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University Microfilms, Inc., Ann Arbor, Michigan the UNIVERSITY of OKLAHOMA This dissertation has been microiUmed exactly as received 68-17 591 LAWRENCE, Gerald Charles, 1931- THE ASSIMILATION OF NEWTONIAN MECHANICS, 1687-1736. The University of Oklahoma, Ph,D,, 1968 History, modem University Microfilms, Inc., Ann Arbor, Michigan THE UNIVERSITY OF OKLAHOMA GRADUATE COLLEGE THE ASSIMILATION OF NEWTONIAN MECHANICS, 1687-1736 A DISSERTATION SUBlfflTTED TO THE GRADUATE FACULTY in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY BY GERALD CHARLES LAWRENCE Norman, Oklahoma 1968 THE ASSIMILATION OF NEWTONIAN MECHANICS 1687-1736 APPROVED BY —] DISSERTATION COMMITTEE ACKNOWLEDGMENTS To Professor Duane H. D. Roller who provided the initial stimulus to my study of the history of science, and to Professor Thomas M. Smith who guided me through my first year as a graduate student in the history of science, for their suggestions and criticisms concerning this dissertation. To Professor David B. Kitts for awakening in me the interest in the structure of scientific knowledge that provided the main thesis of this dissertation, and for his reading and criticism of it. And'^to my wife, Dora, without whose constant support this work would not have been possible. Ill TABLE OF CONTENTS Page INTRODUCTION................................... 1 Chapter I. THE MECHANICAL THEORY OF NEWTON'S PRINCIPIA. 18 II. THE NEWTONIANS AND ANTI-NEWTONIANS......... 69 III. FRENCH MECHANICS IN TRANSITION.............. ILA IV. FRENCH AND ENGLISH MECHANICS IN CONFLICT..... 216 CONCLUSION..................... 254 BIBLIOGRAPHY.............. 260 IV THE ASSIMILATION OF NEWTONIAN MECHANICS, 1687-1736 INTRODUCTION The period extending from the publication of the Philosophiae naturalis nrincipia mathematica of Isaac Newton (1642-1728) in l687 to the publication of the Mechanica sive motus scientia analvtice exposita of Leonhard Euler (1707-1785) in 1736 is one that shows no profound new developments in mechanical theory and is, for this reason, passed over in works dealing with the development of mechanical thought on a large scale.^ However, precisely because there seems to be so little advance, this period is of interest from the standpoint of the process through which ideas are assimilated by what might be~t.ermed second-rate thinkers. These are the men who perform the work of criticism and elaboration on the ideas provided by the men of superior creative insight. The par­ ticular period under consideration here is unusually illuminating for a number of reasons : the tension in the political atmosphere between England and France, the impact of the initial phases of industrial rev­ olution, but especially because of the nature of Newton’s innovations in See René Dugas, A History of Mechanics (New York: Central Book Company, Inc., 1955), Eugen K. Duhring, Kritische Geschichte der allgemeinen Prinzioien der Mechanik (Leipzig: Fues's Verlag, 1887) Ernst Mach, Die Mechanik in ihrer Eutwickelung historisch-kritisch dargestellt (Leipzig: F. A. Brockhaus, 1904). 2 mechanical thought and in the conception of the nature of scientific explanationo In the Princinia. Newton laid out an extremely impressive, but somewhat obscure theory of mechanics. It takes a good measure of hind­ sight and a considerable amount of analysis to make out the true nature of Newton's thought, so that the vast array of theorems presented in the Princinia seemed to his contemporaries more an achievement inviting awe and belief than an understandable theoretical system. In contrast to this, Euler, in his Mechanics. elaborated mechanical theory in terms of analysis, as is indicated in the title of the book, and, in so doing, produced a work that represented an understandable system, provided of course that one understood analysis, i.e., the differential and integral calculus. Euler wrote that the use of geometrical demonstrations— the means of demonstration employed by Newton— serves to convince one of the truth of a statement of principle, but does not give understanding. This 2 can only be achieved in analysis. Euler's use of the word "understanding" seems to imply more than comprehension of a merely logical system. It demands insight into the actual physical processes whose observable consequences are represented by theory as well as insight into the ultimate nature of the matter involved in these processes. This sort of understanding is what was provided by the calculus. 2 Leonhard Euler, Leonhard Euler's Mechanik oder analvtische Darstellung der Wissenschaft mit Anmerkungen und Erlauterungen. heraus- gegeben von J. Ph. Wolfers (Greifswald: C, A. Kogh's Verlagshandlung, 184.8), I, pp. 3-4.. 3 However, since Euler's formulation of mechanical theory, as well as those of Joseph-Louis Lagrange (1736-1813) and William Rowan Hamilton (l805-l865), was mathematically equivalent to Newton’s formula- tion, it seems likely that both, or all, were founded on the same mathematical basis. Further, there is the age-old distinction between mathematics as a method of discovery and mathematics as a means of demon­ stration to consider: how did Newton come by the discoveries which he proved in the traditional, geometrical manner? Since Newton was the inventor of an infinitesimal calculus, the so-called calculus of fluxions, there is a possibility that calculus was the tool used in the construc­ tion of his theory. As such, the calculus would constitute the "under­ standable" structure of the theory. It is upon this thesis that the present work rests; with the assumption that analysis is the implicit structure of Newton's mechanics the period under examination takes on, in one aspect, the form of a dissemination.of a new type of mathematical thought, i.e., the infini­ tesimal calculus. This would suggest that Gottfried Wilhelm Leibniz (1646-1716), who was an independent inventor of the infinitesimal calcu­ lus, might have exerted a large influence on mechanical thought in the period. In fact, as will be shown, the influence of Leibniz, especially through John Bernoulli (1667-174-8), was more decisive than that of Newton on the French mechanicians, who were, on the whole, far advanced over their English contemporaries. O Ernest Nagel, The Structure of Science. Problems in the Logic of Scientific Explanation (New York: Harcourt, Brace and World, Inc., 1961), p. 158. u With this in mind, the study of the history of mechanical thought between 1687 and 1736 can be broken down into a number of major, problems: the mathematical nature and origins of Newton's theory of mechanics, the difficulties that that theory entailed for his English followers, the differences between English and French mechanical tradi­ tion, the nature and scope of Leibniz's contributions to mathematical- mechanical thought, grounds for the French acceptance and English rejection of Leibniz, and finally the basis on which a reconciliation of French and English mechanical thought could be made. These subsidiary problems suggested by the mathematical aspect of the development of mechanical theory can be more easily and adequately treated when the relation of mathematics to physical theory is understood. According to Ernest Nagel, scientific theory can be analyzed into three major components: an abstract calculus^ which is the logical skeleton of the theory; a set of rules that assign an empirical content to the abstract calculus (so-called rules of correspondence); and an interpretation for the abstract calculus, which gives "flesh" to the skeletal structure From this analysis of the component parts of theory, the infinitesimal calculus invented by Newton and Leibniz should correspond to the logical structure of mechanics. That is, the system of postulates and definitions that constitute the basis of the theory should form an abstract relational structure for the terms of the theory which is the same as the infinitesimal calculus. For instance, the relationships between force, distance, velocity, and acceleration defined in the '^Ibid. ; p. 90. 5 mechanical theory should correspond exactly to the relationships between similar terms in the infinitesimal calculus. If the abstract calculus were the only significant aspect of scientific theory, the history of mechanics in the period would be simply a matter of tracing the spread of mathematical understanding; anybody who could operate with the calculus could understand and accept the corres­ ponding theory of mechanics. However, the other two components of theory are of equal importance and are capable of producing controversy and even of obscuring the understanding or preventing the acceptance of the cal­ culus as a proper relational structure for mechanics. With regard to the matter of assigning empirical content to the theory, a long and acrimonious dispute was carried on between Newtonian and Leibnizian adherents over the proper empirical determination of force in a moving body; the Newtonians insisted that force was proportional to the velocity and the Leibnizians insisted that it was proportional to the square of the velocity. Both of these results could be derived from the theory and verified in experience, depending on whether one assumed that the time factor or the distance factor was of basic significance in the understanding of force. The interpretation of the abstract calculus was, however, the popularly significant aspect of any mechanical theory, from the point of view of its acceptance or rejection. As has been stated, the interpre­ tation gives "flesh" to the abstract calculus; it provides the physical and metaphysical elaboration that ties the theory to reality. The pic­ ture of reality carried in Newton's mechanics, for instance, offended many men because in it particles of matter could affect other particles of 6 matter without being in contact with them; it offended others because it seemed to make the world too deterministic and to leave no place for the free action of God or the freedom of the human mind. Leibnizian ideas on mechanics, on the other hand, were associated with his theory of "monads," which had a somewhat mystical character and was simply unacceptable in an individualistic and materialistic age; matter as hard massy particles did not have real existence for Leibniz.
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