48 Journal of the Oughtred Society

Mr. Milburne and the Serpentine Line

Panagiotis Venetsianos

Foreword it in the Parish Register. He may have died and been buried at some other place, while fleeing the sacking of Brancepeth by In Charles Hutton’s Mathematical Tables1 we can read that, the Scots. “about the year 1650”, logarithmic lines were drawn in a “spe- cial form by a Mr. Milburne of Yorkshire”. However, Hutton Milburne’s Family did not describe this special form (though he partially lifted the veil in another book2 by saying that the logarithmic lines Little is known about Milburne’s family. He had an elder were in a spiral form) nor did he give any detail on this Mr. brother, Robert, who became a stationer and kept Milburne (not even his Christian name). “the Greyhound in Paul’s Churchyard”.6 Robert and William Many later articles on the history of the seem were the sons of Robert Mylborne (sic) and were baptised in to have simply borrowed the little information provided by 1595 and 1599 respectively. Charles Hutton. Even stated in his history of the logarithmic slide rule3 that according to Hutton “a Mr. Curate of Brancepeth7 Milburne of Yorkshire designed the spiral form of slide rule about 1650”. Cajori also stated that he had “not been able to The Clergy of the Church of Database (http://www. secure more detailed information relating to Milburne”. We theclergydatabase.org.uk/index.html) informs us that as from find the same statement in Leon Lalanne’s Instruction sur les July, 1615, Willimus Milborne or Milburne had been sizar at Règles à Calcul.4 “We have not been able to verify Hutton’s Christ’s College of Cambridge University (a sizar is a student informations on Wingate and Milburne. The name of the lat- who receives some form of assistance such as meals, lower ter is not even mentioned in the catalogue of the Bibliothèque fees or lodging during his or her period of study). William Nationale nor in any other bibliography”. was aged 22 when he was awarded the Bachelor of Arts on This article is an attempt to discover who Milburne was the 23rd of December, 1621. No birth place is given but curi- and why, being credited with the invention of the spiral ously, the database says also that, according to the Ordina- scales, so little of his work in this field is known to the 21st tion Register, he “was born both in Chesterford Magna, Essex, century collector. and Meldreth, Kent”. The same source says that Milburne was ordained deacon the day he graduated with a Bachelor Span of Life of Arts, on the 23rd of December, 1621. Five years later, on the 24th of December 1626, he was awarded the Master of The available information is not fully conclusive, but our Arts at the same Cambridge University and was ordained a William Milburne5 was most probably born at Great priest by the bishop of London, George Montaigne. Chesterford in the County of Essex (East of England) in the William Milburne, according to another source6 “gained year 1599. his B.A. degree in 1619-1620, entered holy orders, and pro- He died at an early age, in 1640, in the County of Durham ceeded to M.A. in 1623”. In the early 1630s Milburne was (North of England). His exact date and place of death are not eventually made curate at Brancepeth near Durham “divid- known, nor is the place of his burial. He might have been ing his time between his duties as curate of the parish and buried at Brancepeth where he lived, but there is no record of the prosecution of astronomical observations”.8 Volume 19, Number 2, Fall, 2010 49

FIGURE 1. St. Brandon’s Church in Brancepeth where William Milburne was curate

Troubled Times, the Bishops’ Wars9 Apparently, it was during the first Bishops’ War that most of Milburne’s documentation was destroyed. Was his William Milburne was curate at Brancepeth in a time of tur- death connected with the sacking of Brancepeth? Did he die moil and civil war: “...the state of things in England in the while fleeing the Scottish invasion? I have not been able to beginning of the seventeenth century was by no means find anything about this, not even a beginning of an answer. favourable to scientific pursuits; and towards the middle of it, the great commotion, which convulsed the frame of civil Mathematics and Astronomy society, threatened the extinction of science altogether”.8 In the summer of 1639, Charles I, king of England and Milburne was well versed in mathematics and astronomy and Scotland, in his attempts to reform the Scottish Church, was kept up a correspondence with others interested in these led to march toward the border of Scotland. He was con- fields. He is said to have extracted the approximate root of an fronted with a well-prepared Scottish army. None of the equation of the fifth degree before he had seen Harriot’s belligerents were very keen to fight; they concluded an agree- Praxis, the reference work on the subject at that time. ment known as the Pacification of Berwick. Sherburne10 states though that “...his greatest Labours King Charles had not abandoned yet his plans to sub- were in Astronomy, and his Observation of the Stars, he due Scotland. Being short of money, he was obliged, after used a good Cross Staff, and a Sextans of five foot Radius, more than ten years of absolute power, to call a Parliament in he discovered the weakness of Langsbergius his Astronomy, order to raise funds. He finally didn’t agree with the terms of and verified Kepler’s Tables, which he turned into Decimals”. the Parliament and dissolved it. This led to the second Bish- Milburne’s knowledge of astronomy must have been ops’ War: the Scots invaded England, without notable oppo- quite impressive as he was regarded by Sherburne as one of sition of the English army and, among other parts of En- the “four Lights of the northern hemisphere”, the three other gland, the County of Durham was overrun. Newcastle, which Lights being: William Gascoyne, William Crabtree, and controlled London’s fuel supply, was occupied by the Scots Jeremiah Horrocks. His observations were unfortunately in August, 1640. destroyed by the Scots in 1639 but some records were, in 1675, in the hands of Sir . 50 Journal of the Oughtred Society

Teacher of Mathematics and Astronomy III. Of mans timely remembring of his Creator. Heretofore communicated to some friends in written copies; William Milburne, who had been a pupil of Joseph Mede at but now published for the generall good.” Christ’s College, was apparently a good teacher and dis- This small octavo, containing two tracts by Thomas Jack- seminated mathematics and astronomy among the young men son and one sermon by John Donne, was unfortunately falsely of his parish. Jonas Moore, for instance, the famous English attributed to William Milburne by his brother Robert. This , identified Milburne as being his first teacher: case of almost plagiarism was much deplored by William in a “Upon the first comming in of the Scots 1640. in a solitary letter dated 20 April 1638 to his rector John Cosin: “I hope my retyrednesse, with a settled resolution, I fell upon the studyes brother of London hath bene mindfull to send you some of Mathematicall, animated thereunto by the promised helpe of the bookes of that copie which I made bold with your wor- Mr William Millburne, Minister of Brauncepeth, in the County ship to read before it went to presse, intitled be mee Sapientia of Durham, my most worthy friend, and a great Master in all Clamitans. The two first treatises in it (as I heare) are Dr. parts of Learning, who not many weekes after departed this Jackson’s which I alwayes suspected by the stile; as you life; leaving me either in choise to give over my journey or may remember I sayd unto your worship. And the other (some travel without Guide or Company.”6 say) is a sermon of Dr. Donne’s. I am mightilie vexed at my In a somewhat contradictory statement though, Moore brother, because it is so printed upon the title page as that also said that he owed all his knowledge to men being unacquainted with the matter take mee as the au- and his Clavis Mathematicae. As remarked by Frances thor, and not as the publisher onelie.”12 Willmoth, author of a book about Jonas Moore6, “this need not to be taken so literally as to devaluate the prior Milburne’s Serpentine Line acknowledgement. Oughtred, after all, was then alive, highly influential, and worth flattering; nevertheless, it was According to Frances Willmoth6, Milburne’s serpentine line Milburne, less well known and long since dead, whom Moore was advertised in The many uses of the spirall or serpentine chose to identify as his first teacher.” line &c, usefull for all in generall and for ingenious architects, measurers of land, carpenters and Milburne’s Scientific Works other mechanics in particular. First applied to these sev- eral practices by William Milburne M.A. and reduced into Apparently, not many of Milburne’s scientific works were this form with many additions by Jonas Moore, Professor of preserved after his death: “... his Observations and other the Mathematicks. This title, now lost, was entered in the Papers, &c. were unhappily lost, by the coming in of the Stationer’s Register in 1658; it is not known if it ever ap- Scots, in the year 1639”.10 but, thanks to his correspondence peared in print. with other mathematicians and astronomers, some of his thoughts were not wholly lost. Did William Milburne Invent The Serpentine Line? There is evidence that around 1650 some of Milburne’s belongings were in the hands of ; this latter There is a controversy as to who invented the spiral, or ser- writes, the 13th of August, 1650, that he “bought of Mr. pentine line. This paragraph borrows the information pro- Milbourn all his Books and Mathematical Instruments”.11 One vided by Florian Cajori in his History of the Slide Rule3. can only speculate whether there was a slide rule among Leybourn states in his The Line of Proportion13 that ac- these Mathematical Instruments bought by Ashmole. cording to Wingate “...Mr. Milbourn, a Yorkshire Gentleman, Milburne’s writings do not seem to have been under- disposed it in a Serpentine or Spiral Line, thereby enlarging standable by just anyone. Elias Ashmole, in his autobio- the divisions of the Line...... One T. Browne, a Maker of graphical notes (cited by footnote [6]), says that he had to Mathematical Instruments, made it in a Serpentine or Spiral cast a horoscope to find out whether he “shall ever under- Line, composed of divers Concentrick Circles, thereby to stand anything in the book [he] now had of Mrs. Milborn”. enlarge the divisions, which was the contrivance of one Mr. Milburn, a Yorkshire Gentleman, who writ thereof, and com- Wisdome Crying Out to Sinners municated his Uses to the aforesaid Brown, who (since his death) attributed it to himself...”. This would demonstrate Milburne’s sole religious work seems to have been a compi- that William Milburne was the inventor of the serpentine line lation of sermons - by other authors - published in 1638 (with and that Thomas Browne was merely the maker. reprints in 1639 and 1640) and engagingly entitled: Sapientia A privileged witness of that time though, William clamitans: wisdome crying out to sinners to Returne from Oughtred, does not even mention Milburne in his Epistle14 Their Evile Wayes: contained in three pious and learned and attributes the invention of the spiral line to Thomas treatises, viz. Brown. Oughtred says that the spiral form “was first hit upon I. Of Christs fervent love to bloudly Ierusalem. by one Thomas Browne a Joyner,... the serpentine revolution II. Of Gods just hardning of Pharaoh. being but two true semicircles described on severall cen- ters”. Volume 19, Number 2, Fall, 2010 51

Thomas Brown did not publish about his instrument but dius, he discovered the weakness of Lansbergius his son, John Brown, did. In his The Description and Use of his Astronomy, and verified Kepler’s Tables, which a Joynt-Rule, published in 1661, John Brown asserts that his he turned into Decimals, and made Tables after father had made a rule “into a serpentine form”. As stated by Kepler’s subsidiary way which were sent to his Cajori, we have no way to know whether the description of Brother Mr. Milbourn a Stationer in London, to be the serpentine line made by John Brown fits the instruments Printed; but never passed the Press, being yet pre- developed by his father in about 1632. served in MS. in the hand of Sir Jonas Moore Knight. All his Observations and other Papers, &c. were most Conclusion unhappily lost, by the coming in of the Scots, in the year 1639”. William Milburne, born in 1599 at Great Chesterford, York- shire, was ordained curate of Brancepeth, Durham County, in Acknowledgments the early 1630s. He was an amateur mathematician and as- tronomer who was keen to share his knowledge with the Most of the information contained in this article has been young men of his parish. There is indirect evidence that he either induced by partial data found with Google Books(tm)15 wrote a book about the use of the serpentine line; it is not or entirely found with it. One can only wonder what Florian known whether this book ever appeared in print. Almost all Cajori’s History of the Slide Rule and Allied Instruments of Milburne’s work was destroyed during the first Bishops’ would have been like, had he had Google Books(tm) at his War in 1639 or 1640; this might explain why there is so little disposal. I should like to express a special thanks then to the information available about him. authors and to the proprietors of this formidable search en- William Milburne died in 1640. The statement that he gine. drew spiral lines about the year 1650 would have to be ad- justed to before the year 1640. There is a controversy as to I should like also to thank: who invented the spiral line; some attribute its invention to William Milburne, but others, and among them William • Tim Eggington, Whipple Librarian, Department of History Oughtred, attribute it to Thomas Brown. As I have not been and Philosophy of Science, who was kind enough to send me able to find any publication, either from William Milburne or a photocopy of the entry for Milburne in Sherburne’s Cata- from Thomas Brown, wherein one of them claims the inven- logue of Astronomers10. tion, I will leave the dispute open. Many of the modern ar- • Peter Cargill from the Brancepeth Archives & History Group ticles on the history of the slide rule, though, incline to favour who forwarded my request for information about Milburne to the invention as being by Brown. Peter Storey. Was William Milburne particularly interested in the slide • Peter Storey, Chairman of the Brancepeth Archives & His- rule, or was his Many uses of the spirall or serpentine line a tory Group who checked the Parish Archives and provided mere pastime? Has his slide rule ever been made? It is hard to the picture of St. Brandon’s Church. know and with the little information left after his death it may • Peter Hopp for providing a copy of a reference I had over- be that we will never know. looked, and also for his useful advice. • Otto van Poelje who helped me improve the content of my Sherburne’s Catalogue of Astronomers article with his constructive criticisms and his questions.

Many of the works I have consulted to write this article cite Final Remark Sherburne’s Catalogue of Astronomers - appended to his Manilius10 - as a source for their information about Milburne. I was hoping, when I first started to gather documents about I had almost finished this article when I finally was able to lay William Milburne, that I would succeed in getting more infor- hands on a copy of the entry for William Milbourn (sic). This mation than I finally was able to obtain. is the oldest infomation I could find about him. Though the I wish this article will induce some readers to continue entry is not as comprehensive as I had hoped, here is the full the search further and-one may be optimistic-discover in a transcript of it: pile of old documents, forgotten in some attic of the “1640. WILLIAM MILBOURN Master of Arts, Cu- Ashmolean Museum at Oxford, a copy of Milburne’s The rate at Brancespeth near Durham, aged about forty many uses of the spirall or serpentine line. years, was very knowing in Arithmetick, particularly in Algebra (having in the year 1628 extracted the Root of this Equation, 1,000 = aaaaa-aaaa- 18 April 2010. 4aaa+3aa+3a. before he had seen Hariott’s Praxis) Panagiotis Venetsianos and in Geometry. But his greatest Labours were in Avenue de la Basilique 317-46 Astronomy, and his Observation of the Stars, he used B-1081 Bruxelles a good Cross Staff, and a Sextans of five foot Ra- Belgium 52 Journal of the Oughtred Society

Sources Page 402. Smith, Elder, & Co. London. 1899. • John Peile. Biographical Register of Christ’s College, 1505- Frances Willmoth’s Sir Jonas Moore. Practical Mathemat- 1905, and of the Earlier Foundation, God’s , 1448- ics and Restoration Science has been a breakthrough in my 1505. Page 302. University Press. Cambridge. 1910. quest for information and deserves a special mention. Be- • Eva Taylor. Mathematical Practitioners of Tudor and Stuart sides Frances Willmoth’s book and other sources already England. Published first by Cambridge University press, 1954. listed at the end of this article, I have made use of the follow- [Kindly provided by Peter Hopp.] ing documentation: • Jeanne Balsiger. The Kunst-und Wunderkammern: a Cata- • Bulletin des Sciences Mathématiques, Astronomiques, logue Raisonné of Collecting in Germany, France and En- Physiques et Chimiques. Tome premier. Page 69. Treuttel et gland, 1565-1750. University of Pittsburgh. 1970. Würtz. Paris. 1824. • Mordechai Feingold. The Mathematicians’ Apprenticeship. • E. Mackenzie and M. Ross. An Historical, Topographical, Science, Universities and Society in England, 1560-1640. and Descriptive View of the County Palatine of Durham. Page 111. Press Syndicate of the . Volume II. Page 314. Mackenzie and Dent. Newcastle upon Cambridge. 1984. Tyne. 1834. • Reid Barbour. Literature and Religious Culture in Seven- • Penny Cyclopaedia of the Society for the Diffusion of Use- teenth-Century England. Page 265. Press Syndicate of the ful Knowledge. Volume XI. Page 305. Charles Knight and Co. University of Cambridge. Cambridge. 2002. London. 1838. • S. Mutchow Towers. Control of Religious Printing in Early • The Edinburgh Review. No. CLVIII. Pages 409 and 410. Oc- Stuart England. Pages 63, 64 and 76. Boydell Press. tober, 1843. Woodbridge. 2003. • John Holmes Agnew. The Eclectic Magazine of Foreign • Pious. Webster’s Quotations, Facts and Phrases. Pages 128 Literature, Science and Art. January to April 1844. Pages and 159. Icon Group International., Inc. San Diego. 2008. 107, 108 and 109. Leavitt, Trow, & Co. New York and Philadel- • Treatises. Webster’s Quotations, Facts and Phrases. Page phia. 1844. 159. Icon Group • Geo. L. Craik. Sketches of the History of Literature and International., Inc. San Diego. 2008. Learning in England. From the Accession of Elizabeth to • http://www.archive.org the Revolution of 1688. Vol III. Page 173. Charles Knight & • http://books.google.be/bkshp?hl=fr&tab=wp Co. London. 1845. • http://www.durhamweb.org.uk/dit/brancepeth/index.htm • The Pictorial History of England. Volume IV. Page 768. • http://gallica.bnf.fr/ Harper & Brothers. Charles Knight and Co. 1846. • http://www.geometry.net/scientists/moore_jonas.php • George Ornsby. Sketches of Durham. Page 184. George • http://www.wikipedia.org/ Andrews. Durham. 1846. • Collections of the Massachusetts Historical Society. Vol. I. Footnotes of the third series. Page 243. Reprinted Charles C. Little and James Brown. Boston. 1846. 1. Charles Hutton. Mathematical Tables: containing com- • James Eccleston. An Introduction to English Antiquities. mon, hyperbolic, and logistic . Page 36. Page 373. Longman, Brown, Green, and Longmans. London. Printed for G.G.J. and J. Robinson, and R. Baldwin, Pater- 1847. noster-Row. London. 1785. • Augustus De Morgan. Arithmetical Books from the Inven- 2. Charles Hutton. Tracts on Mathematical and Philosophi- tion of Printing to the Present Time. Page 50. Taylor and cal subjects. Volume I. Page 331. Printed for F.C. and J. Walton. London. 1847. Rivington; G. Wilkie and J. Robinson,; J. Walker; &c. • George L. Craik and Charles Macfarlane. The Pictorial His- London. 1812. tory of England. Volume IV. Page 739. Harper & Brothers. 3. Florian Cajori. A History of the Logarithmic Slide Rule New York. 1848. and Allied Instruments. Page 15 and pages 141 to 143. • William Fordyce. The History and Antiquities of the County Originally published in 1910. Reprint by The Astragal Palatine of Durham. Vol I. Page 604. A. Fullarton and Co. Press. Mendham, New Jersey. 1994. ISBN 1-879335-52-2. London and Edinburgh. 1857. 4. Léon Lalanne. Instruction sur les Règles à Calcul et • William Whewell. History of the Inductive Sciences, from particulièrement sur la Nouvelle Règle à Enveloppe de the Earliest to the Present Time. Third edition. Volume II. Verre. Page V. Librairie de L. Hachette et Cie. Paris. 1851. Page 112. John W. Parker and Son. London. 1857. 5. Also spelled Milbourne, Milbourn, Milburne, Milburn, or • Charles Knight. Biography or Third Division of The En- Mylborne. glish Cyclopaedia. Volume III. Page 494. Bradbury, Evans, & 6. Frances Willmoth. Sir Jonas Moore. Practical Mathemat- Co. 1867. ics and Restoration Science. Pages 32 to 36. The Boydell • . Dictionary of National Biography. Vol. Press. 1993. XXXVIII. Page 373. Smith, Elder, & Co. London. 1894. 7. Also spelled Brancespeth, Branspeth or Brauncepeth. • Sidney Lee. Dictionary of National Biography. Vol. LX. 8. Article. Sir and his Contemporaries. The Volume 19, Number 2, Fall, 2010 53

Edinburgh Review. Page 409. October, 1843. Durham. Part I. Pages 221 to 223. Published by the Soci- 9. So called because Charles I wanted to impose Bishops on ety by Andrews & Co., Durham. Blackwood & Sons, the Scots. Edinburgh. 1869. 10. Edward Sherburne. The sphere of Marcus Manilius made 13. William Leybourn. The Line of Proportion or Numbers, an English poem with annotations and an astronomical Commonly called Gunter’s Line, Made Easie. Preface to appendix. Pages 91 and 92. Printed for Nathanael Brooke. the reader, and pages 127 and 128. London, 1673. London. 1675.Catalogue of Astronomers appended to 14. William Oughtred. To the English Gentries, and all others Manilius. studious of the Mathematicks.... Published without date 11. The Lives of those eminent Antiquaries Elias Ashmole, and bound in with Oughtred’s Circles of Proportion in Esquire, and Mr. , written by themselves. the editions of 1633 and 1639. Page 312. Printed for T. Davies. London. 1774. 15. Property of Google(TM). Google Book was formerly 12. The Correspondence of John Cosin, Lord Bishop of known as Google Print Library Project.

My First Electronic Slide Rule

David Sweetman

FIGURE 1. Hewlett-Packard HP-45

While the demise of the slide rule is attributed to the four first electronic slide rule was the HP-45, the immediate suc- function calculator, in reality the introduction of the scien- cessor to the HP-35. tific calculator, which is an easier and quicker to use tool, The HP-35 was the first scientific handheld calculator or signaled the demise of the traditional slide rule; see [1]. My electronic slide rule. It was developed at Hewlett-Packard