DIE NATURWISSENSCHAFTEN 63. Jahrgang, 1976 Heft 2 Februar History of Classical Mechanics Part I, to 1800 C. Truesdell Professor of Rational Mechanics, The Johns Hopkins University, Baltimore, Maryland 21218, U.S.A. This article sketches the main discoveries in the quantitative, mathematical science of mechanics. Part I, after referring to the origins in Greek and Mediaeval times, traces the growth of the science in the seventeenth and eighteenth centuries. The savants of those centuries, Euler above all, gave to mechanics most of its major concepts, and they formulated several parts of it as clear, succinct, and fairly definitive disciplines, which have retained their identies to this day. The second part of the article will carry the history of mechanics down to the present. I know that it will bee said by many, That I might have of "pure" mathematics. At the other, it is invention beene more pleasing to the Reader, if I had written the of machines or practice with them, described sugges- Story of mine owne times; having been permitted to tively if loosely in terms which some will think to have draw water as neare the Well-head as another. To this been borrowed from mathematical science, while I answer, that who-so-ever in writing a moderne Historie, others will regard them as providing the basis in experi- shall follow truth too neare the heeles, it may happily ence for the corresponding concepts of mathematics. strike out his teeth. There is no Mistresse or Guide, that Between these two extremes lies what physicists call hath led her followers and servants into greater miseries. mechanics. ... It is enough for me (being in that state I am) to write of the eldest times: wherein also why may it not be said, The Folklorish History of Mechanics that in speaking of the past, I point at the present, and taxe the vices of those that are yet lyving, in their persons However "objective" may be science itself, it is the that are long since dead; and have it laid to my charge ? certified preserve of a jealous guild or cult and thus has its folklore. This folklore is usually inculcated Sir Walter Ralegh, imprisoned on a capital charge in the Tower of through notices labelled "history" in textbooks. London, 1614 Because most of the natural sciences pursued today are inventions of the last century, in order to produce a history of science having a respectable antiquity it Background of this Sketch is necessary to fix attention on mechanics, and, so as to fit preconceptions as to what natural science Mechanics is or at least ought to be, this "history" of mechanics Next to mathematics itself, mechanics is the 01dest is largely invented. Although purveyed originally in of the logical sciences. While algebra and analysis refer textbooks of physics, it is now disseminated even only to sets and functions, irrespective of how they more intensely in introductory courses on the biologi- may be suggested by experience, and while geometry cal sciences and psychology. reflects experience only through relations among posi- This folklorish history may be summarized in a few tions, irrespective of what occupies them or how it lines. Despite the temporary advance toward godfree may come to do so, mechanics enriches the discourse and hence "scientific" thought made by the Greeks, by providing logical models for time, mass, force, mankind fell back into piety. The Middle Ages lay energy, and, finally, heat and temperature. Thus inert beneath a pall of scholastic repetitions, appealing mechanics has many aspects. At the one extreme, it to Aristotle instead of to experiment. Copernicus said is mathematics-indeed, to the layman indistinguish- Aristotle was wrong, and Galileo dropped weights able from algebra, analysis, geometry, and other parts from the tower of Pisa so as to shatter scholasticism Naturwissenschaften 63, 53-62 (1976) by Springer-Verlag 1976 53 54 Naturwissenschaften 63, 53--62 (1976) O by Springer-Verlag 1976 by an irrefutable, simultaneous thud. From then on, It is full of gaps, gaps which reflect my ignorance only reactionaries (non-scientists) set up theories with- of some parts of mechanics as well as of many parts out first collecting heaps of data. Kepler proved Coper- of its history, but I prefer to reveal that ignorance nicus right to within eccentricity and set up empirical by silence rather than by parroting the fruits of others' laws of planetary motion. Descartes and Leibniz were labor or carelessness. The reader will perceive my bias. put to shame for their failure to adhere to the nine- I hope he will perceive also that that bias is the result teenth century program, but Newton showed Kepler's not of prejudice but of judgment, judgment induced laws to be consequences of the fact that each body from a lifetime of study in which the past and present in the universe attracts every other one by a force of creative mechanics have illuminated each other inversely proportional to the square of the intervening mutually. distance. To do so, he had to lay down (on the basis of experiment) three Laws of Motion. In the words Ernst Mach (1838-1916) wrote in his famous history Old Cultures of mechanics-the acknowledged classic of this folk- Archimedes (A.C. 287-212) lore- "Newton discovered universal gravitation and completed the formal enunciation of the mechanical Archimedes' amazing insight into mathematical pro- principles now generally accepted. Since his time no cesses and superb standard of mathematical rigor in essentially new principle has been stated. All that has reasoning about problems of mechanics have inspired been accomplished in mechanics since his day has been everyone who could read his works. He showed how a deductive, formal, and mathematical development to use the law of the lever, and ever since his day of mechanics on the basis of Newton's laws." Mach it has been a keystone of mechanics. He set up axioms refers, of course, to "classical" mechanics, the history for the equilibrium of floating bodies. His theory did of which makes up all but the last eighty years of not reveal much about fluids but was specially designed the history of all kinds of mechanics. for the particular problem he studied: to find all posi- Nearly a century has passed since Mach's book was tions in which a given body, such as a segment of published. More serious students, willing to take the a paraboloid of revolution, may float, and to determine trouble to learn before generalizing, have scrutinized their stability or instability. He regarded a position and analyzed, line by line, the works of discovery, as stable if the body when displaced from it and then have brought to light and published dozens of volumes constrained to remain at rest suffered a torque tending of sources previously unknown. Mach's picture of the to restore it to that position. development of mechanics, though it remains Although ancient Greece produced many other fine accepted folklore, as history has been shown to be mathematicians, I can find no evidence that any of so largely false as to mislead even in regard to such them turned his attention to mathematical theories details as it does recount more or less justly. of mechanics, or that Archimedes' discoveries were enlarged. The only culture to develop a mathematical science of mechanics - rational mechanics - is the Eur- Present State of the True History of Mechanics opean West. Although other cultures, both older and younger ones, had expert and sometimes creative No competent man today would dare to write a general schools of arithmetic, algebra, number theory, geo- history of mechanics. Too much remains dead on metry, and celestial kinematics, in their remains I can library shelves, buried in print as yet unread by any find no evidence of even the most special or primitive of the inframinority who know enough science and original mathematical thinking about mechanics. To enough history to follow and comprehend them word see that achievements of the utmost skill and success by word and equation by equation-for science with- in mechanical construction and contrivance need not out accurate detail, "general" science, is mere sociolo- lead to any scientific discipline or quantitative theory gy or propaganda, neo-Machism. The now numerous of mechanics, we need only consider that notoriously competent studies of various special topics remain un- unmathematical people, the Ancient Romans. The digested and unconnected. The gaps between them central idea of scientific mechanics is force as a mathe- are as long as the stretches they cover. The student matical quantity, and force is a characteristic concept who searches for historical truth is blocked by the of the European West. vast middens of words on which those eager to exalt their own incompetence in the science of all periods into professional expertise in the history of science Origins in the West raise their hogans ever higher, words which, while rarely trustworthy, nevertheless cannot be flatly ignored. The Middle Ages The nature and properties of motion were studied again and again in the Middle Ages. Jordanus de The Nature of this Sketch Nemore (before 1260) asserted that the weight of a The text I present here expresses my view of some of body was diminished when it fell along a direction the major stages in the creation of classical mechanics. oblique to the vertical. In his reasoning he appealed Naturwissenschaften63, 53-62 (1976) by Springer-Verlag 1976 55 to a special case of what came much later to be called in steady flow and distinguished accurately between the principle of virtual work. He set up for study and the whirling of a vortex and the rotation of a wheel.