of mathematical adepts in Europe was not so extensive as to consume large press runs; and markets, especially for

115 only to serve the British book market, but to serve a world wide English-speaking market, we might ask how Macmillan’s international trade may have influenced the progress of mathematics through the influence that Macmillan’s mathematical books extended upon the contexts in which these books were read and used by students, teachers and institutions of education inside and outside Britain.

2. Nineteenth century British publishing and Macmillan

Simon Eliot has compiled several ‘bibliometric’ studies that quantitatively describe publishing trends within the nineteenth century British book trade (Eliot 1994, 1995). Eliot has also published one study that looks quantitatively at Macmillan and Co. in particular (Eliot 2002). Eliot’s approach to the history of the book trade is unique. One of the major challenges of doing book history in the nineteenth century is accounting for the sheer volume of material that was produced. In his article about how to undertake a book historical approach to the study of nineteenth century science, Jonathan Topham identified the abundance of material as one of the major challenges that has discouraged scholars from attempting book history in the modern period (Topham 2000: 562). Since its inception as a discipline, book historical studies have focused more frequently on the early modern period, neglecting analysis of books and printed materials as mass-produced objects. Simon Eliot’s bibliometric studies are highly useful to modern book historians, as they provide a ground upon which one can build a contextualized picture of British mathematical publishing, for example, using Eliot’s study of nineteenth century British publishing as a baseline.

Eliot has provided a quantitative overview to nineteenth century British publishing in his work, Some Patterns and Trends in British Publishing, 1800-1919.143 In 1840 approximately 3,000 new titles were produced in that year by the British publishing industry. By 1903 almost 12,000

more elementary works, were often decidedly local and limited” (Rider 1993:108). By contrast, late nineteenth century markets in mathematics, especially for elementary works, were global and open. Steam-powered printing altered the economics of publishing. Mathematical publishing was affected by these changes. 143 Eliot gleaned his quantitative data primarily from lists of books in The Publishers’ Circular, Bent’s Monthly Literary Advertiser, the British Museum’s Copyright Receipt Books and Annual Reports, The British Library General Catalogue CD-ROM records from 1800-1919, and the Stationer’s Company Registry Books.

116 new titles or editions were produced per year. The nineteenth century witnessed immense growth: Eliot’s study shows a four-fold increase in the amount of new book titles produced per year between 1840 and 1903. The increase in printed matter overall however – not just book production – reveals even more about how dominant print media had become by the turn of the century. In 1840 England consumed about 40,000 tons of paper. By 1903 it was using 800,000 tons, a twenty-fold increase in paper consumption in sixty years. The massive increase in the amount of paper used in one year is a result of the increased production of all manner of printed culture, including catalogues, newspapers, magazines, pamphlets, forms, tickets, labels, posters and books (Eliot 1994: 7-10).

Unsurprisingly, Eliot’s study of the book marketplace finds the overall production of books grew substantially in the nineteenth century, both in the number of titles produced and in the quantities in which these titles were printed. However, rather than consistent year over year growth, the trend towards overall growth was punctuated by intermittent inflations or depressions in the market coinciding with significant political-social events and economic crises (Barnes 1985). Rather than seeing the industrial book revolution as a continuous historical progression occupying the entire nineteenth century, Eliot conceptualizes it as a two-stage process: an initial “distribution revolution” between 1830-55, and then a “mass-production revolution” during the 1875-1914 period (Eliot 1994: 107).

In finding that book production experienced a marked surge in the late 1840s and early 1850s, Eliot hypothesizes that the events of the Great Exhibition in 1851, the death of Wellington (the popular former Tory Prime Minister and Napoleonic war veteran) in 1852, and the beginning of the Crimean War in 1854, helped to spur this increase (Eliot 1994: 8). At the same time the Oxford movement caused a “pamphlet war on religion on an almost unprecedented scale” (Eliot 1994: 9). Eliot finds these events together boosted the number of new titles produced in the early 1850s in England. Gradual reduction on the ‘taxes on knowledge’ in the 1850s (i.e. paper duty), similarly had an amplifying effect on print production. Eliot notes that the coming of the railway, steam-driven presses, case bindings, and the Foudrinier paper-making machine were all aspects that lead to the spike in production during the distribution revolution in mind-century (Eliot 1994: 107).

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Statistics from the same sources show book production decreasing periodically, particularly during the 1826 depression, the Crimean War, and during the First World War period from 1915- 1918. Eliot also found that the 1855-1875 period witnessed something of a plateau in the growth of new book production (measured in number of new titles per year).

In the late 1840s and 1850s, Eliot suggests that there was a major change in the price structure of the book market. ‘Cheap books’, which Eliot defines as having a price of 3s. 6d. or less, rose to dominance. Eliot notes that frequently a book’s low price correlated with longer and more frequent print runs of these so-called cheap books (Eliot 1994: 24).

1875-1914 was another period in which the English book trade once again evolved a distinctly new organization and shape. Between 1875 and 1900 the number of new book titles produced annually doubled, while the amount of paper used in printing increased seven-fold (Eliot 1994: 13). The whole market for books and printed culture shifted, with print-runs of book titles in the 1880s and 90s expanding drastically. The vast expansion in the amount of copies that could be made of books at this time signaled a mass-production revolution during the last decades of the nineteenth century as well as the years prior to the First World War.

In the 1880s and 1890s, structural changes affected the printing and publishing industry overall, including the development of professional writers, syndicated content, mass circulation of daily newspapers, emergence of literary agents, the development of public libraries, the expansion of printing capacity with the use of large web-fed rotary presses, and the founding of several writers and publishers associations. These developments taken together, signal the maturation, in some sense, of the publishing industry as a self-conscious and established industry. Eliot provides an apt description of English print culture of the last quarter of the century, describing these circumstances as “The confluence of almost universal literacy with cheap and large print runs serving an apparently endlessly expanding international English-reading market, and, most important of all, the absence of any other form of universally available popular entertainment, made the period 1880-1910 a fleeting golden age…at least it must have seemed to those who benefitted from it most” (Eliot 1994: 14).

Quantitative studies looking at print-runs of books published in the nineteenth century have not been extensive, as Eliot notes. Eliot’s article ends by suggesting next steps for understanding the nineteenth century book trade as consisting of further study of individual publishers’ and

118 printers’ records. From these, Eliot suggests mapping data about the number of new titles, print runs, price and cost structure, and comparing this individual publisher data to the global picture he has described (Eliot 1994: 107-8).

While the records for undertaking such comparisons don’t exist for every nineteenth century publisher, Macmillan and Company’s publishing records allow for this sort of quantitative analysis. Eliot himself even undertook a bibliometric analysis of Macmillan’s publishing history, mapping and comparing the data from four sample years during Macmillan’s nineteenth century operations. For titles published in each sample year, Eliot was able to collect information about the print-runs of 75-89% of all the titles published, giving some reasonably reliable benchmarks for how many books Macmillan was producing during various decades, and in particular, about which books were Macmillan’s most successful titles (Eliot 2002: 23).

Unsurprisingly, Eliot’s figures show remarkable growth in the company’s production between the first sample year (1856) and the last (1886). In 1856 Macmillan produced 41 new titles whereas in 1886, they produced 171. However, there was a twelve-fold increase in the total output of books printed, with 29,450 books printed in 1856, and 372,350 copies of Macmillan’s new titles produced in 1886. This suggests, as Eliot observes, that Macmillan’s initial print run of new titles had increased substantially in thirty years.144 This correlates with Eliot’s overall observation that after 1875 the “mass-production revolution” had affected the British book trade. Macmillan, as one of London’s largest publishers at the time, also transitioned into the publishing model of mass-production: for their most successful titles, first editions and reprintings were ordered up in amounts of ten or twenty thousand copies at a time.

Eliot observes that the 1860-1870 period was an important decade for Macmillan, in which they founded their future success as publishers. Even while Macmillan printed more books overall in the 1880s and 90s, several books printed in the 1860s went on to sell at high volumes for decades to come, enduring through longer print-runs and having greater lifetime success than their books published in later decades. Most crucial to this study, Eliot observes that overwhelmingly Macmillan’s greatest successes from the 1866 sample year are educational and scientific titles,

144 This number reflects total copies printed of all their new titles in the sample year, excluding reprintings from Macmillan’s backlisted books that may have also occurred in that year.

119 suggesting that these genres were elemental to the company’s overall business success (Eliot 2002: 24).

Macmillan’s unqualified publishing successes in the year 1866 included Rev. T. Dalton’s Arithmetical Examples (total 55,000 copies printed), T. H. Huxley’s Lessons in Elementary Physiology (total 199,845 copies printed), H. E. Roscoe’s Lessons in Elementary Chemistry (total 430,000 printed), Barnard Smith’s A Shilling Book of Arithmetic (total 430,000 printed), Answers to Examples in Barnard Smith’s Shilling Book of Arithmetic (total 104,500 printed) and Isaac Todhunter’s Trigonometry for Beginners (total 108,500 printed). These were the most successful titles from just one year in Macmillan’s highly successful 1860s period.

Unfortunately, Eliot’s study of the general trade does not help us place Macmillan’s scientific publishing program in a well-formed context of scientific, educational or mathematical publishing in the overall British book market in the nineteenth century. In general, Eliot concludes that the nineteenth century saw the replacement of books on religious topics with books on secular topics (Eliot 1994: 58). However, his chapter providing statistics about the growth or diminishment of particular genres within nineteenth century publishing is unfortunately the weakest within Eliot’s overall study, a fact that reflects the limitations of the available source material, which he himself admits (Eliot 1994: 106).

Eliot finds that titles classified as “education” fluctuate from 12% of the market in 1814-46, to 11% in 1870-9 and 1880-9, 12% in 1890-9 and then dropping to 8% in 1900-9 and to 6% in 1910-19 (Eliot 1994: 43-52). These figures are likely inaccurate, due to misclassification by genre in The Publishers’ Circular and the other primary materials Eliot draws upon. While Eliot’s figures do not show increasing production of books for the educational sector, important developments in education occurred during this time. The passing of the Elementary Education Act of 1870 began a series of reforms that lead to the institution of a system of education for all young children in Britain. Educational books became ever more important in the 1870s and 1880s to the publishing programs of both Macmillan and Company and Cambridge University Press. Educational titles grew to occupy a greater share of overall book production during these decades at these two major publishers.

It is disappointing that Eliot’s study of publishing by genre is not more descriptive of how science publishing may have grown during the nineteenth century. Eliot finds that titles classified

120 together as “arts, science, mathematics and illustrated books”, fluctuated from 9% of the marketplace in 1814-46, to 8% in 1870-9 and 6% in 1880-9, dropping to 3% in 1890-9 before rising to 8% in 1900-9 and to 15% in 1910-19 (Eliot 1994: 43-52). Given Eliot’s genre figures, it is difficult to get a decisive picture of whether there may have been growth in the market share devoted to science publishing within the British book industry as a whole in the latter half of the nineteenth century.

What Eliot concludes with regards to Macmillan, is that the company published more books in the pure science genre than the average British publisher, and Macmillan published more successfully in the science and mathematical genre than most British publishers. The book trade journal The Publishers’ Circular lists 8% of trade books as having “pure science” topics between 1870-99. By comparison Macmillan’s catalogue contained between 14-17% “pure science” titles during a roughly similar period, 1866-1886 (Eliot 2002: 31). While knowledge about science publishing as a whole in the nineteenth century is far from complete, Macmillan was unique in Britain during the period for their production of scientific books.

3. Macmillan’s publication record in mathematics and science

An employee of Macmillan, James Foster, compiled A Bibliographical Catalogue of Macmillan and Co.’s Publications from 1843 to 1889, a book issued by the company in 1891 (Foster 1891). From this source, it has been possible to extract statistics about Macmillan’s publishing activity by genre, breaking out what ratio of their published books were written about topics in mathematics and science (see Table 2).

It is also possible to produce approximate sales figures for Macmillan’s published titles in these genres, as entries in Foster’s bibliographical catalogue can be cross-referenced with listings in Macmillan’s first editions book. Macmillan’s editions book was the place where the company kept a record of how much stock in a particular title was ordered. In it, the amount of initially printed copies and successive reprintings for all published book titles were recorded. The first editions book contains information about books printed and reprinted throughout much of the nineteenth century and into the early twentieth century. In the twentieth century subsequent editions books were kept as well as a supplementary card catalogue recording twentieth century printings and reprintings that extend beyond the first editions book. Statistics in the present work were prepared using Foster’s bibliographic catalogue, and Macmillan’s first editions book only.

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In order to identify Macmillan’s books that were “mathematical” in genre, criteria as introduced by Peter and Ruth Wallis in their Biobibliography have been adopted here (Wallis and Wallis 1986). In their seventeenth and eighteenth century mathematical bibliography, the Wallis’ include publications on topics broadly defined as mathematical. Besides work on arithmetic, geometry, mechanics, algebra, theory of equations, and other purely mathematical topics, the Wallis’ include books on topics in applied mathematics as well, including astronomy, navigation, surveying, building, dialling and clockmaking, motive power, electricity, accounting and insurance (Wallis and Wallis 1986: v). In devising which books within Macmillan’s publishing program were considered mathematical, a similarly broad definition of “mathematical” has been adopted in the present study. Books have been determined mathematical by applying the Wallis’ criteria for what constitutes pure and applied mathematics as best as possible. The genre category of a Macmillan book has been deduced largely from knowledge of its title and author.145

Year Range Mathematics General Total Math as % Science as % Math and Science Publications of Total of Total Science as % of Total 1843-49 13 2 74 18% 3% 20% 1850-59 41 15 340 12% 4% 16% 1860-69 90 51 967 9% 5% 15% 1870-79 103 182 1221 8% 15% 23% 1880-89 134 164 1540 9% 11% 19%

Table 1 Proportion of Macmillan’s publications on topics in mathematics and science, 1843-1889 (Source: Foster 1891)

145 Physics, including optics, mechanics and treatises on heat, have been included in works deemed mathematical. Books about economics and logic were excluded from the list of mathematical or scientific publications, except where specifically suggestive of symbolic logic, in which case these titles (i.e., works by John Venn) were included as mathematical. Certain treatises on sound and music, where it is suggested the subject is treated scientifically, have been included in the works grouped as mathematical.

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Beyond mathematics, Macmillan published numerous books on scientific subjects, including on various topics in chemistry, botany, zoology, ornithology, hygiene, entomology, natural history, agriculture, medicine (anatomy, surgery, disease, pathology, epidemiology, pharmacology, embryology, psychiatry, neurology), heredity, psychology, anthropology, evolution, religion and science, meteorology, metallurgy and mining, geology, paleontology, agriculture and forestry.

From Table 1 it can be seen that approximately half of all the titles Macmillan published in pure science were mathematical, broadly defined. Some of the mathematical topics on which they published books included history of mathematics, mechanical philosophy, natural philosophy, mechanics, symbolic logic, trigonometry, algebra, calculus, differential equations, determinants, geometry, arithmetic, dynamics, statics, probability, astronomy, engineering and applied technological subjects such as hydrodynamics, steam, magnetism, electricity, heat, sound, telegraphy, surveying, optics, weights and measures, and approximating errors. They also published a book about how to approximate pi and at least two treatises on quaternions.

Including their books in mathematics with their books in other areas of science, Macmillan came close to maintaining a ratio of 20% of all titles in their publishing program being devoted to subjects in the science genre, and 10% of all titles published being mathematical specifically. Macmillan devoted a significant portion of its publishing program to these subjects, given that the Publisher’s Circular, the best source of book titles and genres within the general nineteenth century publishing industry, suggests that books on mathematical or pure science topics occupied 8% or less of all books in the marketplace (Eliot 1994: 43-51).

4. Macmillan’s mathematical books

Average initial print-runs at Macmillan varied commonly between 250 and 2,000 copies. In his bibliometric analysis, Eliot considered all titles with accumulated print-runs of more than 10,000 copies as unambiguous successes for the company (Eliot 2002: 20). From Eliot’s study we know that Macmillan published some of its most successful, longest-selling titles in the 1860s, and that represented among these are a significant number of mathematical textbooks. What about the other decades of Macmillan’s nineteenth century operations? What can be said of the success of their mathematical titles during those years?

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Between 1854 and 1889, Macmillan published eighty mathematical books that were printed in quantities over 10,000, or, eighty mathematical books that we can consider unambiguously successful for the company. Twenty-six of these titles, or roughly 33% of their unambiguously successful mathematical books, were extremely successful, with more than 100,000 copies printed over the lifetime in which Macmillan kept the book in print. A list of Macmillan’s mathematical books with lifetime print runs of over 100,000 copies is given as a list in Table 2.

Total copies Year of first Last year Author Title Price* printed printing printed**

693,000 1863 1917 I. Todhunter Algebra for Beginners 2s. 6d.

608,000 1885 1937 H.S. Hall and Elementary Algebra 3s. 6d. S.R. Knight

597,500 1854 1920 B. Smith School Arithmetic 4s. 6d.

525,000 1862 1903 I. Todhunter Euclid 3s. 6d.

430,000 1865 1906 B. Smith Shilling Book of Arithmetic, Part I 1s.

362,000 1872 1925 B. Stewart Science Primers: Physics 1s.

295,000 1889 1931 H.S. Hall and A Textbook of Euclid’s Elements, 3s. S.R. Knight Parts I & II, Books I-IV

270,000 1887 1930 H.S. Hall and A Textbook of Euclid’s Elements, Part 2s. S.R. Knight I, Book I & II

253,000 1888 1932 H.S. Hall and A Textbook of Euclid’s Elements, 4s. 6d. S.R. Knight Book I-IV & XI

215,000 1869 1931 I. Todhunter Mensuration for Beginners with 2s. 6d. Numerous Examples

211,000 1879 1929 J. Thornton First Lessons in Bookkeeping 2d. 6d.

210,500 1889 1922 H.S. Hall and A Textbook of Euclid’s Elements for 1s. F.H. Stevens the Use of Schools, Book I

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206,500 1886 1929 J.B. Lock Arithmetic for Schools 4s. 6d.

176,100 1887 1938 H.S. Hall and Higher Algebra 7s. 6d. S.R. Knight

173,240 1881 1929 S.P. Elementary Lessons in Electricity and 4s. 6d. Thompson Magnetism

167,000 1874 1920 J.N. Lockyer Science Primers: Astronomy 1s.

153,500 1866 1928 B. Smith Shilling Book of Arithmetic with 1s. 6d. Answers

138,500 1858 1911 I. Todhunter Algebra for Colleges and Schools 7s. 6d.

138,380 1887 1936 J.T. Four Figure Mathematical Tables 2s. 6d. Bottomley

133,500 1870 1934 W.S. Jevons Elementary Lessons on Logic 3s. 6d.

121,000 1886 1932 C. Smith Elementary Algebra 4s. 6d.

108,500 1866 1921 I. Todhunter Trigonometry for Beginners 2s. 6d.

104,500 1866 1901 B. Smith Key to Shilling Book of Arithmetic 6d.

104,000 1882 1937 J.B. Lock Treatise on Elementary Trigonometry 4s. 6d.

102,500 1870 1911 B. Stewart Lessons in Elementary Physics 4s. 6d.

102,000 1872 1910 J. Brook- Arithmetic in Theory and Practice 3s. 6d. Smith

Table 2 Macmillan’s mathematical books with print runs greater than 100,000, 1843- 1889 (Source: Macmillan’s First Editions Book, British Library). *Note: Price refers to either the most stable price or the price on first printing. **Note: Some titles were reprinted beyond the last year given here. Calculations of lifetime print-run given in this chart were calculated from Macmillan’s first editions book only.

Unsurprisingly, most of Macmillan’s mathematical books with lifetime print runs greater than 100,000 copies were schoolbooks of one sort or another. Many of them, about half or more, were also cheap books: according to Eliot’s definition for cheap books, they sold for 3s. 6d. or less.

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Also notable is the list of authors in Table 2. Several of these authors of Macmillan’s most successful mathematical and educational books were involved with the Macmillan’s as more than just textbook authors. Balfour Stewart, Isaac Todhunter, William Stanley Jevons, J. Norman Lockyer and Silvanus P. Thompson all served as readers for the publishing house, advising on manuscripts and publication schemes during the years 1867-1896 (see Appendix B). As such, Macmillan turned to their most successful and lucrative textbook authors for advice with regards to plans for other publishing projects. After Lockyer published Elementary Lessons in Astronomy in 1868 and became the founding editor of Nature in 1869, Alexander Macmillan referred to Lockyer as his “consulting physician in regard to scientific books and schemes” (quoted in Graves 1910: 262). The authors listed in Table 2 were not only the authors of successful textbooks for Macmillan, they also held influence over the fashioning of Macmillan’s publishing program in math and science generally.

As the next section demonstrates, a long running and successfully selling book title could result in lucrative income streams for both author and publisher. The commercialization of mathematics, through book publication, joined mathematical authors with book publishers as they pursued goals that were mutually beneficial. Beyond being authors of commercially successful textbooks, Stewart, Todhunter, Jevons, Lockyer and Thompson also used Macmillan to publish several academic, polemical, and obscure titles with Macmillan. On an intellectual and financial level, and occasionally also through the engagement of personal friendship, these authors wielded influence within the publishing house, on Macmillan’s decisions about their own books that would be published, as well as regarding the publication projects of other authors.

Lockyer, as well as being the founding editor of Macmillan’s general science periodical Nature, also published several books with Macmillan including Why the Earth’s Chemistry Is As It Is (part of Macmillan’s Manchester Science Lectures Series, 1877), The Education of our Industrial Classes (1883), The Chemistry of the Sun (1887), Outlines of Physiography (1887), and The Cycle of Sun-Spots and Rainfall in Southern India (1879).

Macmillan published several titles on economics and logic written by Jevons, including The Coal Question (1865), The Substitution of Similars for the True Principles of Reasoning (1869), Elementary Lessons in Logic (1870), The Theory of Political Economy (1871), Political Economy (as part of Macmillan’s Science Primers Series, 1878), Studies in Deductive Logic

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(1880), The State in Relation to Labour (1882), Methods of Social Reform (1883), Investigations of Currency and Finance (1884), and The Letters and Journals of W. Stanley Jevons (1886).

Todhunter published more books with Macmillan than can be listed here: between 1843 and 1889, forty-one of Macmillan’s titles were attributed to him (see Table 4). While many of these were textbooks aimed at an educational market, Macmillan also published more specialized titles written by Todhunter, including History of the Calculus of Variations (1861), Researches in the Calculus of Variations (1871), A History of the Mathematical Theories of Attraction and the Figure of the Earth from the Time of Newton to that of Laplace (1873), The Conflict of Studies and other Essays on Subjects Connected with Education (1873), and An Elementary Treatise on Laplace's Functions, Lame’s Functions, and Bessel’s Functions (1875). None of these titles of Todhunter’s went beyond the first printing.

Macmillan also published (although, without putting their name on it) Todhunter’s Answer to Mr. Lund’s Attack (1858), in which Todhunter defended himself against public accusations by Thomas Lund that Todhunter had plagiarized other mathematics textbooks. Lund had publicly accused Todhunter of stealing material from James Wood’s popular book The Elements of Algebra (Barrow-Green 2001: 197). Evidently Macmillan sided with Todhunter in the dispute, as they published his polemic defending himself against Lund’s accusations. Although the Macmillans published several of Lund’s textbooks previously, they replaced these titles with works on similar subjects written by Todhunter.

For Silvanus Thompson, Macmillan published Light Visible and Invisible (1897) and Manufacture of Light (1906). Balfour Stewart published several physics textbooks with Macmillan, as well as The Unseen Universe, or Physical Speculations on a Future State (1875). Co-authored with P. G. Tait but initially published anonymously, The Unseen Universe was an attack on scientific naturalism, offering a defense of religion’s compatibility with modern science.

The relationship built between Macmillan and these five authors in particular were multifaceted. A lucrative partnership was forged between author and publisher with both benefitting financially from the sale of more than 100,000 copies of a textbook. These authors also benefitted in less tangible ways from being on favourable terms with Macmillan. In publishing their more academic, less commercially rewarding books, Macmillan furthered their ambitions

127 and intellectual work. In some cases, by printing and circulating their polemical writings, Macmillan gave authors like Todhuunter, Tait and Stewart a platform on which to publicly stake an intellectual claim or defend their metaphysical beliefs.

5. Contracts, royalties, and revenues from publishing

In the latter half of the nineteenth century, the publishing industry was in the midst of a significant maturation in its approach to writer-publisher contracts. The most common form of contract since the eighteenth century had been outright sale, where an author simply sold their work without conditions for a flat fee. This agreement more often than not was struck between an author and a bookseller. It wasn’t until the early nineteenth century that the act of publishing separated from the occupation of bookselling. From the ranks of the larger booksellers rose publishers who sold only their own publications and concentrated on the publishing function (Potter 1997:162). Macmillan, founded in the mid-nineteenth century, became one of the so- called ‘leviathan’ publishers whose books (along with Longmans, Rivington, Murray, etc.) dominated much of the nineteenth century book market.

A century of change affected the practices of authors and the author-publisher relationship, just as it formed a new landscape in which publishers conducted their business. By the late- eighteenth century, outright sale agreements evolved into more sophisticated types of contract, agreements that were more sensitive to, and protective of, authors’ rights. In the case of a limited sale arrangement, for example, a fee would be negotiated for a particular edition or limited number of copies of a work (Sprigge 1890: 33). If additional copies were to be printed, the author would receive further payments or renegotiate a further fee (Feather 2006: 133). Increasingly, such modifications to the traditional author-publisher arrangement meant that authors retained some control over the future uses of their work.

In the nineteenth century, the amount paid to authors for the outright sale of their work ranged widely. In her history of the firm Kegan Paul, Trench, Trübner & Co., Leslie Howsam noted that Henry S. King paid between £12 and £250 to acquire outright the copyright in various fiction titles (Howsam 1993: 59). Around 1900, Cambridge University Press was paying between £40 and £70 for works purchased through outright sale (McKitterick 2004b: 83). Outright sale was often the way in which publishers compensated editors, illustrators, engravers and other ancillary

128 artisans for their work for the publishing industry.146 In the 1890s, Cambridge University Press paid their editors a flat fee of £25 for the copyright of their work (McKitterick 2004b: 82).

Another common form of author-publisher arrangement was the commission agreement. With books published on commission, the author assumed the financial risk of publication. The publisher arranged to print, bind and distribute the book in exchange for a fee as well as possibly a percentage of sales. With books published on commission, the publisher’s name still appeared on the title page, making books published on commission indistinguishable from books in which the publisher assumed the financial risk (Howsam 1993: 58). Commission offered a way for publishers to offload some of the financial risks of publishing. Books published on commission were generally not expected to sell beyond the first printing, or at least the publisher did not expect sales to recoup the cost of production. Although other forms of contract increased in popularity in the latter nineteenth century, commission remained a staple during the period. In 1899, approximately 20% of Macmillan’s offers to publish were made on the commission basis (Eliot 2002: 44).

The dominant form of contract for much of the nineteenth century was the half-profits agreement, although outright sale and commission persisted in their use. The emergence of a profession of authors in the nineteenth century, along with the rise of publishing-focused businesses, meant that writers increasingly negotiated contracts such that they were able to earn a living from their work (Sprigge 1890). The half-profits agreement went a further step towards recognizing and rewarding authorship as creative work. Under the half-profits system, the publisher assumed all the costs incurred in producing a book, and then split profits with the author in either a 50%-50% share or in a two thirds to the author, one third to the publisher, ratio (Howsam 1993: 59). Although authors could make an income from this form of contract, authors were not guaranteed to receive an income if the book failed to “pay out” (recover its production costs). Unless an advance had been made, the publisher recouped manufacturing costs first, before the author earned any income.

146 For the illustrated edition of Charles Kingsley’s bestselling book Westward Ho! Macmillan paid illustrator Charles Edmund Brock £300 to do 100 drawings. He was paid £100 up front, and the remainder just over one month later, presumably when the work had been completed. Agreement between Macmillan and C. E. Brock, 9 November 1894, Terms Book I, Macmillan Archive, Palgrave-Macmillan head office, Basingstoke, UK, p. 123.

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In the latter part of the nineteenth century, authors’ unions were formed, and these organizations pointed out that the half-profits model left authors open to abuse by publishers. It was publishers’ account books, after all, that determined when a book turned a profit. In part due to lobbying from authors’ unions, the half-profits agreement began to fall out of favour by the end of the century. The royalty system, which had become popular in America, slowly began to replace the half-profits agreement in Britain. Although many variants of the royalty system existed, the basic principle of a royalty agreement was that the author received a fixed amount of income for every book sold, based on a percentage of the sale price of a title (Sprigge 1890: 56-7). Nevertheless, many publishers were slow to relinquish the established forms of contract, and outright sale, commission and half-profits remained common forms of author-publisher agreement for some time into the twentieth century (Howsam 1993: 59, McKitterick 2004b: 83).

When in 1890 the Society of Authors published a book about the standards and practices of publishing, outright sale, half-profits, commission and royalty were the four forms of author- publisher agreement covered in their survey (Sprigge 1890). Macmillan employed all four forms of contract during their nineteenth century operations. The majority of Macmillan’s nineteenth century authors either sold their work outright or entered into a half-profits agreement. However, Macmillan led the industry transition from half-profits to royalties by the end of the century. By 1899, the portion of Macmillan authors offered royalty agreements increased to over 44% (Eliot 2002: 47). The operation of Macmillan’s New York office influenced their transition towards adopting royalty agreements with their British authors as well as their American ones (Eliot 2002: 48).

Macmillan’s contracts with some of their nineteenth century mathematical authors are recorded in Macmillan’s business records.147 From these agreements, we can judge how much income authors earned from the eventual success, or lack of success, of a particular title. As a point of comparison, Table 3 introduces revenues successful fiction writers received from the publication

147 Some of Macmillan’s costing records survive from the 1850s, and from these is its possible to glean information about Macmillan’s agreements with its earliest mathematical authors. Details of author-publisher arrangements are also revealed through Macmillan’s author correspondence. Towards the end of the century, Macmillan began to keep a separate record of contracts in what is called the ‘Terms Book I’, although most of the agreements recorded in the first Terms Book date in the twentieth century. Terms Books for Macmillan are kept at the Macmillan Archive, Palgrave-Macmillan head office, Basingstoke, UK.

130 of popular Victorian novels. In the 1860s, established fiction writers could expect to receive approximately £1000 for the publication of a novel. In 1856, for example, Macmillan courted Charles Kingsley with a deal that would see Kingsley receive £1000 for the first edition of his next book.148

Author Title Revenue Year

Ainsworth, H John Law £300 1864

Ainsworth, H Old Court £150 1867

Collins, W Armadale £5,000 1866

Eliot, G Romola £7,000 1863

Eliot, G Felix Holt £5,000 1866

Meredith, G Rhoda Fleming £400 1865

Oliphant, M Perpetual Curate £1,500 1864

Oliphant, M Miss Marjoribanks £1,200 1866

Trollope, A Belton Estate £1,757 1866

Trollope, A Nina Balatka £450 1867

Trollope, A Last Chronicle of Barset £3,000 1867

Table 3 Revenues obtained from the publication of popular Victorian novels (Source: Haythornthwaite 1984: 101-102) Year signifies date of publication. Trollope’s figures are total earnings over time. Figures do not include additional income the author may have received through translations, serialization, or foreign rights.

148 Daniel Macmillan to Mrs. Kingsley, 6 March 1856, MP 55378 General Letter-Book 1855-56. Kingsley had proved himself a commercially successful author with the publication of Westward Ho! (1855), Macmillan’s first best-selling fiction title. In the same year Kingsley also published Glaucus; or the Wonders of the Shore, a book of popular natural history, which was also successful and entered into several reprintings (Foster 1891: 31).

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Macmillan’s most successful textbook authors earned as much as or more income from their publications as Britain’s most successful Victorian novelists did from theirs. This fact is proven by Macmillan’s author-publisher agreements with some of their most successful authors of mathematics textbooks, for example, H. S. Hall and S. R. Knight, whose publications appear in the list of Macmillan’s mathematical books with print runs greater than 100,000 (Table 2). We can compare the agreements of Macmillan’s highest earning mathematical authors with the projected income and author-publisher agreements of other authors from a range of Macmillan’s nineteenth century mathematical books.

By the time H. S. Hall and S. R. Knight published Algebra for Beginners in July of 1892, they were already successful textbook authors for Macmillan, having published Elementary Algebra for Schools in 1885, which almost immediately went into multiple editions and reprintings (See Table 2, also, Foster 1891: 474). An agreement dated May 15, 1893, saw Hall and Knight set to receive a royalty of 17% on the first 2000 copies of their textbook Algebra for Beginners sold in any year, with an additional 20% royalty received on every copy sold beyond that. Between 1892 and 1924, 468,700 copies were printed, with the book selling for two shillings and sixpence.149 Assuming this author-publisher agreement was not renegotiated at a later date, Hall and Knight earned approximately £11,000 in royalties from Algebra for Beginners during the years from 1892 to 1924. Their contract included further royalty payments for copies sold through Macmillan’s New York office and a 10% royalty on all copies sold of the Americanized edition.150

As for Hall and Knight’s Elementary Trigonometry, which was first published in December of 1893, they received an even better deal, although the book would not be reprinted quite as many times as Algebra for Beginners. For their Elementary Trigonometry, Hall and Knight negotiated a flat royalty of 20% on all copies sold, with a 10% royalty on copies sold through the New York office.151 Between 1893 and 1936, 295,460 copies of the book were printed and sold at four

149 See Macmillan’s First Editions Book, p. 594. Hall and Knight’s Algebra for Beginners is not listed in Table 2 because it was published just after the 1843-1889 period covered by this chart. 150 Agreement of 15 May 1893, Terms Book I, p. 13, Macmillan Archive, Palgrave-Macmillan, Basingstoke, UK. 151 Agreement of 18 January 1894, Terms Book I, p. 14, Macmillan Archive, Palgrave-Macmillan, Basingstoke, UK. Also see Macmillan’s First Editions Book, p. 669.

132 shillings and sixpence. Assuming all of these were sold at the 20% royalty rate, Hall and Knight stood to earn approximately £13,000 in royalties over the forty-three years the book was in print.

In 1887 H. S. Hall and F. H. Stevens published A Text Book of Euclid’s Elements for the Use of Schools, Part I, Containing Books I and II (Foster 1891: 514). Part II of the same book, which contained Euclid’s books three to six, followed the next year in 1888 (Foster 1891: 532). In 1888 Macmillan also published a combined volume of the two books together, containing Euclid’s books one through six, and one year later, a second edition appeared, with Euclid’s book eleven added as a separate volume that could be purchased (Foster 1891: 532, 554-555, 564). Eventually all the parts of Hall and Knight’s Text Book of Euclid’s Elements for the Use of Schools were combined to produce a “complete” edition which was issued on October 26, 1889.152

When it came to A Text Book of Euclid’s Elements for the Use of Schools, Hall and Stevens negotiated an even more lucrative agreement than Hall had received for either Algebra for Beginners or Elementary Trigonometry. Macmillan made a proposal to the authors that as of 1 July 1900, Macmillan would pay a royalty of 20% on the first 10,000 copies of this book sold in any one year, with a 25% royalty for any subsequent copies sold in the same year.153 As 253,000 copies of the complete edition were printed between the years 1889 to 1932, the royalty Hall and Steven’s stood to earn was almost £12,000 on the complete edition alone. Additional royalties from the stand-alone volume of Part I amounted to roughly £2300, and from the combined volume with Part I and II together the royalty would have been approximately £4000. Several other editions and combinations of the book that were also published, stood to earn Hall and Stevens additional revenue as well.

Even in the earliest days of Macmillan’s publishing business, authors of mathematical textbooks commanded significant incomes for their work if their book came with a proven track record of sales. In 1851 Macmillan printed 3000 copies of Thomas Lund’s A Short and Easy Course of

152 Macmillan’s First Editions Book, p. 243. 153 Agreement of 1 July 1900, Terms Book I, p. 274.

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Algebra, which was initially sold for two shillings and sixpence.154 Macmillan’s records project the book’s gross income at £366 if the edition sold out, with the costs incurred by Macmillan on printing, binding and advertising (and interest on the money borrowed to pay for it), being £80. Astonishingly, Lund was compensated £230 of the net profit of £286. Lund commanded approximately 80% of the book’s profit, as well as receiving twenty-five copies of the book bound in cloth, as part of Macmillan’s agreement over the publication. Compared to what Lund would earn, Macmillan stood to gain only £56 from the publication.155

Similarly, when Macmillan acquired the right to print Lund’s A Companion to Wood’s Algebra (12th edition, 1847), Lund was paid £950. With the gross profit from sale of the book expected to be £1284, and costs to print, bind and advertise projected at £154 17s., Macmillan’s share of the profit was comparatively little at £179 3s.156

Perhaps what can be taken from these examples is that Lund commanded a product that was virtually guaranteed to sell. As a consequence, Macmillan paid Lund handsomely for the right to print his books. No doubt Lund’s high rate of commission also motivated Macmillan to further develop Isaac Todhunter as a mathematical textbook author, and cease investing in Lund’s publications. This was the course of action they eventually took in developing their list of mathematical textbooks.157

Contrast the fees Mr. Lund commanded for his work with that of two other authors of mathematical books published during the same period. J. B. Phear stood to gain approximately

154 At some unknown later date, Macmillan raised the price to 3s. 6d. See (Foster 1891: 652) and Macmillan’s First Editions Book, p. 314. 155 Printed catalogue from 1 June 1864, MP 54791, Publications Catalogues with Manuscript Additions, Macmillan Archive, British Library, London UK. 156 Printed Catalogue from 1 June 1864, MP 54791, Publications Catalogues with Manuscript Additions, Macmillan Archive, British Library, London UK. 157 Early correspondence in the Macmillan Archive, British Library suggests that Todhunter was approached to produce a volume that would replace George Salmon’s A Treatise on Conic Sections. George Boole’s book A Treatise on Differential Equations (1859), was seen by Macmillan as replacing John Hymer’s book of the same subject. See Daniel Macmillan to Isaac Todhunter, 26 December 1854, MP 55376 General Letter Book 1854-55, and Daniel Macmillan to Dr. Hymers, 16 September 1855, MP55377 General Letter Book 1855.

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£40 on the printing of 1000 copies of his Elementary Hydrostatics in 1852.158 While Lund had sold his work to Macmillan for a cash fee (an outright sale agreement for a limited number of copies, or single edition, printed), Phear had struck a half-profits agreement with Macmillan. As previously described, in a half-profits agreement, the publisher usually recouped the costs of printing and production before it paid any income from book sales to the author.

For J. C. Snowball’s The Elements of Plane and Spherical Trigonometry (7th edition, 1852), 2000 copies were printed and sold at seven shillings and sixpence. This book had gone through several editions elsewhere, with Macmillan first acquiring copies of it in 1845, and selling these copies for 10s. 6d.159 Presumably after selling these copies successfully, Macmillan invested in a new print edition of the book in 1852. The cost to print 2000 copies of the book was £211 14s. With the new lower price of seven shillings and sixpence, Macmillan estimated the gross profit from this edition at £512. Snowball was paid in two installments, at one and two years following publication, a total of £154 for his copyright in the work.160 Macmillan’s estimated profit on the edition was roughly on par with that paid to the author, £146 6s.

Snowball was an author from whom Macmillan had, in their early days, acquired the right to print several textbooks that were stock and trade for Cambridge students at the time. From Snowball, they published An Introduction to the Elements of Plane Trigonometry (received from elsewhere in 1847), The Elements of Mechanics (2nd edition, 1846), and Lund’s edition of Snowball’s Cambridge Course of Elementary Natural Philosophy, which had originally been published elsewhere, and for which Macmillan acquired the right to print the fifth edition in 1846. Although Macmillan continued to reprint Snowball’s The Elements of Plane and Spherical Trigonometry several times between 1852 and 1891, Macmillan largely moved on from authors of stock and trade Cambridge textbooks, developing new authors for their mathematical texts.161

158 Printed Catalogue from 21 June 1851, MP 54790, Publications Catalogues with Manuscript Additions, Macmillan Archive, British Library, London UK. The cost to print Phear’s book was estimated at £90, and each copy sold at 5s. 6d. 159 Macmillan’s first Editions Book, p. 482. 160 Printed Catalogue from June 21 1851, MP 54790, Publications Catalogues with Manuscript Additions, Macmillan Archive, British Library, London UK. 161 Macmillan’s first Editions Book, p. 482.

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They turned particularly to Isaac Todhunter, and to other authors like George Boole, that Todhunter advised Macmillan develop.

Todhunter’s first book with Macmillan was published around the same time that Macmillan published the above-mentioned works by Lund, Snowball and Phear. Macmillan published Todhunter’s A Treatise on the Differential Calculus and the Elements of the Integral Calculus in 1852 (Foster 1891: 20). Macmillan printed 1250 copies, and sold them at ten shillings and sixpence. Several editions and reprintings followed. Macmillan estimated the revenue generated by selling out the first printing of this book would be £421 10s. The cost to print Todhunter’s book, including printing, paper, woodcuts, boarding, advertising and presentation copies, was fairly high compared to printing costs for the books of traditional Cambridge authors, at £206 17s. 6d. Under the half-profits contract they agreed to, Todhunter stood to gain £107 6s. 3d. from the first edition.162 Over time, he must have gained more than that, as the book went through five editions, and the fifth edition (of 1871) was reprinted several times until 1923 (although Todhunter died in 1884).163

Recall Isaac Todhunter's book, A Treatise on Plane Co-ordinate Geometry, as Applied to the Straight Line and the Conic Sections, with Numerous Examples (1855).164 Plane Co-ordinate Geometry was a beginner’s textbook. At 299 pages in length, 1250 copies were originally ordered by Macmillan and printed at Cambridge University Press. Each book sold for ten shillings and sixpence. The book proved to be a success and went into several reprintings. A total of 27,750 copies were printed, the last being printed in 1888.165 The book was distributed and sold in London, Oxford, Edinburgh, Dublin, Cambridge, and possibly elsewhere.

In correspondence with Todhunter, Macmillan proposed several schemes of payment for this work, depending on its eventual size and sale price. As proposed by Macmillan, the amount of

162 Printed Catalogue from 1 June 1864, MP 54791, Publications Catalogues with Manuscript Additions, Macmillan Archive, British Library, London UK. 163 Macmillan’s first Editions Book, p. 508. 164 Production details about this book were discussed in chapter two, section ten. 165 Macmillan’s first Editions Book, p. 511.

136 earnings due to Todhunter on the sale of an edition of 1500 copies, ranged from £110-£130.166 If we assume Todhunter ended up earning the smaller amount of these figures, and that the terms of his agreement stayed the same over the various editions and reprintings, then Todhunter (or his estate, as the case may be) stood to gain approximately £2,127 from the 27,750 copies eventually made of this book.

As we can see from a list of Todhunter’s books with Macmillan and their relative circulations (Table 4), twenty seven thousand copies was in the middling range of circulation for one of Macmillan’s Todhunter titles. As someone reflected in an obituary of him, Todhunter’s childhood had been defined by “the bracing discipline of poverty”.167 At death the Oxford Dictionary of National Biography lists the value of his estate at £81,330 7s. 0d. (Mullinger 2004). We can surmise that his accumulated wealth was largely derived from the revenues he accrued through publication. As a point of comparison, Alexander Macmillan’s probate at death was £179,644 19s. 7d. in 1896 (Van Arsdel 2004).168

Todhuunter’s Plane Co-ordinate Geometry was his third book with Macmillan. Already by that time, Todhunter revealed himself as a negotiator, and demonstrated awareness that his textbooks embodied potential future earnings. After Macmillan had proposed a scheme of payment for Plane Co-ordinate Geometry, Todhunter wrote back agreeing, but only committing to publish the first edition with Macmillan. In his reply, Daniel Macmillan offered the following statement:

My dear Sir, we have returned the memorandum about the Conics, its formally signed and a copy of the same for your signature. We should have been glad if instead of the first you but put that we were to have the first offer of future Editions in terms of what you might

166 Daniel Macmillan to Isaac Todhunter, 20 January 1855, MP 55376 General Letter Book, 1854-55, Macmillan Archive, British Library, London UK. 167 June Barrow-Green quotes J. E. B. Mayor’s Cambridge Review obituary in her article about Todhunter and his mathematics textbooks (Barrow-Green 2001: 180). 168 This amount was presumably his personal wealth, as the Macmillan publishing company and its assets continued to exist, with ownership falling to surviving family members.

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think the same. One works with more heart and zeal for what is not likely to be taken away…169

By committing only to an agreement over the first edition, Todhunter left open the possibility of renegotiating a higher fee for subsequent editions if the book proved successful.

Most of the examples of author-publisher agreements mentioned above are for Macmillan’s more successful educational books on mathematical subjects. But what of some of Macmillan’s “higher” books in mathematics? For these, we can offer one early example from Macmillan’s first years as a publisher. In 1847 Macmillan co-published George Boole’s Mathematical Analysis of Logic (1847) with George Bell of London. 500 copies of the book were printed at a cost to Macmillan of £31 19s 10d. The book was offered initially at the price of three shillings and sixpence.170 By June of 1851, only 114 copies of the book had been sold, and the book owed roughly £14 of the expense Macmillan had paid for it.171 While it is not known what kind of agreement Boole had with Macmillan over the book, if he had made a half-profits agreement, he would not yet have earned anything in the first three years the book was for sale, as Macmillan had not yet recovered their expenses.

Similarly small sales were had with Boole’s subsequent work in mathematical logic. Macmillan & Co. acquired the remaining copies of George Boole's Laws of Thought (1854) from Walton & Maberly (the original publisher) in 1872. During the eighteen years it had been available, only 206 copies of the book had been circulated.172

Macmillan’s records demonstrate the firm held two attitudes towards the publication of “higher” books in mathematics. First of all, there was flat recognition that such books were not profitable.

169 Daniel Macmillan to Isaac Todhunter, 28 January 1855, MP 55376, General Letter Book, 1854-55, Macmillan Archive, British Library, London UK. 170 The price was raised at an unknown later date to 5s. (Foster 1891: 583), Macmillan’s first Editions Book, p. 57. 171 Printed Catalogue from 21 June 1851, MP 54790, Publications Catalogues with Manuscript Additions, Macmillan Archive, British Library, London UK. 172 Macmillan's first Editions Book shows 294 copies received in 1872. The original 1854 edition from London's Walton & Maberly is in the British Library. While I am unable to confirm the original print run was 500 copies, this is a reasonable estimate for the first printing of such a book at this time.

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In 1856 Daniel Macmillan wrote to P. G. Tait, regarding the publication of his book, A Treatise on the Dynamics of a Particle, “as these high subjects never sell enough to cover expenses we shall be in no hurry about [its publication]”.173 By comparison, Macmillan was often in a rush to print or reprint a mathematical textbook when an audience was at hand to purchase it.174

However, there was simultaneously the recognition that “higher” works in mathematics were symbols of intellectual achievement, and that publishing these works reflected well on the character and good reputation of Macmillan. Recall Donald MacAlister’s comment regarding several mathematical manuscripts that he regarded as not being likely candidates for commercial success. He nevertheless recommended these as possibly being worth taking on, as such books would bring Macmillan prestige and credibility as a publisher of educational and learned works.175

Authors of books in “higher” mathematics were aware of their reduced position to negotiate financial compensation in their publishing contract. Macmillan’s records suggest that A. G. Greenhill, who published several books with Macmillan in higher mathematical subjects, did not negotiate his author-publisher agreements, whereas some of Macmillan’s highest earning mathematical authors clearly did. Greenhill’s Hydrostatics (1894) was published on the half- profits system, as was his 1892 book, Elliptic Functions.176 Comparing the dates between Macmillan’s first offer to publish and the date of the signed agreement, one week difference between the date of offer and date of agreement suggests that Greenhill did not negotiate the

173 Daniel Macmillan to P. G. Tait, 7 January 1856, MP 55379, General Letter Book 1856, p. 467, Macmillan Archive, British Library, London UK. 174 See the letter from Daniel Macmillan to Barnard Smith, 5 March 1856, MP 55378, General Letter Book 1855- 56, also quoted in chapter one. 175 “Elliptic Functions” by W. A. Greenhill [this is probably A. G. Greenhill], H. B. Halstead’s “Elements of Geometry”, and a book on the calculus of variations were recommended for publication on this basis. See MP 55939 Readers Reports 1885-1886, p. 54; MP 55936 Readers Reports 1883-1884, p. 164; MP 55937 Readers Reports, 1883-1885, p. 73, Macmillan Archive, British Library, London UK. 176 Agreement proposed by G.A.M. to A. G. Greenhill, October 9 1890. Terms Book I, p. 13; Agreement between G.A.M. and A. G. Greenhill, January 27, 1886. Terms Book I, p. 13.

139 contract for his Elliptic Functions.177 By comparison, Macmillan first proposed a contract for Hall and Knight’s Elementary Trigonometry in June of 1889 but an agreement was not reached until five years later in January of 1894.178 Similarly for Hall and Knight’s Algebra for Beginners, a contract was first proposed in June of 1889, but an agreement was only reached in May of 1893.179

6. Promotion and advertising

From the costing records that survive from Macmillan’s earliest days in publishing, we know that their production costs for mathematical books included a budget for advertising, and also frequently included the cost of presentation copies. Records indicate that Macmillan paid to advertise Thomas Lund’s A Short and Easy Course of Algebra (1851), his A Companion to Wood’s Algebra (1847), Todhunter’s A Treatise on the Differential Calculus and the Elements of the Integral Calculus (1852) and Snowball’s The Elements of Plane and Spherical Trigonometry (1852). In 1855 Macmillan planned to spend £26 on advertising for Todhunter’s A Treatise on Plane Co-ordinate Geometry, but Daniel Macmillan wrote to Todhunter prior to its publication that, “I fear we are sure to go a good deal beyond that sum”.180 In the case of George Boole’s Mathematical Analysis of Logic (1847), Macmillan budgeted for presentation copies, but did not budget for advertising.181

In the 1860s Macmillan expanded their capacity to advertise mathematical textbooks. Todhunter’s books, for instance, were widely advertised by the printing of prospectuses. In 1861, 14,000 prospectuses were prepared to promote the publication of his Theory of Equations (1862) (Barrow-Green 2001: 187 f.n. 51). In 1860 Macmillan ordered 3,000 prospectuses promoting

177 G.A.M. proposed the arrangement to Greenhill on January 15, 1886. He accepted within a week. Terms Book I, p. 13, Macmillan Archive, Palgrave-Macmillan head office, Basingstoke, UK. 178 Terms Book I, p. 14, Macmillan Archive, Palgrave-Macmillan head office, Basingstoke, UK. 179 Terms Book I, p. 13, Macmillan Archive, Palgrave-Macmillan head office, Basingstoke, UK. 180 Daniel Macmillan to Isaac Todhunter, 20 January 1855, MP 55376, General Letter Book, 1854-55, Macmillan Archive, British Library, London UK.

181 Printed Catalogue from 21 June 1851, MP 54790, Publications Catalogues with Manuscript Additions, Macmillan Archive, British Library, London UK.

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Barnard Smith’s Exercises in Arithmetic (McKitterick 2004a: 396). Into the 1870s, Barnard Smith’s mathematical textbooks continued to be advertised by the circulation of prospectuses. In October of 1871, 20,000 leaflets describing Barnard Smith’s mathematical books were printed at Cambridge University Press with 10,000 more ordered by Macmillan in January of 1872 (McKitterick 2004a: 397).

Macmillan kept special educational lists and catalogues, and routinely offered presentation copies of its books to potential volume buyers.182 They placed presentation copies in the hands of teachers who might adopt these books for their classrooms. Macmillan’s correspondence with their textbook authors shows that they consulted over the lists of people to whom presentation copies would be sent. For instance T. R. Birks, author of On Matter and Ether (1862) and P. G. Tait, co-author with W. J. Steele of A Treatise on the Dynamics of a Particle (1857), were consulted in this way.183 Barnard Smith’s School Arithmetic (1854) was sent to Rev. I. Newton at Brighton College.184 Copies of the second edition of Barnard Smith’s book Arithmetic and Algebra (2nd edition, 1856) were sent to India, to Cambridge, to Dr. Peacock, to the Committee of the Council on Education, to Rev. I Smith, to a Mr. Hawtrey, to Rev. W. S. Wayte of Trinity College Oxford, and to a Mr. Whittington, Master of the Proprietary School, Islington, in April of 1856.185 Macmillan also wrote to booksellers inquiring as to sales of their mathematical textbooks. These letters inquired as to stock on hand, asking booksellers to give reports if a particular book has ceased to garner consistent sales.186

182 See “List of Mathematical Class Books”, MP 55379 General Letter Book 1855-56, p. 231, Macmillan Archive, British Library, London UK. 183 Daniel Macmillan to T. R. Birks, MP 55379 General Letter Book 1856, p. 245, 252, 282; Daniel Macmillan to P. G. Tait, 19 February 1856, MP 55379 General Letter Book 1856, Macmillan Archive, British Library, London UK. 184 Daniel Macmillan to I. Newton, 5 October 1854, MP 55376 General Letter Book 1854-55, p. 35, Macmillan Archive, British Library, London UK. 185 Rev. Dr. Peacock served as the Dean of Ely, Mr. Hawtrey may have been the Rev. S. Hawtrey of Eton College. Daniel Macmillan to Barnard Smith, letters of 26 and 29 April 1856 and 5 May 1856, MP 55378 General Letter Book 1855-56, p. 281, 300, 335, Macmillan Archive, British Library, London UK. 186 Daniel Macmillan to Mr. Hamman’s Bookseller Oxford, 20 August 1856, MP 55378 General Letter Book 1855- 56, Macmillan Archive, British Library, London UK.

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Apparently during Isaac Todhunter’s early friendship with the Macmillan brothers, his encouragement had been one influence prompting their founding a monthly magazine (Morgan 1943: 56). In November of 1859, Macmillan’s Magazine began publication. A philosophical and literary paper, it was the first of the shilling monthly magazines. Its pages serialized popular fiction, including Charles Kingsley’s Water Babies and Henry James’ Portrait of a Lady (Morgan 1943: 58). Current issues of the day, including religion and science, were also debated in its pages, by men including W. K. Clifford, T. H. Huxley, Herbert Spencer, and Alfred Russel Wallace. Macmillan’s Magazine successfully established itself with a readership of middle-class English people during the 1850s and 1860s (Dawson 2004). Publication in Macmillan’s Magazine helped raise the public profile of its contributors, many of who were also authors of books published by Macmillan.

Macmillan went on to found several periodicals that were outlets for scientific publishing specifically. They founded the general science journal Nature, edited by Norman Lockyer, in 1869, as well as several medical journals, including The Journal of Anatomy and Physiology (f. 1866), Practitioner: A Monthly Journal of Therapeutics (f. 1868), Brain: A Journal of Neurology (f. 1878), and the Journal of Physiology (f. 1878). Interestingly, Nature operated at a financial loss for the first twenty years of its publication, but Macmillan saw it as worthwhile because it developed authors for, and patrons of, its line of scientific books (Baldwin 2012: 145). 1890 was the first year that income from subscriptions and advertising exceeded the costs of printing the journal. In the 1880s, Frederick Macmillan explained his view to George Macmillan that Nature was a convenient way to advertise their scientific publications (Baldwin 2012: 154 f.n. 95). Indeed the pages of Nature in the 1870s and 1880s contain not only advertisements for Macmillan’s own scientific books, but also advertisements for scientific and mathematical books published by other British publishing companies. Historians David McKitterick and Melinda Baldwin offer similar views, concluding that in developing contributors and readers for their books, Macmillan’s periodical publications served the company’s primary interest as a book publisher (Baldwin 2012, McKitterick 2004a: 400). Beyond advertisements for their own books in Macmillan periodicals, the company also advertised its books in other magazines including

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The Athenaeum, The Educational Times, and the Publisher’s Circular (see Figures 15 and 16).187

Macmillan’s books themselves served as advertising vehicles for the company’s catalogue of other book titles. Percival Frost’s edition of Newton’s Principia (1854) contained extensive advertising of Macmillan’s catalogue of books on its very first and final pages. Frost served frequently as examiner for Cambridge’s mathematical Tripos examination, in which knowledge of the Principia was essential. Frost’s book was recommended to students as preparation material for this exam (Besant 1893: 18). Macmillan’s advertising in Frost’s book was intended to attract the attention of Cambridge mathematical students.

Inside the front cover and prior to the title page is a listing of “New Educational Works from Macmillan & Co.”. This list of ten titles includes Phear’s works on mechanics and hydrostatics, Grant’s astronomy, Puckle’s conic sections and algebraic geometry, Snowball’s trigonometry and Lund’s algebra (Frost 1854). A complete list of Macmillan’s Mathematical Class-Books for Colleges and Schools is given over four pages after the end of Frost’s text, listing twenty-five works, and signaling (as indicated in Table 1) that after a decade in business, Macmillan had invested significantly in the publication of educational works about mathematics. This advertisement records already published books as well as books in preparation, with some titles accompanied by positive “blurbs” or testimonials by school masters or college tutors, or quotations from reviews in periodicals such as The Athenaeum, Philosophical Magazine, English Journal of Education, The Educator or Educational Times. Following the list of mathematical class-books is an extensive 16-page catalogue of what appears to be, as of November 1854, an alphabetical listing of all of Macmillan & Co.’s publications (See Frost 1854).

By the time Macmillan published the fourth edition of Frost’s textbook in 1883, the publisher’s advertising had been substantially scaled back. Instead of multiple lists of books published by Macmillan, there are only two pages of advertising at the very back of the text. Both pages are

187 Advertisement for “Macmillan and Co.’s List”, The Anthenaeum, August 4 1883, no. 2910, 132; advertisement for “Macmillan’s Books Suitable for the College of Preceptors Examinations, Midsummer and December, 1909”, The Educational Times 62 (n.s. 574), February 1 1909, p. 83.

143 devoted to advertising other Macmillan books by Frost: a new edition of his Solid Geometry and An Elementary Treatise on Curve Tracing (Frost 1883).

Figure 13 1870 Advertisement for Macmillan and Co.’s Scientific Publications (Source: Nature, vol. 1, no. 16, 17 February 1870, p. 419)

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Figure 14 1880 Advertisement for Messrs. Macmillan and Co.’s New Books (Source: The Publisher’s Circular, 17 January 1880, p. 17)

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Macmillan also displayed an awareness that attaching the endorsement of a celebrity scientist to their book products was one way to sell copies of a publication with otherwise limited appeal. As Roy MacLeod has noted, historians of book culture must be sensitive to both the actual content of books as well as to the image and desirability (or lack thereof) of the perceived content (MacLeod 1980:63). Both the actual content of a book, as well as the value placed on acquiring or being associated with a book or its author, were crucial to the business of publishing and specifically to the aspect of advertising books.

In 1881 Daniel MacAlister considered in his readers’ reports the value of publishing an English translation of the German botanist Hermann Müller’s book Die Befruchtung der Blumen durch Insekten. Before Macmillan took the decision to publish it, Daniel MacAlister consulted with botanists Sydney Howard Vines and Alexander Dickson, afterwards writing to Charles Darwin for his opinion on the value of an English translation. Vines and Dickson recommended the translation, but could offer no opinion as to how such a book would sell. Darwin, when consulted, wrote: “Whether it would answer for a publisher I can be of no opinion”.188

Donald MacAlister, on the other hand, whose job it was to assess the financial sensibility of prospective publishing projects, strongly encouraged Macmillan to connect Darwin’s name as prominently as possible to Müller’s book as a way to make the work desirable to the English audience. The addition of a preface by Darwin, MacAlister suggested, would be a coup, and then Darwin’s name could be used to “striking effect” in Macmillan’s advertisements:

I thought the last thing was to get Darwin’s opinion, my own after that of Vines and Dickson’s being only of small importance. You will see how cordially [Darwin] endorses the recommendations of the other botanists – so that there can no longer be any doubt of the value of the book and the importance of the translation. What however must also interest you is the chance of a remunerative sale. My opinion about this can scarcely be of great value, but there is one suggestion which I think if carried out would do much to render this success less problematical. I mean that as Darwin is so much interested in the appearance of the translation he should be asked to provide a preface or preparatory

188 Charles Darwin on the question of translating Müller’s Befruchtung der Blumen, MP 55935, Readers Reports 1880-1883, p. 92, Macmillan Archive, British Library, London UK.

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introduction. This could have a striking effect on advertisements, like that of Roscoe's name in Joule's chemistry and would do much to sell the book. In a certain way Darwin has already done much to advertise Müller's name, for every scrap of botanical news which Müller sends him is forthwith sent to Nature and appears in big print. There is therefore a large circle of readers who know Müller's work and the high esteem in which Darwin regards it. This is the fact which makes me hopeful of the translation’s success. This and the fact of Müller’s helping to make the English book practically a new edition, should I think tell with you powerfully in deciding. These facts were not before the previous publisher referred to, and I think materially alter the problem of successful publication. These are the materials on which I base my judgment and I give them to you as they are in preference to stating the judgment simply.189

In the end, Müller’s book was translated by D’Arcy Wentworth Thompson and published in English by Macmillan as The Fertilisation of Flowers, in July of 1883. It included a four page prefatory note by Charles Darwin, whose name appeared prominently on the title page.

Macmillan recognized the power of scientists as public figures. They traded on that celebrity and they helped to build it. One of the ways in which they promoted scientists as celebrity figures was through the production and sale of engraved portraits. Several of Macmillan’s own scientific authors were depicted in this way. Macmillan’s portrait gallery of eminent scientific figures included physician Francis E. Anstie, botanist Joseph Dalton Hooker, chemist Henry Enfield Roscoe, physicist George Gabriel Stokes, biologist Charles Wyville Thomson, astronomer George Biddell Airy, physicist James Clerk Maxwell, and mathematician William Spottiswoode. All of these men had been at one time or another, Macmillan authors.

Macmillan’s portrait gallery of eminent scientists also included engravings of people who were not Macmillan authors. Their series of scientific portraits included depictions of Robert Wilhelm Bunsen, Charles Darwin, Michael Faraday, William Harvey, Hermann von Helmholtz, John Tyndall, Charles Wheatstone, James Prescott Joule, Louis R. Aggassiz, Charles Lyell, Richard

189 Donald MacAlister on the question of translating Müller's Befuchtung der Blumer, December [1881], MP 55935 Readers Reports 1880-1883, p. 92, Macmillan Archive, British Library, London UK. Darwin mentioned that Kegan Paul had previously consulted him on the possibility of translating the work. Although he had recommended it, they never followed through with the project.

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Owen, William Thomson (Lord Kelvin), Lord Beaconsfield, John Couch Adams, C. W. Siemens and Arthur Cayley (Foster 1891). These engravings were commissioned from either Charles Henry Jeens or George J. Stodart.

Macmillan’s series of scientific portraits had been originally created for Nature, in which an occasional series of articles celebrating “Scientific Worthies” began as an irregular series paying tribute to great men of science. Sometimes these biopics (the portrait, along with a biographical article), appeared while the subject was alive and sometimes as a posthumous honour. Michael Faraday received the first tribute in the September 18, 1873 issue of Nature. Frederick Gowland Hopkins received the final tribute in 1938, the last in a list of forty-eight scientific men who had been so profiled (Barr 1965: 354). As well including them in the journal Nature, Macmillan offered these portraits of famous scientific figures for sale as individual engravings. The production and sale of such portraits offered the image of scientific greatness for public consumption.

7. Mathematics for the world

As John Feather has noted in his history of British publishing, the book industry was one of Britain's major conduits for foreign exchange in the nineteenth century, and during that time it exported about 40 per cent of its total output in books (Feather 1988: x). A proportion of this export was mathematical books. Some work has already been done on British mathematical books produced for foreign markets (Aggarwal 2007; Chatterjee 2006). From the 1850s onwards there was a constant exchange of English-produced books with America, Canada, India, Australia, New Zealand, Japan and South Africa (Rukavina 2010). In the 1860s, Macmillan specifically sold books into Cape Town, Glasgow, Dublin, Leipzig, New York, Melbourne, Sydney, Adelaide, Hobart and Philadelphia (McKitterick 2004a: 397-8). Macmillan sold books into more international markets than any other English publisher. As historians of book publishing have reflected, “Macmillan’s aspirations spanned the English-speaking world, as a general publisher, an educational publisher, and as a periodical publisher” (McKitterick 2004a: 400).

While many mathematical authors wrote textbooks that were used in schools and universities, the scale of Todhunter’s enterprise singles him out among the mathematical authors of his time, both within the general trade of mathematical textbooks and within Macmillan’s book list specifically

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(Barrow-Green 2001:189). As mentioned previously, Todhunter had nearly forty titles attributed to his name under the Macmillan imprint (see Table 4). As an example of how Macmillan’s mathematical books circulated in the worldwide market, we might consider Todhunter’s books as one example.

Year of first Title Price* Total copies appearance printed**

1852 A Treatise on the Differential Calculus and the 10s 6d. 24,250 Elements of the Integral Calculus

1853 A Treatise on Analytical Statics 10s. 6d. 9,000

1855 A Treatise on Plane Co-ordinate Geometry 10s. 6d. 27,700

1857 A Treatise on the Integral Calculus and its 10s. 6d. 17,500 Applications

1858 Algebra for the use of Colleges and Schools 7s. 6d. 138,500

1858 Answer to Mr. Lund’s Attack on Mr. Todhunter Not known 2,000

1858 Examples of Analytical Geometry of Three 4s. 4,000 Dimensions

1859 Plane Trigonometry 5s. 86,500

1859 Spherical Trigonometry for the use of Colleges 4s. 6d. 32,530 and Schools

1861 A History of the Progress of the Calculus of 12s. 500 Variations During the Nineteenth Century

1861 An Elementary Treatise on the Theory of 7s. 6d. 13,500 Equations

1862 The Elements of Euclid 3s. 6d. 525,000

1863 Algebra for Beginners 2s. 6d. 693,000

1865 A History of the Mathematical Theory of 18s. 1,000 Probability from the Time of Pascal to That of Laplace

1866 Trigonometry for Beginners 2s. 6d. 108,500

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1867 Mechanics for Beginners 4s. 6d. 56,000

1868 Key to Algebra for Beginners 6s. 6d. 21,000

1869 Mensuration for Beginners 2s. 6d. 215,000

1870 Key to Algebra for the use of Colleges and Schools 10s 6d. 14,000

1871 Researches in the Calculus of Variations 6s. 500

1873 The Conflict of Studies 10s. 6d. 1,000

1873 A History of the Mathematical Theories of 24s. 500 Attraction and the Figure of the Earth

1873 Key to Trigonometry for Beginners 8s. 6d. 6,000

1874 Key to Plane Trigonometry 10s. 6d. 7,000

1875 An Elementary Treatise on Laplace’s Functions, 10s. 6d. 1,000 Lamé’s Functions, and Bessel’s Functions

1876 An Abridged Mensuration with Numerous 1s. 5,000 Examples for Indian Students

1876 Macmillan’s Series of Text-Books for Indian 2s. 6d. 10,000 Schools: Algebra for Indian Students

1876 Macmillan’s Series of Text-Books for Indian 2s. 27,000 Schools: The Elements of Euclid for the use of Indian Students

1876 Macmillan’s Series of Text-Books for Indian 2s. 42,000 Schools: Mensuration and Surveying for Beginners

1877 Natural Philosophy for Beginners, Part I 3s. 6d. 11,000

1877 Natural Philosophy for Beginners, Part II 3s. 6d. 6,000

1878 Key to Mechanics for Beginners 6s. 6d. 4,000

1880 Key to Exercises in Euclid 6s. 6d. 9,500

1886 Key to Todhunter’s Mensuration for Beginners (by 7s. 6d. 2,750 L. McCarthy)

1887 Solutions to Problems Contained in Plane 10s. 6d. 1,000 Coordinate Geometry (ed. C. W. Bourne)

1888 Key to Todhunter’s Differential Calculus (by H. St. 10s. 6d. 2,750 J. Hunter)

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1889 Key to Todhunter’s Integral Calculus (by H. St. J. 10s. 6d. 2,250 Hunter)

Table 4 Isaac Todhunter’s publications with Macmillan 1843-1889 (Source: Macmillan’s First Editions Book, British Library) *Note: Price refers to either the most stable price or the price on first printing. **Note: Some titles may have been reprinted beyond the last year given here. Calculations of lifetime print-run given in this chart were calculated from Macmillan’s first editions book only.

In England, Todhunter’s books were featured in articles on the Mathematical Tripos contained in nineteenth century editions of the Student’s Guide to the University of Cambridge. Twelve of Todhunter’s textbooks were recommended as useful reading for the Cambridge undergraduate in the 1893 edition of this guide. Todhunter’s book were used as course texts by the Universities of Manchester, Leeds, Liverpool, Edinburgh and Bristol well into the twentieth century (Barrow- Green 2001:189). Todhunter’s books were familiar pedagogical materials within many of Britian’s foremost centers where one might seek further education in mathematics. Todhunter served as an intermittent examiner for the Mathematical Tripos and Smith’s Prizes at Cambridge, and worked as an examiner for London University, the Royal Military Academy at Woolwich, the East India Company military college and the Indian Civil Service (Barrow-Green 2011: 184). He wrote to his wife in 1878 “there is a library of mathematical books provided by the Civil Service Commission [of India] for the use of the Examiners. It consists of fourteen volumes, ten of which are by myself” (quoted in Barrow-Green 2011: 184).

American editions of Todhunter’s textbooks became set texts for particular markets in the United States (Barrow-Green 2001: 187). In 1882 the New York edition of Todhunter’s Algebra for Beginners was the prescribed text for the public schools (i.e. government funded schools) in the Canadian province of Nova Scotia. English-language editions also surfaced in Australia.

Between 1881 and 1885 at least eight of Todhunter’s textbooks and four of his keys were translated into Japanese. It is suspected that the appearance of Todhunter’s books in Japanese was in part due to Dairoku Kikuchi, who had been a student at University College, London

151 before going to St. John’s College, Cambridge in 1873. Kikuchi returned to Japan in 1877, and became the first Japanese professor of mathematics at the newly founded University if Tokyo. He was keen to promote a Cambridge-like education in Tokyo, and used several of Todhunter’s textbooks at the university. Kikuchi himself subsequently wrote several of his own textbooks on geometry (Barrow-Green 2001: 185 f.n. 35, 187 f.n. 56).

It is unlikely that the Japanese translations of Todhunter’s mathematical textbooks were “authorized” by Macmillan or that the printing of these books benefitted Todhunter financially. “Pirated” English books were almost as common in foreign markets as imported English ones. International copyright agreements were not put in place until the beginning of the twentieth century. No legal agreement or law prevented the reproduction and sale of a foreign title in a domestic market. Although in some circles it was looked down upon as disrespectful, this attitude did not prevent enterprising publishers from producing cheap editions of popular foreign titles without offering compensation to the original author or publisher. Particularly in the United States, pirating British periodicals and books was something of a sport, and a practice that enriched many entrepreneurial printers.

A report in Nature charged The Tokio Bookselling Company of Japan of pirating copies of English and American schoolbooks, with Todhunter’s Elementary Algebra and Euclid among the books being reproduced. The report states: “An examination of the reprint of Todhunter’s Algebra shows letters upside down, wrong fount letters, letters misplaced, and words improperly spelt, testifying to the slovenly way in which the books have been printed. There is said to be scarcely a page in the book which does not contain one or more errors in orthography, and the mathematical formulae, which always require such care at the printers’ hands, must be in a bad state when the ordinary words are so neglected” (Anon. 1883).

Todhunter’s mathematical textbooks enjoyed popularity in India. Macmilllan began publishing mathematical books specifically for India in 1873. However British books were imported into India before that. London bookseller Thacker & Co. was established in Calcutta and Bombay in 1857 and acted as bookseller and publisher to the Universities of India. By the end of the century Thacker offered more than 200 English titles in mathematics (Aggarwal 2007: 11). However, Macmillan was the only British publisher who published educational texts, and specifically

152 mathematical ones, for the use of Indian schools and colleges in the nineteenth century (Aggarwal 2007: 14).

In 1876 Indian editions of Todhunter’s Mensuration and Surveying and Algebra were prepared by Macmillan, printed in Cambridge at the Pitt Press, and then sent to India. Similarly, a special edition of Todhunter’s Euclid was prepared for the use of Indian schools in 1877. However, there was a need in India for mathematical textbooks in local languages, as well as in English. This prompted the pirating and translation of English mathematical textbooks into local languages. Todhunter’s Euclid and his Algebra for the use of Colleges and Schools were translated into Urdu in 1871 and Hindi translations were made of Todhunter's Euclid and Mensuration between 1850-1870 (Barrow-Green 2001: 196, Aggarwal 2007:14). Todhunter's Algebra and Geometry were translated into Bengali and his Geometry into Urdu.

Translators of British mathematical books were frequently teachers in need of material, particularly the mathematics teachers at Agra College, Calcutta Sanskrit College, professors at Lahore Oriental College, Benares Sanskrit College (established 1792), and Delhi College (established 1792).

Bapu Deb Shastri taught mathematics and natural philosophy at the Benares Sanskrit College from 1842. He was very interested in European science and translated many English books into Sanskrit. Shastri compiled Sanskrit treatises on geometry, trigonometry, analytical geometry, conic sections, mechanics, differential and integral calculus, and the solar and lunar eclipses. However, most of the English books he used to prepare his treatises are not known, as he did not generally acknowledge or refer to other works in them (Aggarwal 2007:16). It was commonly the case that mathematical books translated into local languages did not detail their provenance.

Koonj Behary, a teacher of mathematics at Agra College, produced Hindi translations of books covering the topics of trigonometry, arithmetic and geometric progressions, finite and infinite series, and cubic equations. Some of these translations replaced English trigonometric terms for specifically Hindi ones and Indian alphabet letters, rather than English ones, were used to label the vertices of geometric figures (Aggarwal 2007:16).

Canadian mathematician J. C. Fields used several British textbooks during his time as a high school student at Hamilton Collegiate Institute. These included a new Toronto edition of Isaac

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Todhunter’s The Elements of Euclid for the use of schools (1876). When Fields matriculated into the mathematics department at the University of Toronto, Todhunter’s Spherical Trigonometry and his Theory of Equations were used in his first year as assigned texts (Riehm and Hoffman 2011: 21).

There is evidence Todhunter’s geometry textbooks were also translated into Chinese, that they circulated in Australia, and that his Algebra for the use of Colleges and Schools (1858) was published in Italian in 1871 (Barrow-Green 2001: 187 f.n. 55, 196).

Despite their success, Todhunter’s textbooks were criticized for their lack of originality and their inclusion of errors. The English geometer Thomas Archer Hirst pointed out that the proof of convergence of the binomial theorem Todhunter offered in his Algebra was invalid for certain conditions of n. Hirst expressed surprise that Todhunter, a student and disciple of Augustus De Morgan, would allow four editions of his Algebra textbook to be published without correcting “a logically false demonstration of an important theorem” (Hirst quoted in Barrow-Green 2001: 188). Todhunter also faced criticism that his Algebra was imprecise in its use of language, and that his textbooks perpetuated the confusions and errors existing in older works on the same subjects (Barrow-Green 2001: 196).

As Barrow-Green reflects in her article about him, despite his involvement in and knowledge about mathematics education, rather than being a supporter of reforms to mathematical teaching, Todhunter was in fact a staunch defender of the status quo (Barrow-Green 2001: 190). The English pedagogical status quo valued the instillation of rigorous mathematical reasoning into students, valuing the process of mathematical instruction over the accuracy of facts or the relevance of results.

Todhunter shared an attitude with Donald MacAlister that when it came to a mathematics textbook, the way in which the material is presented outweighed the value of originality in the material itself. It was their opinion that the only room for innovation in a mathematics textbook was in the form in which the material was presented, not in its content. MacAlister went so far as to suggest that originality would actually detract from the eventual success of a mathematics

154 textbook.190 Subscribing to a similar philosophy, most of Todhunter’s textbooks contained little or no original content (Barrow-Green 2001: 199).

8. Conclusion

In her article about the founding and administration of the scientific journal Nature, Melinda Baldwin presents an interesting analysis suggesting that the age and generation of Nature’s scientist-contributors affected how they viewed and used Nature as a publication vehicle. Baldwin finds that the older generation of contributors, men whose lives ended around the turn of the twentieth century, differed in their pattern of contribution to Nature compared to the younger generation of scientists who had been born around 1850 (Baldwin 2012: 138). She suggests that while the older generation, men like P.G. Tait, Herbert Spencer, Joseph Hooker, T. H. Huxley, Alfred Russel Wallace and Charles Darwin, contributed book reviews or popular pieces to the magazine, they did not see Nature as a desirable forum in which to write about their own scientific work. The older generation had largely published and presented arguments for or against a colleague’s scientific theory in the popular press, alongside articles on politics, religion, literature and philosophy, in magazines like the British Quarterly Review or the Nineteenth Century (Baldwin 2012: 143-4).

The younger generation by comparison, engineer John Perry, physicist Oliver Lodge, zoologist E. Ray Lankester, naturalist George John Romanes, botanist William Turner Thiselton-Dyer, and chemist Raphael Meldola, had a different attitude towards publication and how publication related to their career aspirations. It was the younger generation, writes Baldwin, who embraced Nature and helped turn it from a general interest periodical about science, as it had first been intended as a periodical written by scientists for the public, into a forum in which scientists largely communicated information to one another.

190 About a manuscript by R. Hudson Graham on “Comparative Statics”, MacAlister writes: “This manuscript goes more fully into the subject than any other English manual. Its information is useful though it is to be found more or less explicitly scattered over various books. In other words little but the grouping is original. That is no draw back in a textbook.” MP 55932, Readers Reports, 1867-1882, p. 37.

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What Baldwin’s article raises is the important fact that during the period 1850 to 1900, the world of publishing, and the practice of science, were both evolving rapidly, and the relationships forged between these two worlds were constantly under negotiation. A more detailed overview of Macmillan’s advertising strategies, and the successful sale of their mathematical and scientific books, would have to take into account how authors and audiences for science and scientific materials, in education and intellectually, changed over these fifty years.

The present study has attempted to discover some quantitative facts about the circulation of, and monetary remuneration earned from, Macmillan’s mathematical books. It does not escape notice that a more interesting story, perhaps, might be to investigate further how Macmillan evolved during this time as a scientific publisher of books and periodicals, and how the behavior and decisions of authors and publishers reacted to the changing landscape of both science and publishing in the last part of the nineteenth century.

The work presented here raises questions about how publication informed and changed audiences for mathematics and science during the nineteenth century, and how authors used publication as one of the tools that brought the practice of science further respectability, authority, and patronage. Publication also offered a source of income for authors when few paid positions for scientists had yet been created in university or institutional settings. Successful textbooks or popular books on science or mathematical subjects provided a reliable stream of income to both author and publisher. For the scientists, this could mean a supplement to a profession with otherwise limited options for earning income. To the publisher, reliable income from a successful book title helped subsidized new endeavors, and helped mitigate the perilous trade of publishing and in what was an otherwise risky business.

Income generated by university-affiliated authors, for successful textbooks at least, were in fact as lucrative to the publisher as income generated by their successful fiction authors. Under the Macmillan model, profits from successful ventures in textbook publishing forged relationships out of which the printing of higher books could be subsidized. For Macmillan, the books in higher mathematics helped make their reputation as serious publishers of learned works. The impression of intellectual rigor formed by their science books list may have helped to counter assumptions about the credibility and erudition of the textbooks on their educational books list. For authors of successful textbooks for Macmillan, the relationship forged through a successful

156 publishing venture might mean the publisher was more willing to risk losing money on the publication of their more obscure or polemical manuscripts. In negotiating these author-publisher relationships, the model of an academic publishing house, particularly one that published science, was invented by Macmillan in this period.

Publishing, including science and mathematical publishing, was connected and influenced by colonialism and economics. Knowledge flowed along lines and links established by geo-political movements and international trade, price structures, and markets. Due to the increased cost of printing mathematics, the cost to enter the market with a mathematical book was higher than for books on other subjects. This exaggerated the cost to benefit ratio of the mathematical book. The change in the conditions of the nineteenth century British book market, conditions Simon Eliot sees as causing what he calls the “mass-production revolution”, meant that Macmillan, already heavily invested in the production of mathematical textbooks, spread the English image of mathematics around the world through the trade and export of these books.

The forces of industrialization came to dominate England’s book production, and this fact may have influenced the forming of educational structures of mathematics in developing countries, through the increased peddling and higher circulation of English-originated books. The English image of mathematics, through the use of English textbooks, may have taken hold in more places than it otherwise might have, if the industrial revolution had not driven outwards from England an English intellectual product within the material product of the book.

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Chapter 5 Enabling a Mathematical Culture: The Development of Mathematical Printing and Publishing in Canada

1. Introduction

In 1995 Tom Archibald and Louis Charbonneau wrote an overview to the history of mathematics from its very early beginnings in the Canadas up to 1945 (Archibald and Charbonneau 1995). This article demonstrates that until fairly recently, mathematics in Canada existed in a somewhat marginal and rudimentary state. Perhaps this estimate – or self-estimate, as the case may be – that Canadian mathematics has been unimportant, marginal or rudimentary explains why only one historical overview of mathematics in Canada has been written to date.

Most relevant to this chapter, Archibald and Charbonneau recognize that printers and publishers served an important function in developing a mathematical culture in Canada. In order to develop a mathematical culture, they write, three key aspects of a society play a role. First, a population or governing regime must place value on the acquisition of mathematical skill. Secondly, an educational infrastructure, including teachers, teaching materials, the curriculum and its objectives, is critical in shaping and developing a local practice of mathematics. Thirdly, they note, people who are interested in mathematics rely on the activities of the book trade: publishers and printers make available basic mathematical knowledge.

This chapter will explore in what respect the book trade shaped the development of mathematical practice and knowledge in Canada, focusing primarily on Anglophone Canada. In the late nineteenth and early twentieth century, book printers and publishers in Canada were struggling to establish themselves within a context that was structured in many ways to guarantee the continued dominance of printed materials originating from Britain and America over Canadian- originated materials. In so far as mathematical educators, and printers and publishers, identified as Canadian, both communities often shared a desire to nurture local knowledge. What I suggest in this chapter is that the development of a book and publishing trade in Canada was connected to the development of a specifically Canadian culture of mathematics. It is demonstrated how the

158 printing and publishing of mathematics in Canada was connected to larger goals of nation building and the definition of Canadian national identity in the years between 1850 and 1930.

Section (2) begins with a brief history of printing and publishing before Canadian confederation (prior to 1867). Section (3) overviews scientific and mathematical culture in Canada during the nineteenth century. The following sections look at specific examples of Canadian mathematical authors and the publishers with whom they collaborated. (4) looks at the Montreal based publisher John Lovell, Canada’s largest and most powerful publisher in the years leading up to Confederation. Lovell published a successful series of English-language schoolbooks, with the teacher and physician John Herbert Sangster authoring Lovell’s schoolbooks on the subjects of natural philosophy, chemistry, arithmetic, algebra and mensuration. (5) looks at James Gordon MacGregor, a native Nova Scotian who held the Munro Chair in physics at Dalhousie University in the 1880s. MacGregor turned to London’s Macmillan and Company as the publisher for his An Elementary Treatise on Kinematics and Dynamics (1887). Opportunities to publish science in Canada were limited in the nineteenth century. As a result, scientists often relied on foreign firms for the publication of their work.

The final section (6) looks at John Charles Fields, Canada’s first research mathematician, and his collaboration with the University of Toronto Press on the publication of the Proceedings of the International Mathematical Congress held in Toronto in 1924. Fields spent four years stewarding this massive technical publication through the press. In doing so, Fields helped build the University of Toronto Press’s capacity to handle mathematical printing. Because of this, after 1930, technical publications difficult to typeset and produce, could emanate from a Canadian publisher, rather than only from abroad. I argue this development further established a mathematical culture that was recognizably and distinctively Canadian.

2. Printing and publishing mathematics in pre-confederation Canada

While this chapter primarily focuses on mathematical practice and mathematical printing in the Anglophone context, the earliest examples of mathematical culture in Canada began in Nouvelle France (or New France), in an area that is now the province of Québec. The exploration of land and navigation of the St. Lawrence River were skills of preeminent importance to this developing French colony. Partly to impart relevant skills in cartography and navigation, the

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Collège de Québec was founded in 1659. For the next hundred years, the Jesuit Collège offered mathematical courses to its priests in training, overseen by a series of hydrographers who were royally appointed in France. Jean Deshayes, who came from France to teach astronomy and cartography, established the first science library in New France, containing approximately fifteen volumes including the Marquis de l’Hôpital’s famous treatise Analyse des infiniment petits pour l’intelligence des lignes courbes (1696) (Archibald and Charbonneau 1995: 4). However, the mathematical activity that had been established dispersed during and after the battle for New France in 1759. After Great Britain assumed political control, the Collège closed. Afterwards the evolution of mathematics in Anglophone and Francophone Canada developed at more or less the same rate (Archibald and Charbonneau 1995:1).

The earliest known printing in Canada took place in 1752. At that time, the few presses that existed in British North America served the exclusive needs of the government (Dewalt 1995: 12). Printing still barely existed by the beginning of the nineteenth century, with only nine printing offices in British North America at the time. However, that situation was to change dramatically. The first few decades of the nineteenth century brought great waves of immigration, and with a larger population came economic growth and greater efforts from residents to take control of matters of local importance. Both factors created a greater need for printing in the colony (Dewalt 1995: 13).

Most printing that took place in nineteenth century Canada was small in scale and most printers did not use steam-powered machines. The typical country printer would have worked one hand press with the assistance of a journeyman and possibly an apprentice or two. In many cases the organization was even smaller consisting only of the printer with the possible assistance of his family (Dewalt 1995: 21). Prior to confederation, Montreal, Halifax and Quebec were the dominant centers of printing and printed culture. Montreal was the largest printing center, with the most heavily capitalized printers as well as the most developed infrastructure in the allied printing arts, including engravers, lithographers, and a type foundry.191

191 In the 1830s The Montreal Type Foundry became the first producer of type in British North America. The Dominion Type Foundry also began its existence (in Montreal) to serve nineteenth century printers. Both firms produced type and acted as agents for foreign suppliers, bringing in imported types, presses, and printing supplies.

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Partly as a result, Montreal was an important cultural center, and was the place where some of the first efforts towards initiating a local literary and intellectual culture began. In the early years of the nineteenth century, Michel Bibaud, a Montreal-based journalist, educator and poet, launched several historical, literary and scientific journals with the goal of ameliorating the local intellectual climate. Bibaud wrote in his inaugural issue of the Magasin du Bas-Canada that to his dismay, a visiting man of letters would not find one literary or scientific journal in a province of half a million people (Parker 1985: 55). This dearth of cultural material, said Bibaud, gives the impression that “Que parmi les Canadiens d’origine française, il n’y a pas un seul homme capable de conduire un journal de ce genre, ou pas assez de lecteurs instruits, ou amis de l’instruction, pour le soutenir” (Bibaud, quoted in Parker 1985: 55). Although Bibaud did not find much success with his publications, his goal in undertaking them was to raise the cultural level of discourse among the residents of Lower Canada (Cyr 1985).

Besides being a journalist and writer, Bibaud published one of the earliest and most successful manuals of arithmetic in Lower Canada. Its full title is L’arithmétique en quatre parties, savoir: l’arithmétique vulgaire, l’arithmétique marchande, l’arithmétique scientifique, l’arithmétique curieuse, suivie d’un précis sur la tenue des livres de comptes, d’eux-mêmes et sans Maître, ou s’y perfectionner (Montreal, 1816). The four parts of Bibaud’s arithmetic were common arithmetic, commercial arithmetic, scientific arithmetic, and recreational arithmetic. Bibaud’s text was a compilation from other sources, which he indicated in the book.192 While the original version was intended for self-study, it was also used in schools, leading Bibaud to republish the book in 1832 as L’arithmétique à l’usage des écoles élémentaires du Bas-Canada (Bibauld 1832).

192 Bibaud’s book borrowed material from the first arithmetic published in Quebec, that is Traité d’arithmétique pour l’usage des écoles (1809) by Jean-Antoine Bouthiller. Bouthiller studied in Montreal and worked as a surveyor, journalist, translator, inspector of highways, and justice of the peace. His book received limited success, perhaps because it encouraged the memorization of rules rather than comprehension (Archibald and Charbonneau 1995: 10). Nevertheless Bouthiller’s book was printed in several editions until 1864. Bibaud also borrowed material from Francis Walkingame’s The Tutor’s Assistant, Being a Compendium of Arithmetic and Complete Questionbook (a popular British textbook, which received a Montreal edition in 1818), Abbé Sauri’s Compendium des institutions mathématiques de l’Abbé Sauri, and M. Despiau Choix d’amusements physiques mathématiques (London 1800) (Archibald and Charbonneau 1995: 10-11; Bibauld 1816: i-iv).

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Compared to Bibaud’s L’arithmétique en quatre parties, his 1832 arithmetic for elementary schools is simplified and shortened. L’arithmétique en quatre parties is 199 pages in length compared to his school-text which is 108 pages. L’arithmétique en quatre parties is organized according to its four named sections, and then subdivided into numbered chapters and sections. By comparison, Bibaud’s 1832 book is organized primarily by subject matter, and excludes his previous treatment of logarithms, probabilities, and recreational mathematics. Bibauld’s 1832 L’arithmétique is principally pragmatic. It includes calculations of currency appropriate to the country, complex multiplication and division focus on the calculation of pounds, shillings and pence. A significant section on decimals and calculating decimals is included, as is the rule of three, and sections dealing with the calculation of interest, exchange and trade.

The preface of both texts highlights Bibauld’s motivation to improve society through the publication of these works, from which he intends the reader to learn more mathematics. Bibaud dedicates his 1816 book to those who want to learn the subject but who lack a Master to teach them. In dedicating oneself to the text, Bibauld says, the reader will direct himself towards self- improvement, or at least towards maintaining mathematical skills he may have learned in school. Bibaud’s 1832 preface also explains how he sees his book functioning in society. Priced within reach of the less fortunate, he says, the book can be purchased by teachers, school trustees, or given as a reward to poor children, at a time when “le nécessité de l'instruction être universellement sentie dans la Province” (Bibauld 1832: 3). While his 1816 book notably cites previous school-textbooks as inspiration, the preface of his 1832 edition does not include credits to any source material.

In English Canada, apart from a few publications related to finance, mathematical printing also developed alongside the general need to teach practical arithmetic. At first local editions of successful American and British texts supplied the market for elementary arithmetical books. Francis Walkingame’s The Tutor’s Assistant, Being a Compendium of Arithmetic and Complete Questionbook, was extremely popular in Britain and America, and widely used in the early nineteenth century (Wallis 1963).193 Walkingame’s The Tutor’s Assistant was popular in Canada

193 The book was first published in 1751. Before the author’s death in 1783, eighteen different editions had been produced. Longman’s continued to publish the book (along with other publishers who issues editions) throughout

162 as well, with nine Canadian editions including printings in Picton, St. John, Toronto and Montreal (Archibald and Charbonneau 1995: 7). Six Canadian editions of Walkingame’s arithmetic exist within the Ontario Historical Textbook Collection at the Ontario Institute for the Study of Education (OISE).194

In the OISE collection, each copy of Walkingame’s The Tutor’s Assistant is printed in the crown octavo size with plain binding, however on inspection each differs from the other in its title page or contents. Comparing the 1830 and the 1841 “stereotype edition”, the contents of “Part I: Arithmetic in Whole Numbers”, appears in differing order although the content is the same. The setting of the 1844 edition is once again, different from the other two. The table of contents is presented differently in the 1844 Toronto edition with the section headings being “Integers, Vulgar Fractions, Decimal Fractions, Superficial Mensuration” rather than “Arithmetic in Whole Numbers, Vulgar Fractions, Decimals, Duodecimals, Questions” as it appears in the 1841 edition. Stereotyping was still fairly new technology in the first half of the nineteenth century. These Canadian editions reflect the many differences (typographic and organizational) of local editions when the same text was set many times at different printers.

The 1830 edition contains an advertisement for the publisher, J. A. Hosington of Montreal. Hosington’s list of book for sale includes, as well as Walkingame’s The Tutor’s Assistant, Simpson’s Euclid, Towles’ Astronomy, Ryan’s Astronomy, Gibson’s Surveying, Gough’s Arithmetic, Adam’s Arithmetic, and Dilworth’s Arithmetic.

An 1849 edition of Walkingame’s The Tutor’s Assistant (a stereotype edition) hails from Picton, announcing it was made from stereotypes plates. On the front cover is a blue paper advertisement pronouncing “Walkingame’s arithmetic, adapted for the use of schools in Canada, Authorized by the Board of Education, Upper Canada”. In the middle of the cover is an embossed illustration of

the nineteenth century, producing an estimated five to ten thousand copies per edition. What is thought to be the 179th edition was produced by Milner and Sowerby of Halifax (England) in 1854 and 1861 (Wallis 1963: 204). 194 Copies in the OISE collection include an 1844 copy published by Eastwood & Co. of Younge Street (Toronto), 1849 and 1853 copies published by Brewer, McPhail & C. of 46 King Street East (Toronto), an 1841 copy from Armour & Ramsay of Kingston and Montreal, an 1830 edition from J. A. Hosington and John Campbell of Montreal.

163 a cube with a small section missing, suggesting a volume problem. On the back is an advertisement for the printer J. McDonald. The advertisement states that McDonald, in addition to carrying for sale Walkingame’s The Tutor’s Assistant, offers for sale “various kinds of school books found in the country. Bibles and testaments, Miscellaneous works such as History, Biography, Political Philosophy, Temperance, … and stationary of every design.”

Early American mathematical textbooks were used and printed in Canada. Popular American arithmetics include Daniel Adams’ The Scholar’s Arithmetic (1801), which later became Adam’s New Arithmetic (1827), and Nathan and David Daboll’s Schoolmaster’s Assistant: Being a Plain Comprehensive System of Practical Arithmetic (1799).195 An 1834 edition of Daboll’s Schoolmaster’s Assistant resides in the Ontario Historical Textbook Collection at the Ontario Institute for Studies in Education.196 The book begins with six recommendations from American teachers hailing from Yale, Rhode Island College, and Plainfield Academy and Billerica Academy in Massachusetts. In the preface Nathan Daboll explains that his goal with the work was to furnish students and teachers with more examples, so that the student not be “hurried through the ground rules too fast for his capacity” (Daboll 1834: v). Daboll’s introduction of the Federal coin (on p. 20) within the context of whole numbers and addition is, he explains, so that readers can acquire an understanding of money even if they don’t proceed to later sections on fractions. In the sections on compound addition, multiplication and division, examples of how to add quantities of sterling money (pounds, shillings, pence), time (seconds, minutes, hours, days, weeks etc.), wine (gallons, quarts, pints), and other measures including apothecaries weight, cloth measure, Troy weight, and avoirdupois weight show, as do many of the other examples, how deeply rooted Daboll’s book is in the practical, local context of its readers (Daboll 1834: 44). Other parts of the book contain rules for calculating simple interest, compound interest,

195 Prior to the creation of regulated public schools, the use of textbooks was not mandated, and a plethora of different books were used in the 1820s period. In Hamilton’s earliest public schools, Daboll’s and Walkingame’s arithmetic books were used to teach mathematics (Smith 1905: 13). In Norfolk Country, arithmetics by Daboll, Dilworth, Pike and Deighman were used in the classroom. The York Common School used arithmetics by Walkingame and Gray (Parvin 1965: 9-10). Charles Hutton’s arithmetic is also mentioned by historians of education in Upper Canada as being in common use (Parvin 1965: 12). 196 Published in Ithaca by Mack & Green, and stereotyped by A. Chandler, New York. This copy was collected from Margaret Beckingham, a former Chairman of the Ontario Teacher’s Federation Centennial Library.

164 brokerage fees, annuities and currency exchange (particularly relevant because several states had their own currencies at the time).

Daboll’s textbook is also subtly, but proudly, American. Various examples require calculations involving the salary of the President. Daboll’s notes praise Congress for the wisdom of introducing decimal currency, while other examples involve calculation of the national debt of England (Daboll 1834: 23, 53, 69). Daboll’s Schoolmaster’s Assistant embodies the national character of its author.

The landscape for early mathematical textbooks in Canada frequently reflected political realities. American textbooks represented republican and democratic ideas. Motivation for the production of Canadian textbooks often derived from a desire to displace American textbooks with books reinforcing British loyalties. The desire to displace American textbooks was particularly present in Upper Canada, where American books were often cheaper and easier to obtain than British ones. In Upper Canada, printers turned out numerous copies of William Fordyce Mavor’s English Spelling Book and Lindley Murray’s English Reader, for example, as a way of reinforcing allegiance to British language and culture (Dewalt 1995: 19).197

Schoolbooks of all kinds, including mathematical ones, carried symbolism communicating the social and political identities of their authors and publishers. John Strachan, who wrote the first arithmetic textbook for Upper Canada, Concise Introduction to Practical Arithmetic: For the Use of Schools (Montreal 1809), was an advocate for the standardization of education and the domestic production of textbooks (Archibald and Charbonneau 1995: 7). Strachan was an important figure in the development of institutions of education, and was involved in the founding of both McGill and King’s College (now part of University of Toronto). He became the first Inspector of Schools in Upper Canada, advocating for the standardization of education and the development of grammar schools (i.e. secondary schools) (Archibald and Charbonneau 1995:7).

197 For more about politicization and the use of text books in Upper Canada, see chapter one, “Textbooks in Upper Canada before 1846” (Parvin 1965), particularly pp. 12-16, and pp. 29-34 in chapter two of the same.

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When Strachan published Concise Introduction to Practical Arithmetic, he was a relatively new resident of Upper Canada just beginning his career in education. After arriving in Kingston in 1899 to become a schoolmaster, Strachan “experienced much inconvenience from the want of school books”, thus motivating his compiling of several treatises into this publication, for the “greater convenience” of his school (Strachan 1809: iii). Seeing his duty as that of making “a useful book rather than an ingenious one”, Strachan borrowed material from Charles Hutton and Robert Hamilton, as well as compiling his own problems used in the classroom (Strachan 1809: v).198 When given the opportunity, Strachan says, he gives his pupils questions in Geography, Natural Philosophy and Astronomy (as well as in arithmetic) (Strachan 1809: vi). Some of these questions, mostly about calculating solar cycles, are included in the appendix. Several practical topics are covered by Strachan’s treatise, including surveying, calculation of annuities, simple and compound interest, the purchasing of stock, forms of receipt, as well as sections on the usefulness of certain measures to the bricklayer, mason, carpenter and joiner, slater, tiller, plasterer, painter and glazier (Strachan 1809: 175-76). As well as sections covering the usual arithmetical operations, Strachan’s Concise Introduction to Practical Arithmetic shows how to calculate with fractions and decimals, and introduces working with proportions, arithmetical and geometric progressions, and calculating roots.

In the early nineteenth century it was a constant source of debate whether Upper Canada should become a more autonomous political entity or stay a servant of the British Empire. These views were reflected in the titles of some early mathematical textbooks. William Phillips, identified as a teacher in ladies schools, authored A New and Concise System of Arithmetic, Calculated to Facilitate the Improvement of Youth in Upper Canada in 1832. By contrast the title of G. and J. Gouinlock’s arithmetic textbook makes a declaration of Imperial loyalty. A Complete System of Practical Arithmetic, for the Use of Schools in British America, to Which are Added, A Set of Book-Keeping by Single Entry, and a Practical Illustration of Mental Arithmetic, Federal Money, Receipts, Bills of Exchange, Inland and Foreign, Explanation of Commercial Terms, etc.

198 Charles Hutton became a professor of mathematics at the Royal Military Academy in Woolwich. Before that, he published several books including The Schoolmaster’s Guide, or A Complete System of Practical Arithmetic (Newcastle Upon Tyne, 1764). Strachan may have been referring to Robert Hamilton’s Introduction to Merchandize: Containing a Complete System of Arithmetic, A System of Algebra, Book-Keeping in Various Forms, An Account of the Trade of Great Britain, and the Laws and Practices Which Merchants are Chiefly Interested In (2 vols. Edinburgh, 1767). Hamilton was a professor at Edinburgh University in the eighteenth century.

166 the Whole Adapted to the Business of Real Life, to the Circumstances of the Country, and to the Present Improved State of Commerce (Hamilton, 1842).

The Methodists, who were disenfranchised by the Tory establishment from control over their educational institutions (King’s College and Upper Canada College), founded their own institution, Upper Canada Academy at Coburg, Ontario (later, Victoria College in the University of Toronto). Canadian-born Methodist Egerton Ryerson, the first principal of Upper Canada Academy, was deeply loyal to the British Empire and supported close affiliation between the colonies (Archibald and Charbonneau 1995: 9).

The copy of Gouinlock’s arithmetic that resides in the Ontario Historical Textbook Collection has several pages of testimonials added to the front by the publisher, Hugh Scobie. The first page contains excerpts of praiseworthy comments about Gouinlock’s geography from various regional newspapers, as well as from the superintendent of education from the township of Whitby as well as Hamilton’s Superintendent of Schools. The gist of these comments are that Gouinlock’s arithmetic is the best arithmetic to emanate from a Canadian press, and that one of its special benefits is that it includes exchange from Canadian money to British and American money (as well as to several other currencies). In the author’s own words, it is the best suited textbook for the needs “of teaching, to real business, the present state of commerce, and the circumstances of the country” (Gouinlock 1847: i).

Similar to Daboll’s arithmetic, Gouinlock introduces up front several measures, conversions and tables that might be useful to a nation interested in natural resources and their processing. Apart from increments used to give wool weight, hay and straw weight, lint or flax yarn measure, several other interesting conversions are given. For example, useful in the very practical aspect of the book’s examples, it is given that 10 skins = 1 dicker of leather, 56 lbs. = 1 firkin of butter, 120 lbs. = 1 faggot of steel, or that 500 herrings = 1 barrel, 280 lb. avoirdupois = 1 sack flour. Calculating the quantities of goods bought and sold were important features in the examples used in both Daboll’s and Gouinlock’s arithmetics.

Montreal dominated English and French language printing until Confederation, after which time English language printing grew stronger in Toronto (Dewalt 1995: 15, Leroux 2007). By mid- century printing shops had been set up in small to medium sized centers including Kingston,

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Saint John, Charlottetown, York (Toronto), Picton, Yarmouth, Mirimichi, Hamilton, Peterborough and Sherbroke (Dewalt 1995: 15).

By the mid-nineteenth century, mechanization and industrialization arrived in the world of Canadian printing. The Queen’s printer George Paschal Desbarats in Ottawa acquired a steam- printing machine in 1842. In Montreal, John Lovell was the first printer to apply steam printing to trade books and periodicals in 1847. By 1867 Lovell’s operated twelve large steam-presses, making his operation for a long time the largest in the country (Parker 1990).

In the half-century between 1800 and 1851, growth in Canadian printing had been swift. The 1851 census records 631 printers and 121 bookbinders. Moreover, printing by that time had become an important component of Canada’s economic activity. In the 1871 census six printing firms were ranked in the top 150 Canadian industrial establishments.199 The building of the Great Western and Grand Trunk railways in the 1850s connected many previously isolated places, and allowed for the movement of people, mail, and products (including printed products) to and from many more communities than had been previously possible. Telegraphy lines were also laid, and roads, stagecoach services and steamships allowed information to be gathered and distributed more cheaply and easily.

As in Britain, most of the growth in printing was related to increased periodical and newspaper printing. In 1857 British North America had 291 newspapers on record (Dewalt 1995: 18). Besides newspapers, printers also undertook job work and government contracts, as well as printing ephemera, directories and catalogues. The first illustrated Massey catalogue was printed in 1862 (Massey was a successful Canadian producer of agricultural and farming machines). Educational primers were a common product of the early presses. These were guaranteed a large enough sale to make them a reliable product in which to invest capital.

Throughout the nineteenth century, books were also imported into Canada. In the eighteenth century, books were brought back to Canada during the shipping season. Travellers put books they had brought back from abroad, up for sale. Individuals also sent orders for books with

199 These firms were Hunter, Rose & Co. (Toronto), Robertson & Cook (Toronto), James Beaty (Toronto), The Globe (Toronto), Isaac B. Taylor (Ottawa) and John Lovell (Montreal) (Dewalt 1995: 22-23).

168 friends who were going overseas. Records of the book trade exist from even this early time in the colony. For example, an advertisement in Halifax’s Royal Gazette from 23 June 1789 lists 230 books for sale on subjects including law, medicine, mathematics, navigation, and architecture, that had been brought into the port of Halifax on the brig Ceres (Parker 1985: 16).200

In the nineteenth century, publishers in the United States, Britain and France produced large editions of standard works, especially the Bible, for export. As well as foreign-printed Bibles, Canadian booksellers also sold book series, or “libraries”, produced by foreign publishers (Dewalt 1995: 14). The Library of Useful Knowledge, a series produced by the Society for the Diffusion of Useful Knowledge, is an example of such a series, containing books on subjects including the sciences, technology, and other self-improving and practical subjects. The new technologies of stereo- and electrotyping also allowed printing plates, from which books could be easily reproduced, to circulate from one country to another. This allowed Canadian printers to produce small editions of books that had proved popular or standard elsewhere.

In general, producing books domestically was more expensive than purchasing imported books. Prior to local paper production in Canada, all the paper required by the colony for the entire year was brought over during the shipping season. In winter the channels became locked up by ice and stormy weather, and the colony was effectively cut off from trade (Dewalt 1995: 22). Only almanacs, primers and catechisms, which were guaranteed a large sale, were worth the trouble to print locally. As Dewalt reflects, “Although local paper mills had been established as early as 1804, large quantities of this essential material were still imported at great expense. Because of the high costs of type and composition, which were incurred up front, and of paper and presswork, which did not decline with volume, the ideal press run for a book [around 1840] was about 1,500 copies. Few books in British North America could hope to find a market of even this size” (Dewalt 2007: 89).

200 James Raven develops an interesting overview to the importing of books to North America in the sixteenth and seventeenth centuries (Raven 1997). While focusing mainly on New England, it does contain some data for the importing of British and European books into Nova Scotia, Newfoundland, and Canada.

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In the nineteenth century several local mills began producing paper.201 At first local paper was wove paper made out of rags and linen. But the industry largely moved on to develop paper from wood pulp in the 1860s and 70s. This paper was used to make wrapping paper and newsprint, but little to no writing or fine book paper was produced in Canada (Dewalt 1995: 38). Printer’s ink, another necessary material for printing, was imported until the 1870s.

3. Mathematical and scientific culture in Canada

Despite the many technological changes that ameliorated the conditions of communication, local book production, travel and trade, mathematics in Canada remained in a nascent state for many years. Over the course of the nineteenth century, mathematical education became more rigorous, with more opportunities for students to study advanced mathematics and garner some insight into the purer side of the subject. Archibald and Charbonneau note that mathematical research of any sort in Canada remained modest until at least the 1930s or after. Factors contributing to the difficulties included a lack of direct contact between mathematical educators within Canada, compounded by their lack of contact with mathematical researchers abroad. Canadians were held back on all fronts, according to the necessary conditions for a mathematical culture, as defined by these authors. They note that an extensive exposure to mathematical literature was difficult to come by. Little value was placed on the pursuit of pure research, and the tiny mathematical community was fully engaged with teaching and widely geographically separated (Archibald and Charbonneau 1995: 20).

Scientists at the time confirm the view that Canadian science in general was in a rudimentary state. James Loudon wrote in 1877, as President of the Royal Canadian Institute, that “The growth of science in Canada, though progressive, is still in a rudimentary state, and stands in want of increased stimulus, both from public and private sources. We have yet to see developed the large and liberal spirit that prompts private citizens to devote their fortunes to the endowment of seats of learning and the foundation of museums, observatories, and free public libraries …the work of building up science has but yet commenced in this country” (Riehm and Hoffman 2011:

201 For instance, the Argenteuil Paper manufactory (founded 1804), the Acadian Paper Mill (founded 1819), James Crook’s mill in West Flamborough U. C. (founded 1827), and the Eastwood & Skinner mill on the Don River, York (now Toronto, founded 1827) (Parker 1985: 49).

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68).

In his inaugural address to the Royal Society of Canada in 1881, President William Dawson, the Nova Scotian geologist and natural historian, lamented that science in Canada had been hindered by the “evils of isolation”, and a lack of books, libraries, publications, professional structures, special collections, and employment for men wishing to pursue science. Dawson reflected, “…It is a time of breaking-up ground and sowing and planting, not a time of reaping or gathering fruit…in science and in literature, in art and education…we see only the rudiments and beginnings of things, but if these are healthy and growing, we should regard them with hope” (Dawson 1883: 6).

One of the critical factors Dawson cited as retarding the growth of science in Canada was a lack of a printed culture of science. This dearth of a printed culture included a lack of sources for learning and for research. Dawson reflected that as a boy his access to scientific books and publications was scant.202 However, it wasn’t just scientific sources that Dawson said were missing. Dawson also remarked at length upon how the lack of a capacity to publish new scientific results in Canada had several detrimental effects on one’s scientific career.

In his address Dawson remarked at length on the lack of availability for adequate scientific publication in Canada. He made three points about the importance of publication. First, he noted that difficulty with securing publication in some cases lead to the loss of priority for the scientist’s work. Furthermore, if the quality of the printing is poor, then the work itself is often also assumed to be of inferior quality, and this can lead to the marginalization of one’s scientific work. A scientific publication may gain credibility because it has received sumptuous presentation, whereas a badly printed one may be overlooked. Lastly, the inability to publish results also meant that Canadian accomplishments are permanently lost or forgotten. Quoting from Dawson’s address:

Again, means are lacking for the adequate publication of results. True we have the reports of the Geological Society, and Transactions are published by some of the local societies, but the

202 As the son of a bookseller from Pictou Nova Scotia, Dawson’s access to books and printed materials had probably been better than most (Sheets-Pyenson 1995: 17).

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resources at the disposal of these bodies are altogether inadequate, and for anything extensive or costly we have to seek means of publication abroad; but this can be secured only under special circumstances; and while the public results of Canadian science become so widely scattered as to be accessible with difficulty, much that would be of scientific value fails of adequate publication, more especially in the matter of illustrations. Thus the Canadian naturalist is often obliged to be content with the publication of his work in an inferior style and poorly illustrated, so that it has the aspect of inferiority to work really no better, which in the United States or the mother country has the benefit of sumptuous publication and illustration. On this account he has often the added mortification of finding his work overlooked or neglected, and not infrequently while he is looking in vain for means of publication, that which he has attained by long and diligent labour is taken away from him by its previous issue abroad. In this way also it very often happens that collectors who have amassed important material of great scientific value are induced to place it in the hands of specialists in other countries, who have at their command means of publication not possessed by equally competent men here. The injury which Canadian science and the reputation of Canada sustain in this way is well known to many who are present and who have been personal sufferers (Dawson 1883: 8-9).

Dawson’s suggestion that Canadian scientists saw their work produced in Canada in “an inferior style” and “poorly illustrated” giving it an “aspect of inferiority” compared to work done elsewhere, is a particularly lucid and provocative suggestion. Making Canadian culture for Canadians often involved lesser production values compared to producers serving bigger markets. As printing historian Brian Dewalt also observed, this economic reality impacted Canadian cultural producers regardless of whether the genre in question was literary or scientific: “Canadian [publishers] competed with British and American competitors who used rapid cylinder presses and industrially produced wood engravings to splash their pages with rich- looking and impressive illustrations” (Dewalt 1995: 39).

Dawson advocated that the new Royal Society of Canada acquire the means to publish its own Transactions as one way to ameliorate the status of Canadian science (Sheets-Pyenson 1995: 194). The first Proceedings and Transactions of the Royal Society of Canada was published in 1883, and proudly noted that it was printed in Canada with Canadian-made materials. With some irony, however, the Canadian wood-pulp paper on which it was produced is now brittle and disintegrating. The longevity of this important landmark in Canadian science may not be great.

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The author notes that the copy she viewed was kept unceremoniously in a storage area of a library basement, not in a special collection. The fact that our earliest local publications are not well preserved today (compared to prized special collections containing mostly rare books from other locales) perpetuates judgments of poor value to be made about Canadian contributions to culture and history.

As President of the Royal Society of Canada, William Dawson, and James Loudon, as President of the Royal Canadian Institute, expressed dismal views of the state of science in Canada. External attitudes reinforced this self-assessment. When the British Association for the Advancement of Science proposed to hold their 1884 annual meeting in Canada, 141 members protested the location. While Canada may not have been a convenient location for a scientific meeting of primarily British membership, the question was raised whether Canada deserved to play host to such a prominent scientific meeting. An article in the Times observed, “a meeting in Canada would merely be a glorified picnic of important men of science, who could have no serious purpose in visiting Canada, a land not great in science…humbler men and less advanced thought would serve equally well for her instruction” (Quoted in Riehm and Hoffman 2011: 23).

Nevertheless, the British Association did meet in Canada, holding their 1884 meeting in Montreal, and returning to meet in Toronto in 1897. Reports about the 1884 meeting suggest it was a success. Nature reported “the addresses are quite up to the average” (Anon. 1884a: 410). With regards to Prof. Lodge’s lecture on “Dust”, Nature’s report on the meeting suggested “He did well to speak strongly to a practical people of the rewards of pure scientific research, though we trust that one result of the meeting will be to open the eyes of the Canadians to the utility of substantially encouraging such research” (Anon. 1884b: 439). In a speech to attendees, the Governor-General Lord Lansdowne said, “In a young country [scientific] pursuits are conducted in the face of difficulties, competition and with material activity necessarily absorbing the attention of a rapidly developing community. We may claim for Canada that she has done her best, and has spared no pains to provide for the interests of science in the future. She has scientific workers known and respected far beyond the bounds of their own nation” (Anon 1884b: 439).

Despite the positive tone of Lansdowne’s words, Canadian born and educated scientists faced prejudice from within Canadian institutions, as well as from outside of them. When James

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Loudon, a tutor of mathematics at the University of Toronto, was proposed in 1875 for appointment to the Chair of Mathematics and Natural Philosophy, he faced opposition on the grounds that his birth and education in Canada disqualified him for the position. The standard at the time was for such positions to be filled by men from Scotland or Britain, who had trained there. In 1875, responsibility for university appointments resided with the Ontario Legislature. A letter-writing campaign saw over seventy letters sent to the Legislature in support of Loudon assuming the position. When Loudon did assume the Chair of Mathematics and Natural Philosophy at the University of Toronto, he was the first native-born Canadian to achieve the title of Professor at an English-language Canadian university (Riehm and Hoffman 2011: 16).

If the practice of science in nineteenth century Canada was difficult and limiting, the practice of original mathematics was non-existent. Loudon for example, ascended the ladder into university administration after becoming Chair of Mathematics and Natural Philosophy. While he was a devoted and lifelong advocate for Canadian science, he published little to no original science or mathematics (Riehm and Hoffman 2011: 21). At the turn of the century, the prospect of expanding the horizons of Canadian mathematics can be identified strongly with a few trail- blazing individuals, most of whom had travelled abroad to study and brought their knowledge and experience of research back to Canada (Archibald and Charbonneau 1995: 27). John Charles Fields is the most renown of these individuals.

When John Charles Fields (1863-1932) graduated from the University of Toronto in 1884, no Canadian University offered a PhD in mathematics. Many of Canada’s mathematics teachers were British, at a time when British universities did not grant doctorates, either. Fields’ desire to pursue a doctorate signaled his high opinion of research, as it was not required to obtain employment (Barnes 2007: 8).

In his lifetime Fields recorded many firsts in Canadian mathematics (further biographical details on Fields are given in section 6 of this chapter). During his tenure as mathematics professor at the University of Toronto, Fields supervised Samuel Beatty, the first person to attain a doctorate in mathematics from a Canadian university, in 1915. Fields was the first Canadian to publish a research monograph in mathematics, the book, Theory of the Algebraic Functions of a Complex Variable (1906). However, Fields’ book was not published in Canada, but overseas in Berlin by Mayer & Müller and in Uppsala, Sweden by Almqvist & Wiksell (Riehm and Hoffman 2011:

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63-4). While his monograph received lukewarm reviews abroad, the perception of Fields within Canada was that “he was respected as a research mathematician and it was accepted that, though his work could not possibly be understood by the public, it could be admired” (Riehm and Hoffman 2011: 77).

Despite all that he had accomplished for mathematics in Canada during his lifetime, Fields still admitted (in 1932) “…progress in mathematics in Canada up to the present has not been all that might have been hoped for, things look more promising for the future. There is a small but increasing group of the younger men who are interested in mathematical research, and some of the latter appointments have been encouraging” (Archibald and Charbonneau 1995: 1).

We can find many accomplished scientific workers who were born, lived and worked in Canada, of whom Fields was one, who turned to foreign publishers and publications to handle their monographs and journal articles. William Dawson self-published works on geology and paleontology in Nova Scotia as well as abroad in Edinburgh and London.203 Dalhousie’s Munro Chair of Physics James Gordon MacGregor turned to Macmillan and Company who published his 1887 treatise on kinematics and dynamics in London and New York (section 5 of this chapter).

It has been observed that many publications in science that did occur within the Canadian context (i.e., printed in Canada) remained obscure and did not have a wide impact (MacDonald and Connor 2007: 182). Moreover, the authors of those Canadian publications also remained unknown, as Bertram MacDonald and Jennifer Connor have noted in their article about scientific authorship in History of the Book in Canada. No known biographical information exists for more than 51 per cent of the authors listed in a bibliography of Canadian scientific writings published before 1914 (MacDonald and Connor 2007: 182). Despite the majority of scientific articles, books or reports published in Canada on record being signed by the author (not published anonymously), “Many authors were obscure…leaving little mark in Canadian history” (MacDonald and Connor 2007: 181).

203 William Dawson’s Acadian Geology was published in 1855 in Edinburgh, London and Pictou, Nova Scotia, by Oliver and Boyd and William Dawson (Sheets-Pyenson 1995: 33-35). In 1868, Acadian Geology was reprinted by Macmillan and Co. of London, who also published a supplement to it in 1878 (Foster 1891: 170, 336).

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Authors who sought recognition at home or abroad sought out American or European publishers. Luckily for Fields, years of attending international conferences and study abroad meant that he had an excellent network of friends in the international mathematical community. In 1902 Fields returned from his post-doctoral work in Europe to take up a teaching job at the University of Toronto. At this time Fields sent the manuscript for his book, Theory of the Algebraic Functions of a Complex Variable, to Gösta Mittag-Leffler, editor of Acta Mathematica, asking for advice regarding its publication. Mittag-Leffler recommended the Berlin publishing house of Mayer & Müller, who had published some of Karl Weierstrass’s work. Mayer & Müller accepted Field’s book and typeset it, but when the book encountered delays because the press was busy with other work, Mittag-Leffler offered to facilitate its printing at the same press that printed for Acta Mathematica, Almqvist & Wiksell Ltd., in Uppsala, Sweden. As Elaine McKinnon Riehm and Frances Hoffman note in their biography of Fields, he visited both Berlin and Sweden in order to oversee the book’s production, and “bulky manuscripts and proofs crossed the Atlantic; and finally, in 1906, [the book] appeared” (Reihm and Hoffman 2011: 62).

Archibald and Charbonneau’s reasons for the slow development of mathematics in Canada echo closely the reasons given by Dawson in his address to the Royal Society of Canada. The lack of access to the most up-to-date sources and experts, as well as the difficulty to create a printed record of accomplishment, are significant aspects of the history of mathematics and science in Canada: “Reasons for the lack of research late in the nineteenth century are not hard to find. While in fields such as physics and chemistry it was still possible at that time for a relatively inexperienced student to undertake experimental work of a meaningful sort, participation in mathematical research at an international level required an extensive exposure to the literature and, ideally, to working research mathematicians. Such literature was difficult to come by in Canada. Furthermore, there were few rewards for engaging in research beyond personal satisfaction” (Archibald and Charbonneau 1995: 20).

The next three sections will continue to examine the themes outlined here by looking at the examples of three scientific men, also published authors, in whose lives and experiences we can see the Canadian context evolve over the three generations. John Herbert Sangster (1831-1904) was born in England but educated in Canada. He worked for many years as a teacher in Canada’s developing public education system before publishing a series of successful Canadian schoolbooks on mathematical and physical topics. James Gordon McGregor (1852-1913) was

176 born in Nova Scotia and trained in natural philosophy and physics in Edinburgh, Leipzig and London. He returned to take up a uniquely well-endowed chair of Physics at Dalhousie University in Halifax, where he remained an engaged and active researcher. He published his monograph with Macmillan and Company in London. John Charles Fields, whose monograph was published abroad in 1906, worked towards furthering of the cause of science and mathematics in Canada for the next twenty years. His involvement with the publication of the Proceedings of the International Mathematical Congress, Toronto, August 11-16, 1924, at the University of Toronto Press during the years 1924-28 is examined in section (6).

4. John Lovell, John Herbert Sangster and Lovell’s series of schoolbooks

John Lovell (1810-1893) was born in Ireland and immigrated with his family to a farm outside Montreal in 1820. Lovell moved to the city of Montreal in 1823 where he got his start in the printing business. He apprenticed with printer Edward Vernon Sparhawk at the Canadian Times and Weekly Literary and Political Recorder, and subsequently worked for several Montreal newspapers including the Montreal Gazette and L’Armi du people, de l’ordre et des lois. He co- founded the tory newspaper the Montreal Daily Telegraph. After the 1837 Rebellion (The Patriot’s War, to Quebecers), Lovell quit the newspaper publishing business and began to focus on job printing, as well as publishing books, magazines, and directories (Parker 1990).

With his brother-in-law Lovell created the first successful literary magazine originating in British North America. The Literary Garland published poems, stories, illustrations and musical compositions by local writers and artists, including John Richardson and Susanna Moodie. Lovell also collaborated on the first children’s magazine in Canada, Snow Drop, or Juvenile Magazine, which ran for a brief period in the 1850s.

As a book publisher, Lovell had broad ranging tastes. He published poetry, law, history, music books and sheet music, religious works, and Canadian fiction in English and French. In his publications Lovell attempted to nurture a national literature, but cannily protected himself from almost certain financial loss with a stable income from rewarding printing contracts. Lovell also specialized in directories and gazetters which served a local market and for which there was no foreign competition. Lovell eventually gained a lucrative contract to print for the Legislative Assembly, which lead to his establishment of offices in Toronto and Quebec. In 1853 his

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Toronto office employed 41 people in addition to apprentices. His Montreal site employed 30 people.

From the late 1850s Lovell began publishing school textbooks, and by the 1860s he began marketing these under the moniker Lovell’s Series of School Books, the first set of Canadian textbooks for Canadian schools.204 John Herbert Sangster was the author of the arithmetic, algebra, natural philosophy, and chemistry books in the series. Lovell’s schoolbooks were successful and assured a large sale, as for several years Lovell was the only Canadian publisher who had a native book approved by the catalogue of authorized textbooks. In order to be eligible for government grants, schools had to adopt textbooks from this list.205

John Herbert Sangster had an interesting personal involvement with the development of public education in Canada before becoming a successful textbook author. Sangster was born in London England. His family immigrated to York via the United States. He arrived in Upper Canada 1836 and his family settled on a large piece of land northeast of the city of York (now Toronto). A studious youth with an appetite for mathematics, he attended Upper Canada College and in November of 1847 entered the Toronto Normal School (i.e. training college) where he was the second person to ever receive a certificate there as a Common School Teacher. Apparently Sangster had come to the attention of the Chief Superintendent of Education, Egerton Ryerson, through a paper Sangster had written on algebra, which had impressed Ryerson. Subsequently Ryerson appointed Sangster as second master in the Provincial Model School in 1848 (Bailey 1981: 179).

204 In her history of authorized textbooks used in Ontario schools, Viola Parvin cites Strachan’s A Concise Introduction to Practical Arithmetic (1809) as the first textbook written especially for students of Upper Canada (Parvin 1965: 6). In the period prior to 1846 schools used a great variety of mathematical textbooks many of which originated in Britain and America. The first textbook series sanctioned for use in Upper Canadian schools were the Irish National School Books, selected by the newly instituted Board of Education in 1846. The Irish series included several books in mathematics, including Arithmetic, Key to Arithmetic, Arithmetic in Theory and Practice, Elements of Geometry, Mensuration, and Appendix to Mensuration. For the next twenty years, until Lovell began his schoolbook series, the Irish National books remained the only authorized textbooks in the province (Parvin 1965: 26). 205 By 1867 Sangster’s Natural Philosophy, and National Arithmetic in Theory and Practice (Adapted to the decimal Currency) were on the approved list.

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Sangster began his career in education under tumultuous circumstances in which major changes were being made to educational infrastructures in Canada West (previously, Upper Canada). In 1840 the Act of Union brought together the governance of Upper and Lower Canada, which stimulated many bureaucratic overhauls, including the installation of Egerton Ryerson as the Chief Superintendent of Education for the Province of Canada in 1844, and the creation of a Board of Education to oversee the development of education in the Province. In 1847 an Act was passed granting cities and towns larger powers in the governance of Common Schools, and municipal governments responded by setting up Boards of Trustees (Smith 1905: 21). These new governance structures brought about major changes to the educational landscape. Centralized “model schools” were set up, run by teachers who had received formal teacher training, with children organized into separate classes, whose work then received grading. Hamilton’s Central School, for example, was a two-story building with twelve rooms with the potential to accommodate 1,000 students. It was the first school of its kind in British North America (Bailey 1981: 179; Smith 1905: 68).

Changes were not received without controversy, however, as the local schools and teachers that had been operating prior to these reforms were largely displaced by the new system. Sangster became the first Principal of Hamilton Central School in 1853 (Smith 1910: 90). At the time, taking on the Principalship of the school was considered a risky proposition given the hostility to the venture expressed by the local community. However Sangster persevered and served as Principal from 1853-1858, forging a new school and applying a new educational structure that came to be regarded, eventually, as a success (Bailey 1981: 179). Sangster was only twenty-one when he accepted the job. He later reflected, “I staked all on the venture. I came to introduce a new system of education. Failure meant to me much more than personal disaster”.206

At Central, Sangster taught the senior boys division arithmetic, algebra and Euclid, natural philosophy and astronomy. He would have worked extensively with the Irish National schoolbooks series, as these were the approved books used in the school (Smith 1905: 29).

206 See “Schooling Open Only to Few Children 100 years ago”, The Hamilton Spectator, 15 July 1946, A History of Education in Hamilton, Scrapbook of Clippings Vol. 1, Hamilton Public Library Reference Collection.

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In 1858 Sangster accepted the position of assistant teacher at the Model Grammar School of Toronto. This was the provincial model for secondary schools. Sangster served as headmaster from 1865-1871. It was during these Toronto years that Sangster developed and published his textbooks for Lovell’s schoolbook series on mathematics, physics and chemistry (Bailey 1981: 179). The library at the Toronto Grammar School contained two thousand volumes to which scholars had free access, something Sangster may have profited from when he prepared his textbooks for publication.207

Two copies of the first edition of Sangster’s National Arithmetic are held in the Ontario Historical Textbook Collection. The first edition was printed in 1860 by Lovell in Montreal and sold simultaneously by the bookseller R. & A. Miller in Montreal and in Toronto. In the preface to the work, Lovell explains how his textbook fills a need within Canadian education: “it has been the constant aim of the author to present to Canadian teachers and students as a [sic] thoroughly reliable Treatise on the Theory and Practice of Numbers, and as an Arithmetic, in some degree, commensurate with the higher qualifications of teachers and the improved methods of instruction now generally found in our schools” (Sangster 1860a: 3). Sangster locates his book as designed to serve the new school system, one in which teacher qualifications were mandatory and multi-room graded schools replaced the one-room schoolhouse.

By the time of the National Arithmetic’s publication in 1860, Sangster and Egerton Ryerson were good friends. According to Sangster, Ryerson himself requested Sangster write a mathematical book designed for the new school system (Sangster 1860a: 3). Sangster’s book was one of the first Canadian textbooks on the approved list, along with a few other Canadian books written by either friends of Ryerson or members of the Council of Public Instruction. Having one’s textbook placed on the approved list was essentially a form of patronage, as such books were guaranteed a large sale. The fact that all the Canadian books on the list were written by people closely connected to Ryerson and the decision-makers who made the list, did not escape scrutiny or public notice, and in fact drew much public criticism (Parvin 1965: 39).

207 See “Saturday Musings”, 29 January 1921, A History of Education in Hamilton, Scrapbook of Clippings, Volume 1, Hamilton Public Library Reference Collection.

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Sangster’s aim with the National Arithmetic, he explains, was merely to adapt the Irish National treatise on arithmetic to the decimal currency and abbreviate some of the more tedious rules. While admitting to borrowing liberally from “whatever [textbooks] he considered good”, he also claimed authorship: “so many alterations and improvements suggested themselves…the Treatise, as at present issued, is, in all essential respects, an entirely new book” (Sangster 1860a: 3).

From the three earliest copies of Sangster’s National Arithmetic present in the Ontario Historical Textbook Collection, it appears that the book may have received several reprintings in the first year alone. One of these books contains a four page advertisement from Lovell dated December 1859, which advertises forthcoming schoolbook titles in geography, history and grammar as well as First Book of Arithmetic, also to be authored by Sangster, listed as “in preparation”. In the advertisement, several of the schoolbook titles are advertised as “in preparation” in the year 1859. This suggests Lovell was a publisher more than happy to capitalize on what he perceived to be a successful and profitable bandwagon: the production of textbooks for the approved list. The final page of the advertisement announces R. & A. Miller as exclusive agents of Lovell’s National School Books series, branding themselves as the “National School Book Depot”, and as located on St. François Xavier Street in Montreal and on Yonge Street in Toronto.

The second edition of the National Arithmetic appeared in 1860. A few changes were made to the second edition. While a small list of errata was included in the first edition, these errors had been corrected in the second. A small publisher’s note says, “the rapid sale of the book having necessitated another edition, these errors have been corrected; and the Publisher has the satisfaction, in issuing this edition, of stating that it has undergone the most rigid and careful revision at the hands of the Author. The next edition will be printed from Stereotype Plates” (Sangster 1860b: 8). On the title page, the book now added the moniker “Sanctioned by the Council of Public Instruction for Upper Canada” as well as the note “Second edition: Carefully revised and corrected”.

In the preface to the second edition, Sangster thanks his fellow teachers in Canada for the kind and welcome reception they have given the book. The second edition also contains three pages of publisher’s advertising bound into the end of the book. The first page provides testimonials from several Canadian newspapers as to the quality of Sangster’s book. Also interesting to note in the following pages are the speed at which Lovell was adding to their schoolbook series. The

181 advertisement, dated April 1860, noted ten new titles in their schoolbook series listed as “just published”, three in preparation, and two in the press.208 Sangster must have been busy in 1860 as his Elementary Arithmetic and Notes and Exercises in Natural Philosophy were listed as “just published” in April of that year, with his Key to the National Arithmetic listed as “in press” at the time and his Elementary Treatise on Algebra described as “in preparation”.

By the time the third edition of Sangster’s National Arithmetic was released in 1862, Lovell had established itself as a major publisher of textbooks, with Sangster as their major author in mathematics and science. In 1862 they had fourteen schoolbook titles available, with six more in progress. English textbooks printed from stereotype plates were also printed in Canada and offered for sale by Lovell.209 An 1866 edition of the National Arithmetic wrapped in a Lovell advertisement dated 1870 shows that Lovell had twenty-nine textbooks in their school books list by that time, with ten of these, on subjects such as arithmetic, algebra, natural philosophy and inorganic chemistry, written by Sangster. In the same 1870 advertisement is the first appearance of a motto Lovell’s had created for themselves. The motto promotes a buy local buy Canadian sentiment. The wrapper on the book has a border, and within the border is printed the phrase “Encourage home talent. Encourage home industry. Encourage home production. Encourage Lovell’s series of school books” (Sangster 1866). Its placement within the boarder literally surrounds the title of the book with this sentiment.

Canadian confederation in 1867 joined the Province of Canada with New Brunswick and Nova Scotia, creating a federal Dominion of Canada with four provinces: Ontario (formerly Canada West), Quebec (formerly Canada East), New Brunswick and Nova Scotia. Within this context, Lovell’s schoolbook series of the 1860s, and its attendant motto, aligned with the country’s emerging national identity. John Herbert Sangster, who had cut his teeth in the school system as Principal at Hamilton’s Central school, was well placed to write books for the series. Sangster

208 Just published titles included Elementary Arithmetic, by J. H. Sangster, Book-Keeping by Single and Double Entry by John G. Dinning, Notes and Exercises in Natural Philosophy by J. H. Sangster, The Elements of Elocution by Jonathan Barber, Outlines of Chronology edited by Mrs. Gordon, The Classical English Spelling Book by George G. Vasey, The General Principles of Language by T. Jaffray Robertson, English Grammar Made Easy by George G. Vasey, and British American Reader by J. Douglas Borthwick. 209 See the publisher’s advertisement at the back of (Sangster 1862).

182 was an experienced teacher, and he held a position at one of the most important schools in the most populous area of the country.

Connections to the social and political realities of the nation are not hard to find in Sangster’s textbooks. The title pages make mention of nationality: National Arithmetic, in Theory and Practice; designed for the use of Canadian Schools (3rd edn. 1862); Elements of Algebra; Designed for the use of Canadian Grammar and Common Schools (1864). Sangster was also identified on the title page as affiliated with the Normal School for Upper Canada.

John Lovell, who since the beginning of his career had shown support for local writers, was conscious of how a series of Canadian schoolbooks could be valued for nationalistic reasons. In his promotional materials for Lovell’s Series of School Books, Lovell wrote: “The undersigned [has] long felt that it would be highly desirable to have a Series of Educational Works prepared 210 and written in Canada and adapted for the purpose of Canadian Education”. One of the testimonials offered to recommend Sangster’s National Arithmetic explains the rationale behind developing this textbook, specifically:

We hail with much satisfaction the appearance of this work, rendered absolutely necessary by the recent introduction of the Decimal Currency into Canada. For a long time the want of a Canadian Treatise on Arithmetic, combining the above mentioned system, with the application of the Modern Scientific methods of analysis and formulae, to the elucidation of the various rules, was felt. Dr. Ryerson, conscious that such a work was needed, requested the Author to adapt the Arithmetic published by the Irish Board of Education, to the Decimal Currency of Canada, and to abbreviate some of the tedious reasons for the rules there given. Mr. Sangster in complying with the request of the Chief Superintendent of Education, transcribed ten or fifteen pages from the commencement of the original work, but finding so many “alterations and improvements” necessary, “abandoned” the design and determined to write a new Treatise on the subject. The admirable volume which now lies before us is the result of that determination.211

210 See the advertisement for “Lovell’s Series of School Books” in the back of (Sangster 1861) 211 This endorsement is included in a back page of Sangster’s National Arithmetic (Sangster 1862), under the heading “Opinions of the Press on the National Arithmetic”, and was reprinted from the Brant Country Herald, Canada West.

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In his prefaces to both the National Arithmetic and his Elements of Algebra, Sangster described his works as containing many original and first-published problems. However, it is clear these textbooks (as most algebra and arithmetic textbooks), were compilations of previously published materials on the subject. In his preface to the arithmetic, Sangster wrote “as it was the sole object of the Author to prepare a complete text-book on the subject of Arithmetic, he has not hesitated to adopt whatever he considered good, either in the Irish National or in the numerous other excellent works on the subject” (Sangster 1962: 3). In his preface to the Algebra, Sangster wrote that in selecting problems that had been previously published, “the author has, he believed, in every case rigidly adhered to the rule, adopted by Todhunter, Colenso, and others, of not inserting a problem unless it had already appeared in at least two British authors – in which case it is to be regarded as common property” (Sangster 1964: v).

Sangster ran as a candidate for the Council of Public Instruction in 1874. During his campaign, the Toronto Printers Hunter Rose & Co. published a pamphlet for the Public School Teachers strongly favouring the election of candidate Goldwin Smith over Sangster (Hunter Rose 1874). It seems that Sangster had not endeared himself to the Public School Teachers Association of Ontario. The booklet charges Sangster with obtaining an improper divorce, with a career in education directed solely towards obtaining personal profit, and with improper conduct towards female students at the Toronto Normal School. A short except offers a taste of the venomous tone of the pamphlet: “From what we have observed of Dr. Sangster’s career, his principle seems to have been to engage in no undertaking that was not of pecuniary benefit to himself. All his efforts in connection with education have been made with a view to making money; and are we to suppose, therefore, that he had been spending the past year perambulating the country, giving lectures on education, &c, from pure devotion to the profession? …the teachers of Ontario, who know him, are not so gullible as to believe it” (Hunter Rose 1874: 6). Although Sangster redressed the accusations in his own public statement, he lost the election to Goldwin Smith.

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Figure 15 ‘Beechenhurst’, The Residence of Dr. J. H. Sangster, Port Perry, Ontario Co. Canada (Source: Beers 1877: 29)

Indications are that Lovell’s series of schoolbooks did make Sangster rich. Following his defeat in the election Sangster left teaching to take up medicine, eventually setting up practice in Port Perry (Parvin 1965: 38). His “Beechenhurst” residence, a fairly lavish looking estate Sangster built in Uxbridge County, is featured in an Ontario illustrated atlas from 1877 (Beers 1877: 29).

5. James G. MacGregor’s An Elementary Treatise on Kinematics and Dynamics (1887)

James Gordon MacGregor was born in Halifax and graduated from Dalhousie University in 1874. He went on to do further graduate work in Europe, studying natural philosophy in Edinburgh and Leipzig. He became a Doctor of Science from University of London in 1876. He returned to Halifax in 1876 to take a position at Dalhousie, but taught physics at a public school for a time while Dalhousie lacked the funds to pay for his salary. In 1879 Nova Scotian industrialist George Munro liberally endowed a chair of physics at Dalhousie, and MacGregor was hired to fill the seat. His new position was fortunate. The George Munro Chair of Physics paid $2,000 yearly, a royal amount when the premier of Nova Scotia was only paid slightly more

185 at $2,400 per year (Waite 1994: 125).212 As Munro Chair, MacGregor continued his research and was active in the community. He gave public demonstrations of physics experiments as amusements at public university events (Waite 1994:182).

MacGregor had an intense temperament and was driven in his work. His laboratory at Dalhousie was simple and he built much of his own equipment. When winter temperatures in Halifax demanded it, he would go about his laboratory business in his overcoat (Waite 1994: 190). His biographer P. B. Waite describes him as a “radical in spirit, disliking rules and regulations almost on principle”, but also as a person with boundless passion for both research and the education of his students (Waite 1994: 190). He was concerned with the maintenance of scientific research funding and suitable laboratories in his home province of Nova Scotia. He supported the efforts towards consolidating the various colleges in Halifax partly because he thought one large university could provide a higher caliber science education (Waite 1994:146).

Waite described MacGregor as a born researcher. He published some 50 papers, mostly in dynamics and kinematics. Some of these papers appear in the Transactions and Proceedings of the Royal Society of Canada, in which, in the first few volumes, he was a frequent contributor. MacGregor spent his summers at the University of Edinburgh laboratory of Peter Guthrie Tait. Tait was a prominent Scottish physicist, and co-author of the famed Treatise on Natural Philosophy by Tait and William Thomson, which redefined the subject after its publication in 1867. In the preface to An Elementary Treatise on Kinematics and Dynamics, MacGregor mentions several works by Tait as influential on the composition of his own treatise (MacGregor 1887: vii). In 1901 MacGregor succeeded Tait in the Chair of Natural Philosophy at the University of Edinburgh (Waite 1998).

An Elementary Treatise on Kinematics and Dynamics (1887) is MacGregor’s only published book. The book was prepared and published in London by Macmillan and Co. during his time as Munro Chair at Dalhousie University in Halifax. On the frontispiece, MacGregor is described as:

212 A native of Pictou Nova Scotia, George Munro immigrated to New York where he made his fortune publishing successful reprints of popular British books such as Dickens, Thackeray and Bronte, songbooks, handbooks, and the first dime novels. As no international copyright agreements existed at the time, American printers did not pay British authors or publishers for printing and selling these books (Waite 1994: 124).

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James Gordon MacGregor, M.A., D. Sc., Fellow of the Royal Societies of Edinburgh and of Canada, Munro Professor of Physics, Dalhousie College, Halifax N.S (MacGregor 1887). It was an impressive list of titles. The book was sold for 10s. 6d (See Foster 1891: 518).

Interestingly, it appears that MacGregor had no special connections to Macmillan, and that his book rose to publication from the pile of unsolicited manuscripts they received. This was something of an accomplishment particularly as MacGregor did not live in the United Kingdom. Sometime in the summer of 1886 MacGregor’s initial proposal came to the attention of Donald MacAlister, reviewer of scientific and mathematical manuscripts for Macmillan and Company. His impression of the book, as MacGregor had seemingly proposed it, was favourable, and MacAlister suggested that Macmillan follow up with MacGregor for more information. Quoting his reader’s report:

I wonder whether Prof. MacGregor knows Lodge’s elementary Mechanics (Chambers). His description of the proposed book seems to me to apply very well to Lodge, whose work has been a great success and practically occupies the ground as an elementary work. If Prof. M’s book is less elementary or in other words more Mathematical, there is a good deal in what he says as in the need for it, and I should certainly like to see the MS [manuscript]. Perhaps the best thing would be to ask him how his work compares with Lodge’s, sending him a copy in case it has not reached Nova Scotia. His answer would be a very useful piece of information.213

MacGregor evidently was contacted, and ended up sending something that was more descriptive of the contents of the book. To this, MacAlister wrote:

I saw from Prof. MacGregor’s syllabus that his work was much more advanced than Lodge’s. It is however on the same lines, and if when the MS comes it proves at all up to my expectations it will be well worth securing. As to pictures it would be an advantage to have them done as carefully and on something of the same plan, as those in Greave’s Statics, to which if acceptable the book would form as I take it a companion volume.214

After MacGregor sent a full draft of the manuscript, entitled Kinematics and Dynamics, it was accepted for publication in September of 1886. After finally having read the entire manuscript,

213 Readers Reports 1885-1886, 55939, p.172 214 Readers Reports 1886-1887, 55940, p. 2

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Macmillan’s reviewer of science and mathematics, Donald MacAlister, wrote an unusually positive and effusive evaluation:

I find this to be a really excellent work, up to the most modern standard, and clearly conceived and expressed. There should be no hesitation in accepting it. I would suggest that it be brought out in the style of Greave’s Statics, to which it is an admirable companion: that the same style of printing (large & small type, paragraphs emphatic words etc.) be adopted, and that Prof. MacGregor be requested to furnish as good drawings for the engraver as he can manage, using thick, thin and dotted lines freely, making the lines to scale where necessary, and generally making the diagrams artistic rather than merely geometrical. A collection of miscellaneous examples at the end would perhaps make it go better at the Universities, but this may want a second edition which ought soon to be called for.

The book came out on September 27 1887, in a run of 2000 copies, from type (not electrotype) and printed by Robert MacLehouse at Glasgow University Press. MacAlister was right that a second edition would be called for. Five years later a second edition was released on June 3, 1902, in a run of 1000 copies. The text was electrotyped “with many alterations” in December of 1904. And in June of 1909, 500 more copies were printed from those plates (with “many alterations” further noted). The plates were destroyed in April of 1924.215

While publishing such a book surely did not make MacGregor rich, selling something close to 3500 copies of this book was something that no Canadian publisher at the time could have imagined, especially for a book aimed at students training in university level physics. His authorship of this book, and its publication with a large and notable London publisher, may have helped Macgregor with his appointment to Edinburgh University in 1901.

MacGregor was not the only early Canadian to have a mathematical book published out of the country with Macmillan and Company. Nathan Fellowes Dupuis (1836-1917) who originated from the area around Kingston, was educated at the University of Queen’s College, receiving his BA in 1866 (one of a graduating class of eight), and his MA in 1868. In 1868 he began teaching chemistry and natural history at Queens, later switching to teach mathematics in 1880 (Archibald and Charbonneau 1995: 19). He published Junior Algebra in 1882 (John Henderson & Co),

215 See Macmillan’s first Editions Book, p. 315, Macmillan Archive, British Library, London UK.

188 which was identified on the title page as his Queen’s College mathematical course. He then transformed this book into The Principles of Elementary Algebra which he published with Macmillan and Company’s New York branch in 1892, and which, in the back pages advertising the book, received several testimonials by American college mathematics teachers. Dupuis also published Elements of Synthetic Solid Geometry with Macmillan in New York in 1893, and Elementary Synthetic Geometry of the Point, Line, and Circle in the Plane with Macmillan in London in 1889 (Foster 1891: 551).

6. John Charles Fields and the University of Toronto Press

Out of the context of Canadian science and science publishing described so far, I would like to suggest that a fairly major event paving the way for better opportunities to publish technical science and mathematics in Canada was the printing of the Proceedings of the International Mathematical Congress, Toronto, August 11-16, 1924, at the University of Toronto Press, in 1928. J. C. Fields initiated Canada’s role in the hosting the 1924 International Mathematical Congress, and he was responsible for the production of the Proceedings that would follow. He raised the money to pay for its publication and acted as the general editor.

Born in 1863 to a leather tanner and schoolteacher, Fields was raised in the industrial city of Hamilton, Ontario, Canada. As a mid-sized city, Hamilton provided Fields with a bustling environment that, despite its cultural immaturity, had ambitions to become a city of some distinction. Notably for Fields, Hamilton built two model public schools in the mid-century that Fields benefited from attending: Hamilton Central School and Hamilton Collegiate Institute.

Fields attended the Central School from 1869 to 1876, when he was age six to thirteen. In 1876 he entered Hamilton Collegiate Institute. At that time, George Dickson, a University of Toronto graduate, was principal, and W. H. Ballard taught mathematics. The school’s science teacher was J. W. Spencer, who had received his PhD in geology from Göttingen, Germany. Both Spencer and Dickson (a chemist, who also instructed Fields) were active in their respective fields. Under Ballard and Dickson’s tutelage, two students from Hamilton Collegiate Institute went on to

189 receive PhDs in mathematics, J. C. Fields and Milton Haight.216 More generally, students from Hamilton Collegiate Institute had remarkable success in the matriculation examinations for the University of Toronto (Riehm and Hoffman 2011: 13). Fortunately for John Charles Fields, the circumstances of primary and secondary education during his youth provided him with an aspirational environment.

Fields was successful in mathematics from his early days. He won a mathematics gold medal in the University of Toronto’s entrance exams of 1880, and continued to win mathematical prizes in subsequent years of his undergraduate study. James Loudon was the only professor in the Department of Mathematics and Natural Philosophy when Fields was a student at the University of Toronto. Not known for producing new results in mathematics, Loudon was nevertheless known as the author of mathematical textbooks used in Canadian schools, and as an advocate of Canadian science. Loudon was a mentor to Fields. After Fields returned from Europe, Loudon hired him at the University of Toronto. They were both were dedicated to the cause of advancing science and mathematics in Canada, and worked towards this goal through involvement with the Royal Canadian Institute.

Given the lack of options for continuing mathematical study in his home country, in 1884 Fields headed for Johns Hopkins University in Baltimore. James Joseph Sylvester was no longer present while Fields was a student there, but the dynamism Sylvester had created remained and influenced Fields’ doctoral experience. His primary mentor was Thomas Craig, with whom he studied theory of functions and differential equations. After a brief stint of teaching in America, Fields went to Paris and Berlin for an extended period of further study. He returned to North America in 1900, when Loudon (at that time, President of the University of Toronto) hired him as a mathematics lecturer. Fields continued to work in the mathematics department at the University of Toronto for the rest of his life, becoming Research Professor in 1923.

After publishing his lone monograph in mathematics, Theory of the Algebraic Functions of a Complex Variable in 1906, Fields’ productivity as a researcher slowed, and he began devoting

216 Like Fields, Milton Haight went on to study mathematics at University of Toronto and then to Johns Hopkins for his PhD. After that, Haight set up the mathematics and physics program at the Imperial Agricultural College at Sapporo, in Hokkaido, Japan, before returning to Canada, where he spent the rest of his career teaching high school (Riehm and Hoffman 2011: 13).

190 more time and energy to the cause of developing science and mathematics in Canada. He was active in the affairs of the Royal Canadian Institute from 1904 until his death, serving as both Vice-President and President. While the Institute was a forum to promote science publicly, and hosted events at which scientists would present results, Fields also tried to make the Institute a vehicle for serious scientific research. While several efforts were made, including an initiative to found a Bureau of Scientific and Industrial Research, not enough money was secured, either through philanthropy or government sources, to get an institution supporting pure research off the ground.

Fields had always been a passionate traveller and an attendee of many international mathematical and scientific meetings. He attended the British Association for the Advancement of Science meetings in Glasgow (1901), Dundee, Scotland (1910) and Australia (1914). In 1902 Fields travelled to France, Norway and Sweden, attending the Abel Centenary (celebrating the life of Norwegian mathematician, Niels Henrik Abel). In 1905 he visited Berlin and Sweden while overseeing publication of his book. Other trips included Dublin (1908), Winnipeg (1909), Berlin and Sweden again (1911), and Cambridge for the Fifth International Congress of Mathematicians (1912) (Riehm and Hoffman 2011: 50).

As a frequent attendee of international meetings, Fields had his first experience organizing one when he chaired the local committee in charge of the Toronto meeting of the American Association for the Advancement of Science in 1921. It was at this meeting that Fields first caught wind of dissention among members of the American Mathematical Society over the invitation that had been made to host the 1924 International Mathematical Congress in the United States.

Beginning in 1919 and lasting for a minimum of twelve years, the constitution of the International Research Council (and therefore, of the International Mathematical Union) required that scientists from countries belonging to the former Central Powers be barred from participating in all activities, of which the International Mathematical Congress was one (Riehm and Hoffman 2011: 120). This requirement seemed plainly absurd to many members of the

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American mathematical community, as it necessitated the exclusion of prominent German mathematicians from the 1924 Congress.217

The 1924 meeting was a political hot potato. Seeing that the American organizers were in trouble over the meeting, Fields saw an opportunity that could further the cause of Canadian mathematics. He volunteered himself, and Toronto, as alternative hosts for the Congress. By the autumn of 1922, the Americans decided that the best course of action was to pass the Congress over to the Canadians. Fields’ decision to organize the 1924 International Mathematical Congress in Toronto meant his acceptance of the required exclusions. It is somewhat surprising Fields so readily volunteered to organize a meeting that to many eyes was illegitimate and not truly international. Fields esteem for German intellectualism, and his firm belief in internationalism, would have conflicted with the requirements of exclusion. However, hosting the conference, even in its compromised state, did serve his goal of furthering the cause of Canadian science.

In order to secure financial support for the meeting, Fields wrote frequent letters to Canada’s highest political offices. In order to convince politicians and other potential supporters to finance the event, Fields emphasized hosting the meeting and publishing the proceedings as an opportunity to develop a level of mathematical professionalism in Canada that had not previously existed. In his campaign to secure funding, Fields corresponded with then Prime Minister of Canada William Lyon Mackenzie King. In June of 1925, Fields wrote to King, extolling the benefits that publication of the proceedings would bring. In the best possible light, Fields communicated that working on the proceedings is

A great opportunity for the University of Toronto to place itself on the international map and therewith help the reputation of the University and that of Canada in the scientific world. There are, I may say, only three or four other presses on the continent which would be qualified to undertake the work. I have hopes also of obtaining for our University Press the

217 The decision to exclude German mathematicians from the International Mathematical Union was not accepted by everyone. Prominent British mathematician G. H. Hardy made his opinion known that he would not stand by as a “re-organization on a political instead of a genuinely mathematical basis” took place (quoted in Riehm and Hoffman 2011: 122). An appeal from the neutral nations (what became known as the “Groningen Action”) urged scientists to reconsider a ban on German science. For more about the politicization of the International Mathematical Union see (Riehm and Hoffman 2011: 115-25) and (Lehto 1998).

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most important mathematical printing in America, which is that of the American Mathematical Society. This would be facilitated if the Press successfully handled the Proceedings of the Congress and this I am sure it can do.218

By October 4, 1926 Fields was writing to the Finance Minister of Canada, J. A. Robb:

We are not yet done, nor shall we be done for some time to come, with the scientific meetings held in Toronto in August 1924. The Press of the University of Toronto has been busied with the printing of the Proceedings…for over a year now and still has hundreds of pages to print. The printing is of the most difficult technical character and it means much to the prestige of Canada in scientific circles that we have a press that can undertake the task. The Proceedings will be much more than a record of the work in the Congress. They will be found in the principal libraries (university, public, industrial) of the world and will constitute a source of reference for research workers not alone in mathematics but in the many other branches of science on the applied side which were represented in the programme of the Congress.219

At the time when the University of Toronto Press handled the composition and production of this two-volume, nearly two thousand page work, it had been scarcely a decade since the Printing Committee at the University of Toronto had even authorized the establishment of a publishing arm of the university press.220 Fortunately for Fields, the University of Toronto Press was in a uniquely beneficial position as an academic publisher. The entire business operation of the Press consisted of a printing plant, a university bookstore, and a distribution service, and the profits from these aspects of the business were turned around and invested in its publishing branch. This would benefit Fields when the project of printing the Proceedings ran over budget. In 1925

218 J. C. Fields to Canadian Prime Minister Mackenzie King, 13 June 1925. This letter is quoted in (Riehm and Hoffman 2011: 157). 219 J. C. Fields to J. A. Robb, 4 October 1926. This letter is quoted in (Riehm and Hoffman 2011: 157-8). 220 The printing facility had been operating since 1901, and in 1919 the University of Toronto approved a publishing program. See Printing Committee Minutes (6 March 1919), A89-0009, Box 001, p. 143, University of Toronto Archives.

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Fields personally guaranteed the cost of the work in excess of what funds were being held by the University Bursar for the project.221

On 1 February 1928, four years after the International Mathematical Congress had taken place in Toronto, volume one of the Proceedings was complete, at 935 pages in length. On November 27 of 1928, volume two was ready, completing the entire work. Small gratuities were given to R. South and W. Cranston, the typesetters who worked on the book at the University of Toronto Press. The Toronto engraver Owen Staples was paid $50 for four etchings used as illustrations. Both volumes were bound in dark blue cloth with Canada’s coat of arms embossed in gold on the front cover (see plate 2).

Plate 2 Proceedings of the International Mathematical Congress, Toronto, August 11- 16, 1924, 2 Vols., edited by J. C. Fields with the collaboration of the editorial committee, Toronto, University of Toronto Press, 1928 (Photo credit: Sylvia Nickerson)

221 Printing Committee Minutes (22 December 1925), A89-0009, Box 001, p. 257, University of Toronto Archives.

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In design and organization, Fields took guidance from the proceedings of previous International Mathematical Congresses. There had been six Congresses prior to the 1924 Toronto meeting: Strasbourg in 1920, Cambridge in 1912, Rome in 1908, Heidelberg in 1904, Paris in 1900, and Zurich in 1897. The proceedings from each of these meetings followed a similar form. However, in choice of font and typographical style, the University of Toronto Press and Fields followed closely the proceedings from the 1912 meeting printed at Cambridge University Press (Hobson and Love 1913).222

Some differences are notable. Not every editor offered a foreward to the proceedings, but Fields did. The tone of the preface communicated the burden Fields endured in his preparation of this work. It had been the only Congress proceedings that had taken four years to produce. The others before it had been published within a year, with the exception of the proceedings of the Paris 1900 meeting, which were published in 1902. Perhaps because of the controversy under which the 1924 meeting occurred, the Toronto volume offers a prefatory note stating that regulations of the International Research Council and International Mathematical Union were adhered to by the host institution. In its oblique reference to the constitution of these governing bodies, Fields distanced himself from what was a morally complicated Congress, deflecting responsibility for the exclusions away from himself and host institution University of Toronto.

The two volumes of the Toronto proceedings are impressive tomes. The first volume contains lists of all the participants of the Toronto International Mathematical Congress, as well as opening remarks and speeches given, the program of activities, and a group photo of the attendees in front of University of Toronto’s Convocation Hall. Also included is an acknowledgement of funding sources (a feature unique to the Toronto Proceedings). Among the other notable extra-mathematical material included is a most interesting map, showing the “transcontinental excursion” on which Fields and willing participants travelled by train from Toronto, Ontario to Victoria, British Columbia and back, after the Congress (see figure 14).

222 Compare (Hobson and Love 1913: vol 1., 67) and (Fields 1928: vol. 1, 85). Their title pages and choice of font are also quite similar, as is the layout of articles.

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Scientists who had attended the British Association for the Advancement of Science meeting that had preceded the Congress attended the transcontinental excursion along with mathematicians. The train trip stopped at the new universities to the west, University of Manitoba, Saskatchewan, Alberta and British Columbia, where delegates were welcomed with displays of scientific equipment, lectures, receptions and banquets (Riehm and Hoffman 2011: 154). While the Proceedings includes no account of the excursion besides this map, the depiction of the amount of land which was then and is still the origin of much of Canada’s wealth and identity, offers a powerful symbol to the reader of what Canada offered the world.

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In November 1928 the University’s Printing Committee, who oversaw the university press, extended formal congratulations to Dr. Fields “on his splendid work in editing this large and difficult work”. The feeling was mutual. Fields later wrote about his experience with the press, “I can never be sufficiently grateful to my two printers for their unstinted devotion and for the persistence of their efforts, always in the sequel crowned with success, to produce the typographical results which I desired. The spirit shown by them is reminiscent of the guilds”.223 Fields also thanked R. J. Hamilton, then manager of the University of Toronto Press, in his brief prefatory note to the work.

For the collected papers that make up the bulk of the work, Fields remarked that despite his best efforts, heterogeneity was the norm: “here and there a national trend is in evidence, while the man in applied science does not always have the same idea as the pure mathematician with regard to the use of mathematical symbols” (Fields 1928, Vol. 1: 7). Fields made the decision to arrange papers into the subject areas into which he felt they most naturally belonged, rather than alphabetically or in the session in which the author had presented. Volume one includes all the papers communicated to Section I: Algebra, Theory of Numbers, Analysis (67 papers), and Section II: Geometry (36 papers). Volume two contains all the communications to remaining sections. This includes communications to Section III: Mechanics, Physics, Astronomy, Geophysics (51 papers), Section IV: Electrical, Mechanical, Civil and Mining Engineering, Aeronautics, Naval Architecture, Ballistics, Radiotelegraphy (47 papers), Section V: Statics, Actuarial Science, Economics (24 papers), and Section VI: History, Philosophy, Didactics (16 papers).

223 J.C. Fields to Prime Minister R. B. Bennett, 21 April 1931, quoted in (Riehm and Hoffman 2011: 160).

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Figure 17 Three pages from Carl Størmer (University of Oslo, Norway), “Modern Norwegian Researches on the Aurora Borealis”, showing different illustration techniques used in the Proceedings (Source: Fields 1928, Vol 1: 141, Fig. 25, 26, 33)

Figure 18 Examples of mathematical typesetting; (left) J. V. Uspensky, “On Some New Class-Number Relations”; (right) P. A. MacMahon, “Expansion of Determinants and Permanents in Terms of Symmetric Functions” (Source: Fields 1928, Vol. 1: 317, 325)

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Fields’ biographers repeatedly make the point that Fields’ health suffered due to his combined efforts to host the Congress and undertake the completion of the proceedings. Fields’ prefatory note to volume one is none too light-hearted, and reflects the reality of a job completed rather than the enthusiasm of his earlier letters to politicians selling the event. In the preface he states that his role as editor “was an unexpected and none too welcome task”, but one nevertheless undertaken solely by Fields when the General Secretary of the Congress, J. L. Synge, left Toronto (Fields 1928, Vol 1: 7).

Seeing the project through was not easy. By 1926 the funds that had been set aside for the printing had already been exhausted, and the printing committee was requesting from Fields “some assurance of what the final amount will be, and the proposed style of the publication, and how payment is to be met”.224 Records of the Printing Committee note that some delays with the work may have been due to Fields’ ill health.225 In the years 1924 to 1928, Fields served as editor on the project (selecting, compiling, proofreading, correcting, corresponding with authors) and raised enough money to pay for printing it.

The final cost of the Toronto proceedings was just over $15,000 (Riehm and Hoffman 2011: 160). This was a large amount when the average annual salary for a worker in Canada in the year 1928 ranged from $1,100 – $1,900 (Meltz 1999: Table E41-48). $15,000 was also a large sum given that the initial budget for the entire Congress had been $55,000. The magnitude of the undertaking had kept growing as papers continued to be received long after sessions were over. Fields had to approach both the Provincial and Federal Governments, along with the Carnegie Corporation, for more money.226 In 1928 the University’s Printing Committee decided to assign $2000 from that year’s publishing earnings towards the printing account of the International Mathematical Congress, which must have come as a relief to Fields.227

224 Printing Committee Minutes (3 December, 1926), A89-0009, Box 001, p. 273, University of Toronto Archives. 225 Printing Committee Minutes (27 June, 1927), A89-0009, Box 001, p. 281, University of Toronto Archives. 226 The federal and provincial governments paid an additional $2000 towards the proceedings, and the Carnegie Corporation paid an additional $1500 over their original pledge of support. 227 Printing Committee Minutes (27 November, 1928), A89-0009, Box 001, University of Toronto Archives.

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In Eleanor Harmon’s book celebrating the centenary of the University of Toronto Press, the chapter “The Printing of Mathematics” describes the press’ specialization in this rare typographical art. Written by Roy Gurney, this chapter acknowledges the Proceedings of the 1924 Congress as the beginning of mathematical printing at the Press. Gurney writes, “The first major mathematical publication undertaken by the Press was the Proceedings of the Pacific Congress of Mathematics [sic] in 1924-28. Even today, this 1941-page work, in two volumes, would be a major publishing project, equivalent in length and complexity to about ten or twelve issues of the Canadian Journal of Mathematics; for a plant the size of the Press at that period, it was an impressive accomplishment” (Gurney 1961: 127).228

It was certainly an achievement that the Proceedings were published in Canada. However, as the most research-oriented mathematical publication to be issued in Canada to date, the Proceedings may still have been out of the reach of aspiring local mathematicians or mathematics students who could have potentially found interest or inspiration in this work. In a “Special Offer to Ontario Teachers” flyer issued by the University of Toronto Press in the 1930s, the list price for these two beautiful and learned volumes was $10, about four times the cost of every other book in the flyer.229 Although Fields had been full of promise when he had suggested to J. A. Robb that the Proceedings would be acquired “in the principal libraries of the world”, one wonders how many librarians or teachers ever purchased it.

Nevertheless, the publication of the Proceedings paved the way for the University of Toronto Press to become Canada’s most capable mathematical printer in the twentieth century. Soon after its printing was completed, the skills of the Press’ composition room were sought for the typesetting of other mathematical works. In 1928 Macmillan Company of Canada approached the press about composing a new edition of Hall and Knight’s Trigonometry, as they were

228 Gurney’s chapter gives the incorrect title for the Proceedings, perhaps confusing Field’s 1928 book with the Fifth Pacific Science Congress, which took place in Victoria and Vancouver in June of 1933, and for which the University of Toronto Press also printed the papers and proceedings. See University of Toronto Press Scrap-book, A89-0009, Box 36, University of Toronto Archives. 229 “The University of Toronto Press Special Offer to Ontario Teachers”, University of Toronto Press Scrap-book, A89-0009, Box 36, University of Toronto Archives.

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“unable to have [the composition work] done elsewhere in Toronto”.230 Prof. Beatty from the Mathematics department contacted the press regarding printing a book about Determinants written by Dean Metsler (a University of Toronto alumnus), which the press agreed to print at cost.

When the Canadian Journal of Mathematics was launched in 1949, the University of Toronto Press served as printer. In Gurney’s essay about mathematical composition at the press, he notes that by 1950, their capacity for mathematical typesetting was “severely taxed”. This motivated the press’ investment in equipment from Lanson Monotype Company for four-line formula setting, which allowed for the setting of mathematics using a keyboard and a caster (Gurney 1961: 127). Professor G. de B. Robinson, managing editor of the Canadian Journal of Mathematics at the time, apparently spent many hours helping the press perfect this system. Several symbols had to be specially punched for use with the caster, and a new integral sign in particular, which was drawn and cast from scratch, cost $98 (regular symbols cost 98 cents) (Gurney 1961: 131).

Fields’ intent around his entire efforts with the Congress was to help build cultural value in, and recognition for, mathematical research in Canada. Although the book itself, Proceedings of the International Mathematical Congress, Toronto, August 11-16, 1924, may have been a white elephant, it was, as other local publications in mathematics had also been, symbolic of national achievement. However, in working with the University of Toronto Press on the Proceedings, Fields built their capacity to print higher-level mathematics. This had a useful and lasting legacy to the mathematical community in Canada, and in this, Fields may have seen some fulfillment of his wish to ameliorate mathematical culture in Canada.

7. Conclusion

Through the episodes discussed here, I hope to have shown how the publication of mathematics in Canada was pursued despite the many odds stacked against it. Mathematical culture in Canada was made possible by repeated investments on the part of individuals dedicated to both the growth of mathematics as a subject and Canada as a country. While these investments took many

230 Printing Committee Minutes (15 June 1928), University of Toronto Archives, A89-0009, Box 001, p. 293.

201 forms, local book publishers and the printing trades assisted in the growth of a mathematical culture in Canada by providing the publishing services necessary for both mathematical education and in some cases, mathematical authors whose own work required publication. The printing and publishing industry was essential to the pursuit of a mathematical culture that was identifiably Canadian.

In the years 1820 to 1930 when Canada was developing as a nation, publication was often tied to motives that were connected with developing national identity and culture. Early local textbook production was cultivated in part by political motives to combat the use of American educational materials. At the same time, popular British or American mathematical textbooks were appended with testimonials, introductions and problems written by local educators in order to “Canadianize” the material for use in Canadian schools. Lovell’s schoolbook series was motivated by a desire to have, in John Lovell’s words, books “written in Canada and adapted for the purpose of Canadian Education”. Fields undertook the organization of the International Mathematical Congress and the publication of its proceedings in part because of what these activities would mean for the building up of value for mathematical research in Canada.

Historically, Canadians suffered from a lack of options to fund the publication of scholarly work. Printers and publishers in Canada were disadvantaged by serving a smaller population saturated with printed matter from the United States and from Britain. In a competitive marketplace, printers had less capital to invest in financially neutral or money-losing projects as mathematical publishing projects were likely to be. The same equation of investment and return applied to scholarly publishing in general. With the Canadian printing and publishing industry at a disadvantage, less investment could be made in the creation of books that could develop Canadian culture at large or scientific culture specifically. James Loudon, as President of the Royal Canadian Institute, noted in 1877 that Canada, unlike the United States, had not become a place where science was endowed by the large personal fortunes of private citizens. This was still the case when J. C. Fields worked to found a Bureau of Scientific and Industrial Research in the early twentieth century, or to fund the International Mathematical Congress. The publishing industry could rarely support the printing of Canadian science, nor could individual patronage be counted on as a reliable source of financial support for these projects.

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English mathematicians enjoyed the advantages of a robust printing trade in their home country. In England, large publishers like Macmillan acted as agents for their mathematical authors, acquiring hard to get copies of mathematical journals and books. For example, Macmillan acquired copies of the German mathematical journal Journal für die reine und angewandte Mathematik (often referred to as Crelle’s Journal) and Annales de mathématiques pures at appliquées (also known as Annales de Gergonne) for William Spottiswoode on his request.231 Macmillan also acted as an agent for George Stokes, when he was looking to acquire Abel’s Oeuvres complètes.232 It seems unlikely that Canada’s nineteenth century publishers would have been connected enough with the European sources of mathematical publications to act as acquiring agents for special publications needed by aspiring Canadian mathematicians in this way. Acquiring up-to-date mathematical literature was expensive and difficult, for English mathematicians and more so for Canadians, who were further removed from the European origins of this literature.

Material culture, or in the Canadian case a lack of it, was critical to the pursuit of truth, and to the practice of pure research. Books and printing were important elements in the material culture of knowledge creation, in the dissemination of that knowledge, and in the formation of a scientific culture that could nurture the development of it. Scientific knowledge has always required material culture for its creation, be that instruments that aid the perception of our raw senses, or in this case, the specific fonts, woodcuts, illustrations, and printing technologies, that allowed scientists to express themselves to one another through print. What we can conclude in the Canadian case, is that maturation of a local printing and publishing industry, and J. C. Field’s work with the University of Toronto Press in the 1920s to develop mathematical printing there, were essential elements to the development of an indigenous mathematical culture in this country.

231 Macmillan acquired copies of Annales de Gergonne at the request of William Spottiswoode. They also offered to supply him with copies of Journal für die reine und angewandte Mathematik (also known as Crelle’s Journal), although he declined the offer. See Daniel Macmillan to William Spottiswoode, 31 January 1855 and 6 February 1855, 55376 General Letter Book 1854-55, Macmillan Archive, British Library, London UK. 232 Daniel Macmillan to George Stokes, November 1854, 55376 General Letter Book 1854-55, p. 91, Macmillan Archive, British Library, London UK.

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Chapter 6 Conclusion

1. The communications circuit

The study of book history and print culture, and the approach to history offered by this discipline, has inspired the present investigation into the development of mathematical knowledge through its representation in printed texts. As mentioned in the introduction to this thesis, Marshall McLuhan and Elizabeth Eisenstein pioneered the idea that communications media, and the printed book in particular, might transform and affect knowledge that has been recorded and transmitted within these objects. In subsequent writings Adrian Johns, Robert Darnton, Donald MacKenzie and others have revised and challenged assumptions about the intrinsic qualities of print, and how these qualities have shaped cultural values and knowledge formation.

In his 1982 essay “What is the history of books?”, Darnton proposed a model to aid the analysis of how books operate in culture. His communications circuit offered a vision for the textual life cycle of book production, showing how a text moves from author to publisher, printer, shipper, bookseller, and reader (Figure 17). The reader completes the circuit of the text, as readers themselves become authors. A text’s interaction with its readers and the public informs the behavior of future authors. As Darnton writes, the communications circuit “transmits messages, transforming them en route, as they pass from thought to writing to printed characters and back to thought again. Book history concerns each phase of this process and the process as a whole, in all its variations over space and time and in all its relations with other systems, economic, social, political, and cultural, in the surrounding environment” (Darnton 1982: 67).

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Figure 19 Robert Darnton’s communications circuit (Source: Darnton 1982: 68)

This thesis has aspired to discover more about nineteenth century British mathematics by asking and answering questions arising from the study of book history and print culture, and applying these questions to the history of mathematical books and publishing. Looking at Darnton’s communications circuit as a general approach, we can see that the questions asked and investigated in this thesis relate mostly to the top, center and right-hand side of the diagram. Chapter two examined mathematical printing using nineteenth century technologies and looked at how publishers and authors overcame these difficulties in reproducing mathematical texts. This chapter attended to questions arising from the application of technologies and techniques of printing to mathematics. Chapter five highlights how the capability of local printers and the circulation of printed matter in Canada affected knowledge production. Both these investigations relate to the right-hand side of Darton’s circuit.

Denoted by a simple double-sided arrow at the top of Darton’s flow chart, the author-publisher relationship is revealed in chapter three as encompassing a fairly complicated network of behind- the-scenes processes and negotiations. Chapter four examines how economics, the law and publicity affected mathematical book publishing. An examination of books sales, author-

205 publisher contracts and advertising demonstrated how very pragmatic, business-oriented aspects of the book trade influenced Macmillan and Co.’s publishing program of mathematical books. These aspects of the current thesis relate to the center and top of Darton’s circuit.

As a whole, the present study has shown what impact printing technologies and the practices of the publishing industry have had on the creation of mathematical books. It has examined what influence printing and publication had on the resulting record of mathematics available in print. A study of mathematical communication through the availability of printed materials in libraries, through booksellers, agents, shippers and bookbinders, etc., would be a valid and intriguing complementary study to the present one. Such a study would answer questions arising from the bottom and left hand side of Darnton’s communications circuit.

Figure 20 The ‘reading’ man, from Richard Corbould Chilton’s Helluones Librorum (Devourers of books), aquatint by Francis Jukes, engraving by J. K. Baldrey (Source: Topham 2000: 318)

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In nineteenth century Britain and Canada, books were central tools used by scholars and students in knowledge production. Figure 18 shows Richard Chilton’s Helluones liborum, in which a Cambridge ‘reading’ man is depicted. The student is depicted hunched over a desk, reading a page in a mathematics book with the assistance of a magnifier and candlelight. Quill and inkpot rest nearby, as well as paper on which the reader has made notes. Pinned to the back wall is a poster entitled Halley’s Scheme for the Transit of Venus. Several other books, open and closed, as well as discarded single sheets of paper are strewn around this spartan room. Everything about the composition of this image, from the lighting to the centrality of the student in his reading activity, suggests that it is less in the world and more inside the text of his books where this student is residing.

Perhaps the reader depicted in Chilton’s Helluones liborum will become a writer himself one day, completing Darnton’s cycle of how culture and knowledge is developed through print. What this image does not depict is what the present study has aimed to reveal. The centrality of publisher and printer, shipper, and bookseller to the printed book is absent from this image, however their role in producing the tools of scholarship is central. Publishers and printers have been as important as authors and readers in the transmission and shaping of knowledge. The printing and publishing industry is the invisible presence in Helluones liborum, and critical to the culture of books, authorship, and reading. The intense interaction between reader and book, knowledge and learning, has been mediated through them.

2. Mathematics in popular culture

Peter and Ruth Wallis' Biobibliography of British Mathematics and Its Applications, Part II complies multiple editions and reprints of more than 10,000 mathematics-related titles published between 1700 and 1760. One of the most important results arising from the Wallis’ work has been recognition that the vast majority of authors and titles in their bibliography are completely unknown today, even to scholars of science and mathematics (Topham 2000a: 566).233 The Wallis’ work demonstrates how many mathematical documents we deem historically important today were scarce in their own time, and that many publications that were voluminously

233 Wallis’ Biobibliography contains entries by 1,090 different authors.

207 produced, and perhaps influential within the culture of mathematics during their own time, have long since been forgotten. The Wallis' bibliography treats the printed culture of mathematics with an egalitarian spirit. All works they considered mathematical are catalogued, regardless of whether we deem them retrospectively as important. Quite rightly, they observe “most histories concentrate on the few works which contributed new knowledge and ignore the much larger number of less innovative works” (Wallis 1974: 449). Taking stock of the large number of less innovative works is, however, critical to the task of relating advances in knowledge to their proper historical context (Wallis and Wallis 1986: v). In contrast to the mainstream history of mathematics that has been available, the Wallis’ work documents and recognizes the widespread, popular culture of mathematics during the eighteenth century.

The present study has revealed historical facts of similar value. In chapter three (and Appendix A), it is shown how scores of unknown authors were actively submitting mathematical manuscripts for possible publication with Macmillan. More mathematical manuscripts were received and reviewed for Macmillan than manuscripts in any other area of science. A study of Macmillan’s records from approximately 1870 to 1890 demonstrates a widespread, popular engagement with mathematics by authors hoping to create new works. One wonders whether the explosion of printed matter in the nineteenth century, particularly the initial distribution revolution, may have facilitated a more widespread engagement with mathematical ideas, given that mathematics was increasingly available in print to readers of different classes and backgrounds.234

Darnton’s communications circuit recognizes books as agents capable of intellectual influence. An increase in the available printed matter relating to mathematics, concurrent with an overall increase in printed matter generally, may have nurtured a growing popular interest in mathematics in nineteenth century Britain. An increase in printed matter about mathematical topics in mid-century might have intensified public curiosity about mathematics, creating

234 Recall Simon Eliot outlines two revolutions in nineteenth century printing and publishing in England. He terms a spike in print production during the 1830-55 years, the “distribution revolution” (Eliot 1994: 107). This period was followed in the late 1840s and 1850s by a major change in the price structure of the book market, with the introduction of cheap books (which Eliot defines as having a price of 3s. 6d. or less). In the 1880s and 90s printed production expanding drastically. Eliot has named this phase the “mass-production revolution” (Eliot 1994). See chapter four, section (2), of the present work.

208 audiences for literary works that imaginatively engaged with mathematical ideas, such as Edwin A. Abbott’s Flatland (1884) and Charles Howard Hinton’s Scientific Romances (1884-1886). Linda Dalrimple Henderson has noted that an increase in popular and non-specialist writings about non-Euclidean and multi-dimensional geometries from the 1860s onwards inspired new trends in spirituality, occultism, theories of perception, fiction and visual art (Henderson 1983).235

In the 1830s several mathematical books were published by the reform societies, the first publishers of mass-produced books for the middle classes of England. Through the application of steam printing to book production, Herschel's books on natural philosophy and astronomy, De Morgan's book on probabilities, and Lardner's many contributions to the Cabinet Cyclopaedia series were produced in large quantities.236 The application of steam printing to these books made them available at cheaper prices than mathematical books produced in earlier times. The novel Crotchet Castle parodies popular engagement with such books in the 1830s. Recall the fictional character of the cook, who falls asleep while reading hydrostatics “in a six-penny tract, published by the Steam Intellect Society” (Peacock 1831: 19).

These early mass-produced books on mathematical subjects may have nurtured a generation of mathematical readers, who later became Macmillan’s (now unknown) prospective authors on mathematics. The technological capacity to mass-produce books on mathematical subjects may have had an influence on nineteenth century commonplace engagement with mathematics. Could

235 Henderson notes that non-Euclidean geometry inspired artists to reconsider the importance of linear perspective, to consider how objects appeared deformed within geometries of non-zero curvature, and that overall these new ideas undermined belief in absolute truth (as the discovery of hyperbolic geometry had undermined the importance of Euclidean geometry). She explores how non-Euclidean geometry and the fourth dimension influenced the fictional writings of authors Oscar Wilde, George MacDonald, Lewis Carrol, Joseph Conrad, Ford Madox Ford, Gaston de Pawlowski and H. G. Wells. She describes how the fourth dimension inspired new ideas in spiritualism, including Theosophy and “hyperspace philosophy” as advocated by Maurice Boucher, P. D. Ouspensky and Charles Hinton Howard. Henderson devotes several chapters to a discussion of how geometrical ideas influenced the modern art movements of Cubism and Futurism, focusing on the work of Marcel Duchamp in particular.

236 The titles within the natural philosophy section of the Cabinet Cyclopaedia series (Society for the Diffusion of Useful Knowledge) included Augustus De Morgan's book An Essay on Probabilities and on their Applications to Life Contingencies and Insurance Offices (1838), Dionysius Lardner's contributed volumes on heat, hydrostatics, and electricity, as well as Treatise on Arithmetic Practical and Theoretical (1834) and A Treatise on Geometry and its Application in the Arts (1840), astronomer Sir John Herschel contributed Astronomy (1833) and A Preliminary Discourse on the Study of Natural Philosophy (1831), David Brewster contributed Optics (1831), Henry Kater co- authored with Lardner a volume on Mechanics (1831). For more see chapter two, section (5).

209 the increasing availability of mathematical books have improved numeracy, engaged minds on these subjects, and increased the curiosity and respect for mathematical practitioners prior to the institution of a public education system that included mathematics as a routinely studied subject? Might authors who submitted manuscripts on astronomy to Macmillan in the 1870s, have read Herschel’s 1833 book on the same subject, and been influenced by it? Books released in large circulations permeated daily, lived experience. Through these works, a very many people had a chance to come into contact with some aspect of mathematics, mixed mathematics, or physical science. Early mass-produced books on mathematical subjects may have influenced a generation of readers and writers, inspiring increased interest in, and possibly further cultural respect for, mathematics and science.

3. Authors, typographic culture and mathematics in print

Florian Cajori's account of mathematical notation throughout history remains the most thorough and authoritative book on this subject. However, Robin Rider has helpfully pointed out that Cajori’s book, while exceedingly thorough, conceives of only one agent in the evolution of mathematical texts over time, that agent being the author. A History of Mathematical Notations only mentions the title, author and nationality of each work studied, it does not record the printers or publishers (if applicable) who produced it, nor does it address the effect the materiality of printing may have had on the choice of particular mathematical symbols or notations used in printed works (Cajori 1928). Robin Rider, by contrast, has aimed in her work to highlight the role of printers and publishers in the appearance of eighteenth century mathematics in print. In doing so Rider recognizes the book as a communications medium requires its own examination.

Darnton’s model of the communications circuit recognizes that several players influence the creation of a book besides its author. Rider similarly recognizes the importance of “typographic culture” and its impact on the appearance of mathematics in print. Acknowledging Rider’s “typographic culture” (and Darnton’s circuit) means asking how “printing with moveable type, the production and reproduction of images by artists, engravers and block cutters, the work of translators and editors, and the efforts of publishers to identify and reach a market for their goods” may have had joint agency with the author of a text on the mathematics that eventually appeared, as well as how it appeared, in print (Rider 1993: 92).

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The present study reveals how both author and “typographic culture” affected the presentation of mathematical texts in the nineteenth century. Isaac Todhunter’s close collaboration with Macmillan over the production of mathematical illustrations, and the general attention to detail with which he paid to how his work was presented, is representative of one type of author whose agency shaped the appearance of mathematics in print.237 On the other hand, mathematical books were influenced by decisions within the publishing house. As an advisor on mathematics at Macmillan and Co., Isaac Todhunter and then Donald MacAlister were consulted on what mathematical texts to publish, and in Todhunter’s case, were directly responsible for bringing forward new authors for publication (for instance, George Boole). MacAlister had a list of qualities he required of mathematical texts, including requirements for their organization, typography, and referencing. With respect to diagrams that were to be produced for Macmillan’s mathematical books, MacAlister recommended mathematical diagrams be aesthetically pleasing in appearance, using a variety of descriptive lines and figures drawn in perspective.238

These details of publication, such as decisions about which works get published and the visual presentation of the work in print, were important. As William Dawson noted, the quality and professionalism of a publication reflected on the perceived quality of its content. Essentially Dawson recognized what McLuhan and Eisenstein point out about communications media; that the medium of communication influences the reception of the content by the public. Both Dawson and MacAlsiter accepted as fact that a badly produced text would be overlooked, no matter its intellectual quality. If the printed treatment was poor, then the work itself was often assumed to be of inferior quality as well. On the other hand, more credibility could be given to a publication if it received a sumptuous or professional visual presentation, in its use of illustrations or in its typographical presentation (Dawson 1883). Authors were aware of this, and struggled to achieve the best possible presentation of their work. We can list many Canadians (J.

237 See chapter two, section (10). Also, recall June Barrow-Green’s study of Todhunter, which also reveals that he demanded high production values from his published work, and was known to pick over publication details, including where to have the best woodcuts produced, etc. (Barrow-Green 2001: 189). 238 See chapter three, section (7).

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C. Fields and J. G. MacGregor are examples) who sought publication abroad for their books, because Canadian printed or published books were seen as second rate.239

In her book The Printing Press as an Agent of Change about how printing revolutionized European culture, Eisenstein goes so far as to suggest that “editorial decisions made by early printers (with regard to layout and presentation) probably helped reorganize the thinking of readers. The thoughts of readers were guided by the way the contents of a book were arranged and presented. Basic changes in book format might well have lead to changes in thought patterns” (Eisenstein 1979: vol. 1, 70-71). She goes on to say “increasing familiarity with regularly numbered pages, punctuation marks, section breaks, running heads, indexes and so forth helped to reorder the thought of all readers” (Eisenstein 1979: vol. 1, 81). While Eisenstein may go too far in assigning the printing press primary causal agency in reshaping European intellectual thought, Florian Cajori’s opposite vision of the author as sole agent of change ought also be amended. A printed text is the result of the combined effort between the author and the author’s collaborators within the typographic culture that shaped its production.

4. Economics, book production and the image of mathematics

During J. C. Fields’ time in secondary school at the Hamilton Collegiate Institute, and during his undergraduate education at the University of Toronto, we know what mathematical books were assigned to him for study.240 As a student of mathematics in Ontario from 1869 to the early 1880s, Fields mostly worked with mathematical textbooks of British origin (including several Macmillan publications), some of which had been “adapted” for the use of Canadian schools, and one of which was French.241 Although Fields always testified to the quality of education he had received in Canada, he did note that his grounding in calculus had been wrong. He later commented, looking back on his Canadian education, “Fifteen years after I had received my

239 See chapter five section (3) and (5).

240 For a list of books Fields studied in high school and university, see (Riehm and Hoffman 2011: 15-17, 21). 241 The Canadian adaptation of British mathematical textbooks typically consisted in the inclusion of an introduction by a well-known local teacher of mathematics, testimonials about the book excerpted from local sources (newspapers, or familiar educational authorities), and the inclusion of examples of local familiarity or interest. Rarely if ever was the main body text of a mathematical book changed in Canadian adaptations.

212 grounding in the calculus I discovered, I am ashamed to say, in a German University, the University of Berlin, that it had been taught to me falsely, irremediably and fundamentally falsely” (Fields quoted in Riehm and Hoffman 2011: 21-22).

During his time as a mathematics student at Cambridge in 1890-93, Bertrand Russell similarly found his mathematical education involved practices and materials that were, he later discovered, outdated or false. As a Cambridge mathematics student, he had never studied nor heard of the work of Weierstrass, Dedekind, Cantor, Frege or Peano (Russell 1959: 39). He later reflected that “the ‘proofs’ that were offered of mathematical theorems were an insult to the logical intelligence” and “my teachers offered me proofs which I felt to be fallacious and which, as I learned later, had been recognized as fallacious” (Russell 1956: 20, 1959: 37-8). Russell, like Fields, reeducated himself after his undergraduate education, exerting much effort to cure himself of his “Cambridge parochialism” (Griffin and Lewis 1990: 65).

Much has been written about the use of mathematics within English society as a norm for truth, and the stifling effect this value had on the educational context for mathematical teaching at Cambridge and on the development of nineteenth century English mathematics (Barrow-Green and Gray 2006, Griffin and Lewis 1990, Richards 1988a, 1988b). We might wonder why the broader English culture of mathematics was so resistant to change, when several English mathematicians, like W. K. Clifford, Arthur Cayley and James Joseph Sylvester, were knowledgeable about continental mathematical ideas.

Thomas Kuhn’s classic book The Structure of Scientific Revolutions invests considerable importance in the role of textbooks in the maintenance and definition of what Kuhn characterizes as “normal science”. Normal science, as defined by Kuhn, is the practice of problem solving within parameters set out by an accepted approach to phenomena or group of theories. Kuhn sees practitioners operating in normal science mode as engaged in tackling problems and gaps within a theoretical structure that has already been accepted as the core theory or approach (Kuhn 1970: 24). Kuhn suggests that in science, more so than in other fields, core values are maintained by the pedagogical use and production of textbooks:

to an extent unprecedented in other fields, both the layman’s and the practitioner’s knowledge of science is based on textbooks and a few other types of literature derived from them [i.e. popularizations, philosophy of science]. Textbooks, however, being pedagogic vehicles for the

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perpetuation of normal science, have to be rewritten in whole or in part whenever the language, problems-structure, or standards of normal science change (Kuhn 1970: 137).

The activity of normal science and the reflection of that body of values and principles in the textbooks it produces, comes for Kuhn at a considerable cost to the overall development of science. That cost is the suppression of “fundamental novelties”, because these are necessarily subversive of the basic intellectual commitments of those invested in normal science (Kuhn 1970: 5).

While Kuhn goes on to make several further claims about the role of textbooks, what is relevant to the present study is Kuhn’s assertion that textbooks are connected with the maintenance of vested interests in a particular scientific program. Kuhn’s point is that scientists who have become successful within the structure of status quo scientific practice continue to perpetuate and profit from the maintenance of that belief system.

This thesis amplifies Kuhn’s now classic observation from the history of philosophy of science by adding that publishers, too, were invested in perpetuating status quo science through the continued production of successful textbooks. Particularly in Britain, where industrialization was applied to book production, publisher’s profits from the sale of cheap reproductions of already- successful textbooks were substantial. By comparison, the development and production of new mathematical textbooks meant a loss of expected profit on the sale of established textbooks. For example, in their early years of business, Macmillan and Co. took risks on the creation of new pedagogical materials in mathematics (particularly under the guidance of Isaac Todhunter), because at that time, developing this new material helped Macmillan establish a niche in the book market. However, as their business matured and became more successful, their pattern of mathematical textbook production became more conservative, they continued to print their established textbooks in large quantities, pushing these books into ever expanding global and colonial markets. This activity helped perpetuate a moribund image of British mathematics in Britain as well as overseas in Canada.

In Macmillan’s records we can see that the publisher, motivated by a desire for profitability and successful economics, made decisions that maintained the status quo in the printed record of mathematics. In some cases a publisher’s actions interrupted what might have been a path towards change in mathematics. When a mathematical textbook was nearly out of print,

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Macmillan frequently recommended reprinting it right away. Reprinting sometimes contravened the wishes of the author, who requested alterations and improvements. The publisher postponed alterations and improvements for a second edition to be produced later, while copies of the first edition continued to be profitably sold.242

As their reader of mathematics, Daniel MacAlister chose to recommend for publication at Macmillan textbooks that fit within the received image of British mathematics, books that he felt were appropriate to English pedagogical needs.243 In this act, he was also an agent of the maintenance of status quo English mathematics, and the values about its habit of study that were, toward the end of the nineteenth century, suppressing the adoption of fundamental changes that had come to the subject in France and Germany. As the British approach to mathematics was perpetuated in part through the use of these pedagogical materials, aspiring mathematicians in Britain and Canada were introduced to an image of mathematics through an education system in which British textbooks played an important part. After their education at Cambridge and in Canada, Fields and Russell had to un-learn certain parts of their mathematical training and excise errors in the mathematics that had been presented to them before they could go on to make new contributions or discoveries in calculus, algebra or logic.

5. Fashioning a history of science publishing

In the year 2000, Jonathan Topham described science publishing in nineteenth century Britain as “a vast and largely unexplored territory” (Topham 2000b: 562). While undertaking the history of science from a publishing history perspective is not new, it is an approach just beginning. Because so little has been known about the history of nineteenth century science publishing, certain assumptions have been made about nineteenth century scientists as authors and the publication of their works. This thesis challenges or proves erroneous some of these assumptions.

242 See Daniel Macmillan to Isaac Todhunter, 3 November 1854, MP 55376, General Letter-Book, 1854-1855. 243 See chapter three, section (7).

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David MacKitterick’s erudite history of the Cambridge University Press includes several chapters about Cambridge’s other publisher of importance, Macmillan and Company. In these chapters he suggests that Macmillan’s literary authors were more important, both financially and in their cultural influence, than their scientific authors. He writes

As general publishers, [Macmillan and Co.’s] list included fiction, travel and poetry as well as school and university studies. …Lewis Carroll, Charles Kingsley, Thomas Hughes, Charlotte Mary Yonge and Mrs. Craik (her husband was a partner in the firm) were all major authors – and financially usually more important than their university counterparts (emphasis mine, McKitterick 2004b: 58).

This opinion has been offered more than once by historians of publishing. While numerous studies in the history of literary authorship exist, there has been a comparative non-interest in the history of scientific (or mathematical) authorship. This study proves that publishers profited from the publication of science, both financially, through book sales, and culturally, by associating themselves with the prestige of recognized authorities on scientific topics. Several facts suggest this point. Macmillan, a commercial publisher with no access to university subsidies, was the most active publisher of science in nineteenth century England. Publishing science and mathematics was profitable, as demonstrated by the fact that nineteenth century science publishing took place primarily at commercial publishers who operated within a free market setting (Topham 2013; McKitterick 2004a: 32, 397). A quantitative study of Macmillan’s mathematical publications (see chapter four), demonstrates how profitable the publication of mathematical textbooks were for Macmillan. Macmillan’s investment in mathematical textbooks and their authors were just as important for the company, if not more important, than their investment in bestselling works of fiction and their literary authors.

Historians of the book have also naively assumed that “few authors of scientific, technical and medical texts were motivated by the possibility of financial benefit for their efforts. Most were primarily interested in informing readers or producing texts that could be used for educational purposes” (MacDonald and Connor 2007: 184). While this statement may not be completely incorrect, to date such opinions have been based largely on assumptions rather than knowledge. As demonstrated in chapter four of this work, some mathematical authors were motivated by the expectation of profit from their publications. Science publishing was not purely altruistic.

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Historians who have undertaken the study of science publishing have revealed that scientific authors often had agendas to push, livelihoods to forge, vanities to preserve, and careers to pursue.244 All these factors came together in scientists’ interaction with the publishing industry and their use of publication and printed media to advance these goals. Scientific authors did not lack the foibles and motives that affected writers of fiction, literature, poetry or other subjects. The same reality of producing printed knowledge within a capitalist marketplace shaped scientific authors and their publications as it did literary authors and their works of fiction.

Further studies of scientific publishing will reveal why and how scientific authors leveraged the publishing industry to achieve their ends. Did scientists network with publishers in order to establish organs of scientific communication, to pursue profits from their intellectual property, to help form a reputation, leave a legacy, or achieve prestige? How did scientific authors use publishing as a way to legitimize and publicize the respectability of their profession? Further work in history of science publishing will help to definitively answer these questions.

244 In her article about the development of the International Scientific Series, Leslie Howsam discusses how Victorian men of science T. H. Huxley, John Tyndall and Herbert Spencer harnessed nineteenth century book publishing to broadcast a particular brand of Darwinism (Howsam 2000). In describing how scientists interacted with the machinery of publication, Howsam notes that scientific books, articles and papers do not emanate unmediated from the minds of their authors. Rather, she writes, “the bland package of a printed and bound book may conceal a complex history of networking and power-broking among authors and publishers” (Howsam 2000, 187).

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Acronyms

MP Macmillan Papers, Macmillan Archive, British Library

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Appendices

A. Mathematical manuscripts received by Macmillan, 1867-1896

The following table is a record of mathematical manuscripts Macmillan and Co. recorded between the years 1868 and 1896 to keep track of received manuscripts and corresponding readers reports. The following list was compiled from the Records of Manuscripts (MP 56016- 56018) and Readers Report books (MP 55931-55940). A year, author or action given in brackets indicates some uncertainty in my interpretation of the paper records. DM, DMcA, and DMA are variations on the initials of Macmillan’s reader of science, Donald MacAlister (see chapter 3). Records appear to be fairly complete between the years 1880 and 1896, while in the 1860s and 1870s the records appear haphazard.

Author Manuscript Year Action Reviewer

Airy, G. B. New edition of Astronomy [1886] DMcA

Airy, Osmund Optics 1869 sent for revision

Aldis, Mr. Great Giant Arithmos' Elementary Arithmetic 1881 accepted DM

Alexander, Tho. Applied Mechanics Elementary Treatise 1878 accepted

DMcA, Allen, A. Jukes Geometrical Dynamics 1884 declined Chambers

Anon. from Hong Kong Arithmetic [1886] [declined] DMcA

Anonymous Key to Todhunter's Spherical Trigonometry 1885 declined DMcA

Aveling, F. W. Light & Heat 1887 declined DMcA

Boevy, Prof. Henry Applied Mechanics 1882 declined DM

Bond, W. Henry Rules and Examples in Algebra 1880 declined

Boole, George Professor Boole's Logic 1868 [accepted] Prof. Price

Bottomley Dynamics [1886] DMcA

Bourne, C. W. Key to Todhunter's Conics 1886 accepted [DMcA]

Bower, J. Elementary Physics 1884 declined DMcA

Briggs Plane Analytic Geometry [1885] [declined] DMcA

Browne, W. R. Papers on Foundations of Mechanics [1881] [declined] [DMcA]

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Calvelly, R. S. Perspective 1884 declined John Sparkes

Candler, H. Help to Algebra 1885 declined DMcA

Carell Calculus of Variations [1885] DMcA

Chundersen, Baba Student's Elements of Resolution of Algebraical Kshirode Expressions 1885 declined DMcA

Clifford, W. K. Collected Lectures and Essays [1879] accepted

Clifford, W. K. Seeing and Thinking [1879] accepted

Clifford, W. K. 1st part Elements of Dynamic 1877 accepted

Coales, Dr. Lectures on Mechanics 1883 declined DMcA

Constable, Samuel Geometry 1881 accepted DMcA

Cotterill, J. H Treatise on Applied Mechanics 1880 accepted DMcA

Cotton, R. H. Geometrical Optics 1882 declined DM

Cumming, Linnaeus Book on electricity 1875 accepted B. Stewart

Cumming, Linnaeus Geometrical Conics 1878

Curtis, William DM, R. B. Fitz-Harry Primer of Arithmetic 1883 declined Hayward

Davison & Mayo Arithmetic Papers 1885 declined DMcA

Dougherty, J. A. Spherics and Nautical Astronomy [1885] DMcA

Dyer, J. M. Algebraical Examples 1884 declined DMcA

Eagles, J. H. Constructive Geometry of Plane Curves 1884 accepted DMcA

Easton, J. G. Algebraical Factors 1884 declined DMcA

Edwards, J. Differential Calculus 1886 accepted DMcA

Elton, E. H. Offer of Trigonometrical Examples 1887 declined [DMcA]

Evans, A. Palmer Arithmetic 1874 declined

Evers, Henry Trigonometry 1883 declined DMcA

Ferguson, J. Mechanical Philosophy 1885 declined DMcA

Fielden, Mrs. Euclid 1882 [declined] [DM]

Fielden, Mrs. Arithmetic Lessons 1882 declined DM

Flint, John Arithmetic and Answers 1879 declined

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Gallaby, W Plane Co-ordinate Geometry 1884 declined DMcA

Gibson and Webb Euclid 1884 declined DMcA

Gillman, C. "-(x-y)2, or the Uselessness of Algebra 1868 declined

Goyen, P. Higher Arithmetic [1886] DMcA

DMA, J. Graham, R. Hudson Comparative Statics 1882 declined Wolstenholme

Greaves, J. Elementary Statics 1885 accepted DMcA

Greenhill, A. G. Integral and Differential Calculus 1885 accepted [DMcA]

Greenhill, A. G. Proposed Hydrostatics 1886 declined DMcA

Greenhill, W. A. [A. G.] Elliptic Functions 1886 accepted DMcA

Hall Euclid proposal 1885 accepted DMcA

Hall and Knight Algebra for Schools 1884 accepted DMcA

Halstead, G. B. Elements of Geometry [1885] import a few DMcA

Hammarion, Miss Astronomie Populaire 1884 declined DM

Hammond, A. de L. Problems in Elementary Mathematics 1880 declined W. J. [Jevons]

Hammond, A. de Lile Exercises in Algebra 1883 declined DM

Heiss Algebraic Problems [1886] [declined] DMcA

Henchie, E. J. Mensuration 1885 declined DMcA

Hewitt, George M Geometry 1884 declined DMcA

Hooker, G. N. Plane Trigonometry 1887 declined DMcA

Silvanus P. Hospitalier Hospitalier's Formulaire [1883] Thompson

Houston Proposed Higher Arithmetic 1884 declined DMcA

Hunter, R. St. J. Key to Todhunter's Differential Calculus [1887] accepted DMcA

Ibbelson, W. I. Elasticity 1884 accepted DMcA

Jackson, Louis Civil Engineering Book 1882 declined [DM]

Perspective Explained on Geometrical DMcA, J. James, H. A. Principles 1885 declined Sparkes

Jevons, S. Elementary Logic 1870 accepted

241

Kirkman, J. P. Exercises in elementary trigonometry [1882] declined

Knight, W. T. Algebraic Factors 1881

Knox, A. Certain Infinitesimal Quantities 1884 accepted DMcA

Knox, Alexander MS on Differental Calculus 1884 accepted DMcA

Köing Question of translating Köing 1881 DM

Lanza Curve-Tracing [1885] [declined] DMcA

Lock Proposal for a second part of his Trigonometry 1883 accepted [DM]

Lock Arithmetic proposal [1885] [accepted] DMcA

Lock, John Euclid proposal [1886] DMcA

Low, D. A. Applied Mechanics 1886 declined DMcA

Numerical Tables & Constants in Elementary Lupton, Sydney Science 1884 declined

Lyle, John Newton Differential Coefficients 1873 declined Mr. Todhunter

Lynam, J. D. Key to Todhunter's Conics 1885 declined DMcA

Maccoll, Hugh Elliptical Solutions of Algebraic Problems [1884] declined DMcA

Macfarlane, Alex Applied Arithmetic 1884 accepted DMcA

MacGregor Mechanics [1886] DMcA

MacGregor, Prof. J. G. Kinematics & dynamics 1886 accepted DMcA

Martineau, C. A. Miss Heat 1878 accepted

Matthews, E. H. Matriculation Mathematics 1880 declined

Mault, A. Natural Geometry 1876 accepted

McAulay, Alexander Quaternions for school boys 1895 declined DMcA

McCarthy Key to Todhunter's Mensuration [1884] accepted DMcA

McClelland and Preston Spherical Trigonometry 1885 accepted DMcA

McClelland, N. M. Spherical Trigonometry 1886 declined DMcA

McClelland, W. J. MS on Spherical Trigonometry [1884] declined DM

McClelland, W. J. Spherical Trigonometry 1884 declined DM

242

McClinton, Thomas Lines Cut Harmonically 1884 declined DMcA

McKinn, Joseph Elementary Plane Trigonometry 1879 declined

McPherson, Dr. J. G. Proposal for a small book on Quaternions 1885 declined DMcA

Milburn, R. M. Mathematical Formulae 1878 declined

Miller, J. B. Elements of Descriptive Geometry 1877 accepted

Elementary treatise on corresponding theorems Mitchison, A. M. in geometry 1880 W. J. [Jevons]

Muir, Thomas Determinants [1878] accepted

Olley, H. R. Geometrical Optics 1882 declined [DM]

Openshaw, T. W. Mathematical Formulae 1883 declined

Pedley, S. Exercises in Arithmetic 1878 accepted

Pedley, S. Useful Mensuration 1887 declined

Pendlebury, C. Arithmetic 1885 declined DMcA

Pinkerton, R. H. Dynamics 1887 declined DMcA

Pluckett, Captain G. J. Orthographic Projection 1881 declined DMcA

Ray, Saradaranjan Elements of Geometry 1896 accepted DMcA

Ray, Saradaranjan Beginner's Algebra 1896 accepted DMcA

Ray, Saradaranjan Algebra 1896 accepted DMcA

Ray, Saradaranjan Elementary Trigonometry 1896 accepted DMcA

Rayleigh, Lord Chapter II of Book on Sound 1876 accepted

Roach, J. Trigonometry 1885 declined DMcA

Roach, J. Trigonometry [1887] DMcA

Roach, J. Trigonometry 1885 declined [DMcA]

Robinson, J. R. Elementary Dynamics 1887 declined DMcA

Robinson, John L. Work on nautical surveying 1881 accepted DM

Saughton, J. K. Nautical Surveying 1872 declined

Senior, M. H. My First Trigonometry [1883] declined DMcA

Sexton, Humbolt Quantitative Analysis 1885 declined DMcA

243

Shann, George Heat in relation to the Steam Engine [1877] accepted

Sheddon, J. Geometry of Curves [1886] DMcA

Shortland, Vice- Admiral Nautical Surveying 1885 DMcA

Cambridge Plane Trigonometry and Silling, J. Mensuration 1872 declined

Smith, Charles Conic Sections 1881 accepted DMcA

Smith, J. Brook Arithmetic 1870 accepted

Smith, R. Prowde Mathematical Examples 1886 declined [DMcA]

Sonnenchein, A. Arithmetic for Children 1870

Stanley, W. J. Properties and motions of fluids 1881 declined DM

Stapley, A. Mackenzie Deductive Logic 1883 declined

Staveley, R. MS on Fresnel's Theory of Double Refractions 1883 declined DMcA

Tebay, Septimus, B. A. Mensuration 1867 declined

Thomas, J. V. Key to Todhunter's Differential 1886 declined DMcA

Thomson, W. Algebra 1885 declined DMcA

Thudichum, Dr. Spectrum Analysis 1869 declined Mr. Lockyer

Vaughn, William Metric Arithmetic 1869 declined

Wace, Henry Method of Logarithms 1870 declined

Wait & Jones Algebra 1887 declined DMcA

Williams, H. A. Factors in Algebra 1884 declined DMcA

Willis, H. G. Geometrical Conic Sections 1879 declined

DMcA, W. Wilson, J., Revised Euclid 1880 declined Jevons

Wolstenholme, Joseph Geometry Problems 1878 accepted

Wood, J. G. Miscellaneous Papers 1885 declined DMcA

Wright, Lewis On Light 1881 accepted D. MacAlister

Young, E. W. Book on engineering 1873 accepted

Mensuration for Army Exams [1886] [declined] DMcA

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B. Some of Macmillan’s readers of science, 1867-1896

The following table lists some of Macmillan’s readers on scientific topics during the years 1868 and 1896. This list was compiled from the Records of Manuscripts Received and Readers Report books from the Macmillan Papers, British Library. This is not a comprehensive list. However, it does reveal some of Macmillan’s trusted advisors on scientific topics, and reflects how frequently, and in what years, these readers were active. I have made some assumptions in producing this list of reviewers, as in some cases I deduced a full name from initials or a shortened form given in the records.

Name Year active as a reviewer (known number Subjects of of reviews in that year) manuscripts reviewed

Donald MacAlister 1880 (1), 1881 (>9), 1882 (>7), 1883 (>7), General science and 1884 (>21), 1885 (>26), 1886 (>18), 1887 mathematics (>9), 1895 (1), 1896 (>4)

John Stewart 1893 Evolution, heredity, Mackenzie ethics, sociology

James H. Cotterill 1895 Engineering

Joseph 1882 (1) Statics Wolstenholme

T. H. Vines 1881 (1) Pathology

H. E. Roscoe 1881 (2) Chemistry

Alexander Dickson 1881 (1) Botany

Charles Darwin 1881 (1) Botany

T. H. Huxley 1868 (1), 1881 (1) Zoology

W. Stanley Jevons 1869 (1), 1878 (1), 1880 (3) Mathematics, economics

C. Schorlemmer 1881 (1) Chemistry

Thistleton Dyer 1883 (1) Micro-botany

M. Foster 18813 (1) Physiology

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R. B. Hayward 1883 (1) Arithmetic

Silvanus P. 1883 (1) Electricity Thompson

T. Lauder Brunton 1878 (1), 1880 (1), 1885(1) Biology, disease

J. Sparkes 1877 (1), 1884 (1), 1885 (1), Linear perspective (for artists)

Chambers 1884 (1) Dynamics

Sir David Ferrier 1878 (1) Medicine

Mrs. Boole 1867 (2), 1872 (1), 1873 (1) Natural Philosophy

Norman Lockyer 1868 (2), 1869 (3), 1873 (1), 1880 (1) Agriculture, geography, mineralogy

Balfour Stewart 1875 (1) Electricity

Prof. Price 1868 (1) Logic

Isaac Todhunter 1873 (1) Mathematics