AN ABSTRACT OF THE THESIS OF WALTER LYLE BELL for the degree DOCTOR OF PHILOSOPHY (Name) (Degree) in GENERAL SCIENCE presented ond; je4 /p74 (Major Department) (Date) Title: CHARLES BABBAGE, PHILOSOPHER, REFORMER, INVENTOR: A HISTORY OF HIS CONTRIBUTIONS TO SCIENCE Red acted for Privacy Abstract approved James Bkrsiokes Spencer i This history concerns the scientific contributions of Charles Babbage (17 91-1 87 1) to mathematics, to the invention of calculating machines, and machine tools,to the development of scientific ideas through a wide variety of scientific investigations and his involvement in several different scientific reforms. Babbage considered himself a philosopher in the broadest sense of the word and looked upon the whole of science as his domain of inquiry.The broad speculative and philosophical aspects of his scientific inquiries; the theoretical and technical aspects of his work relating to mathematics and calcu lating machines; and his ideas concerning the development of science as a profession and the role of government inthe support of science will be examined in relation to his scientific career. Babbage began his scientific career in 1812, when, as an undergraduate at the University of Cambridge, he joined with John Herschel (1792-1871), Edward Ffrench Bromhead (1789-1855), George Peacock (1791-1858), and other students to form the Analytical Society for the purpose of promoting the study of mathematical analy- sis and introducing the methods and notation of the differential calculus of Gottfried Wilhelm Leibniz (1646-1716) to replace the fluxional calculus of Isaac Newton (1642-1716).Babbage and his friends were actually carrying out a reform movement begun by Robert Woodhouse (1773-1827), a professor at Cambridge, whose ideas had not gained much acceptance until the Analytical Society was formed. The mem- bers of the Society published mathematical works which utilized Leibnizian methods and notation; translated and supplemented an elementary calculus textbook by Sylvestre Franiois Lacroix (1765- 1843), a French mathematician; wrote and published three books of examples to accompany Lacroix's textbook; and gained control of the mathematical content at Cambridge by becoming moderators of the annual Senate House examinations and posing examination questions which made use of Leibnizian methods and notation.Through these activities the members of the Analytical Society were successful in achieving their mathematical reform by about 1822. Babbage and his associates continued to promote scientific reform throughout the eighteen twenties and thirties by attempting, unsuccessfully, two reforms in 1828 and 1830 of the Royal Society; by successfully reforming the Nautical Almanac and Astronomical Ephemeris which prior to 1811 had been the foremost work of its kind in Europe; and by forming new scientific societies.After Babbage and his associates were unsuccessful in attempting the reform of the Royal Society in 1830, David Brewster (1781-1839), a scientist and Vice- Chancellor of the University of Edinburgh, assumed the leadership for the group and founded the British Association for the Advancement of Science in 1831.Babbage participated in the British Association between 1832, when he was named a permanent trustee, and 1839 when he resigned because of an intrigue by another trustee of the Associa- tion. These reform activities and his mathematical researches form the first aspect of Babbage's career, between about 1812 and 1840. Babbage established a reputation as a first-rate mathematician through his work in the calculus of functions, in statistics, and in probability theory. As the result of his mathematical work, he was named Lucasian Professor of Mathematics, a chair which Newton had held and which Babbage held from 1828 to 1839.Babbage was also instru- mental in the founding of a statistical section of the British Association in 1833.In 1834, the statistical section was established as a separate society, the London Statistical Society, and it was in this Society that Babbage remained active for the remainder of his life. A second aspect of Babbagets scientific career began about 1820 and was devoted to the development of automatic calculating machines. His first calculating machine, Difference Engine No. 1, was designed to calculate and print mathematical and astronomical tables. Babbage received a gold medal from the Astronomical Society of London in 1823 for the invention of Difference Engine No. 1.He worked upon this engine from 1823 to 1833, during which time he received support from the government. After 1833, following a dispute with his engineer, Joseph Clement, Babbage ceased work upon Difference Engine No.1 and began work upon a new calculating engine, the Analytical Engine.Babbage continued to negotiate with the government concerning Difference Engine No.1 until 1842, when the government formally withdrew its support of the engine. Babbage continued to work upon the Analytical Engine for the remainder of his life.This machine employed many of the features of modern digital computer s--punched cards for data and instructions; an arithmetical-logical unit; a unit to store instructions, data, and results; and a printing device for recording the results of the calcula- tions.In 1848, Babbage also drew up plans for a Difference Engine No. 2 based upon the improvements resulting from the development of the Analytical Engine.While none of the calculating machines were completed, the principles upon which they were based were fully demonstrated by the portion of Difference Engine No.1 which was assembled in 1833; by the advancement of the machine tool industry and mechanical,engineering through the development of new machine tools, new standards of tolerances and mechanical drawings, and a mechanical notation; and by the advanced principles employed in the Analytical Engine which was capable of calculating any function and was therefore an entirely general calculating machine. In addition to his reform activities, mathematical researches, and work with calculating engines, Babbage carried out many varied scientific experiments which were reported in publications throughout his career.Although he is remembered primarily for his work as a reformer and as an inventor of calculating machines, Babbage possessed broad interests and an inquiring intellect as demonstrated by such diverse publications as a book on life assurance societies, a paper on his invention of occulting signal lights for lighthouses, a paper on his experiments with magnetism, and a paper on the prin- ciples of turning and planing metals. 0 1975 WALTER LYLE BELL ALL RIGHTS RESERVED Charles Babba,ge, Philosopher, Reformer, Inventor: AHiStory of His Contributions to Science by Walter Lyle Bell A THESIS submitted to Oregon State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy June 1975 APPROVED: Redacted for Privacy Ass1 ciate Prossor ofHistory Science in charge of major Redacted for Privacy Head of the Department of General Science Redacted for Privacy Dean of Graduate School Date thesis is presented a-"ellie4/5)? /1,77 Typed by Clover Redfern for Walter Lyle Bell TABLE OF CONTENTS Chapter Page PROLOGUE Biographical Sketch Purpose and Scope of the Study Acknowledgements PART I--INDIVIDUAL AND COLLECTIVE EFFORTS TO REFORM SCIENCE IN ENGLAND I.ROBERT WOODHOUSE, A CAUTIOUS REFORMER 2 State of Mathematics in England Woodhouse's Contributions to Reform William Henry Mau le Supports Reform II.. THE ANALYTICAL SOCIETY-- PURE D-ISM OR DOT-AGE? 25 Plan and Goals of the Society Contributions of Society Members to Mathematical Reform Reasons for a Successful Reform Opposition to Reform Critique and Reflections Upon the Reform III.THE EXTERNAL COTERIE--A LIBERAL SCIENTIFIC PARTY WITH ELITIST VIEWS 68 State of Science in England External Coterie Opposes President and Council of Royal Society Order of Bath--Recognition of a Civil and Scientific Elite Resistance to the External Coterie Reform of the Nautical Almanac and Astronomical Ephemeris IV. THE DECLINE OF SCIENCE IN ENGLAND--A CONTROVERSY 100 A Debate on the State of Science in England State of Chemistry State of Mathematics Reciprocal Relation of Science and Education Private and Governmental Support of Science Chapter Page Contributions of College and University Professors to Science A Relative Decline of Science V. THE FOUNDING OF A BRITISH SCIENTIFIC SOCIETY 126 Election of Davies Gilbert as President of the Royal Society Attempted Reform of the Royal Society in 1828 Duke of Sussex and John Herschel Vie for President of Royal Society External Coterie Declines Participation in Reform of Royal Society David Brewster Moves to Form a New Society Implications of the British Association to Science General Conclusions to Part I--Individual and Collective Efforts to Reform Science in England 165 PART IIBABBAGE'S CALCULATING ENGINES VI. BABBAGE's CALCULATING ENGINES 170 General Introduction 170 Speculative and Theoretical Considerations Relating to the 'Calculating Engines 173 VII. DIFFERENCE ENGINE NO. 1--ORIGIN AND EARLY DEVELOPMENT 187 Origin of Ideas for a Calculating Engine Preliminary Models Mechanical and Theoretical Design Importance as an Invention VIII. DIFFERENCE ENGINE NO. 1--THE ISSUE OF GOVERNMENTAL SUPPORT 206 Generating Public Support for the Engine Reception of Gold Medal from Astronomical Society Negotiations with Governmental Officials Attempts to Gain Long--range Governmental Support Moral Difficulties Chapter Page IX. REACTIONS TO