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325 YEARS OF ’S PRINCIPIA

PRADIP K. DATTA*

Newton’s Principia Mathematica was published 325 years ago. The Principia provided a physical and mathematical basis for how basic elements of the universe work and how celestial bodies move and interact with each other and laid the foundation of modern science. In this article we have discussed briefly the contents of the Principia, its publication and the socio-economic background of Newton’s emergence. It has been discussed that the social necessity at that time was responsible for Newton’s emergence and the Principia.

Introduction celestial bodies move and interact with each other. In it he showed how his principle of universal gravitation provided ne of the most important works in the history of an explanation both of falling bodies on the earth and of science, Philosophiæ Naturalis Principia the motions of planets, , and other bodies in the Mathematica (Mathematical Principles of Natural O heavens. The first part of the Principia is devoted to Philosophy), often called simply as the Principia, was first and includes Newton’s three famous laws published 325 years ago on 5 July 1687. (After annotating of motion, forming the foundation of , and correcting the first edition, Newton also published two also Newton’s law of universal gravitation, and a derivation further editions, in 1713 and 1726.) This is one of the of Kepler’s laws of planetary motion (which Kepler first greatest milestones in the history of science and one of obtained empirically). The second part is devoted to fluid the world’s most important scientific treatises. It quickly motion and other topics; and the third part to the system vaulted him to the elite ranks of scientific theorists. Widely of the world, i.e., the unification of terrestrial and celestial regarded as one of the most important works in both mechanics under the principle of gravitation .According to the science of physics and applied mathematics during the French mathematical physicist Alexis Clairaut, “The the , the work underlies much of the famous book of Mathematical Principles of natural technological and scientific advances from the Industrial Philosophy marked the epoch of a great revolution in Revolution (usually dated from 1750) which its tools helped physics. The method followed by its illustrious author Sir to create. It united two competing strands of natural Newton ... spread the light of mathematics on a science philosophy—experimental induction and mathematical which up to then had remained in the darkness of deduction—into the of the modern era. conjectures and hypotheses”. His emphasis on experimental observation and mathematical analysis changed the scope and possibilities The Principia of science. Viewed retrospectively, no work was more seminal The Principia provided a physical and mathematical in the development of modern physics and astronomy than basis for how basic elements of the universe work and how Newton’s Principia. The ‘Principia’ deals primarily with massive bodies in motion, initially under a variety of * Kalpana Chawla Centre for Space and Nano Sciences, Retired Reader and Head, Department of Physics, Presidency conditions and hypothetical laws of force in both non- College, Kolkata-73, e-mail : [email protected], resisting and resisting media. It attempts to cover [email protected] hypothetical or possible motions both of celestial bodies

72 SCIENCE AND CULTURE, MARCH-APRIL, 2014 and of terrestrial projectiles. It explores difficult problems astronomy. It builds upon the propositions of the previous of motions perturbed by multiple attractive forces. Its third books, and applies them with further specificity than in and final book deals with the interpretation of observations Book 1 to the motions observed in the solar system. Several about the movements of planets and their satellites. It shows of the features and irregularities of the orbital motion of how astronomical observations prove the inverse square the Moon. Newton lists the astronomical observations on law of gravitation (to an accuracy that was high by the which he relies and establishes in a stepwise manner that standards of Newton’s time); offers estimates of relative the inverse square law of mutual gravitation applies to solar masses for the known giant planets and for the Earth and system bodies and is universal. He also gives the theory the ; defines the very slow motion of the Sun relative of the motions of comets based on the data obtained to the solar-system barycenter; shows how the theory of from John Flamsteed and from Edmond Halley, and gravity can account for irregularities in the motion of the accounts for the tides, attempting quantitative estimates of Moon; identifies the oblateness of the figure of the Earth; the contributions of the Sun and Moon to the tidal motions; accounts approximately for marine tides including and offers the first theory of the precession of the phenomena of spring and neap tides by the perturbing (and equinoxes. Book 3 also considers the harmonic oscillator in varying) gravitational attractions of the Sun and Moon on three dimensions, and motion in arbitrary force laws. In the Earth’s waters; explains the precession of the equinoxes Book 3 Newton also made clear his heliocentric view of as an effect of the gravitational attraction of the Moon on the solar system, recognized the “deviation of the Sun” the Earth’s equatorial bulge; and gives theoretical basis for from the centre of gravity of the solar system and estimated numerous phenomena about comets and their elongated, the mass ratios Sun: Jupiter and Sun: Saturn. near-parabolic orbits. The opening sections of the ‘Principia’ contain, in revised and extended form, nearly all of the content of The General Scholium is a concluding essay added to Newton’s “De motu corporum in gyrum” (On the motion the second edition, 1713 (and amended in the third edition, of bodies in an orbit) which summarises the topics and 1726). It is best known for the “” (“I indicates where they reappear in the ‘Principia’. do not frame hypotheses”) expression, which Newton used as a response to some of the criticism received after the The ‘Principia ‘begins with ’Definitions’ and ’Axioms release of the first edition (1687). In the essay Newton not or Laws of Motion’ and continues in three books: only counters the of René Descartes Book 1, subtitled ”De motu corporum in gyrum”, and Gottfried Leibniz, but also addresses scientific concerns motion in the absence of any resisting medium. methodology, theological and metaphysical issues. It opens with a mathematical exposition of “the method of Newton’s gravitational attraction, an invisible force able to first and last ratios,” a geometrical form of infinitesimal act over vast distances, had led to criticism that he had . It contains proof of Kepler’s second law, and introduced “occult agencies” into science. Newton firmly relationships between centripetal forces varying as the rejected such criticisms and wrote that it was enough that inverse-square of the distance to the center and orbits of the phenomena implied gravitational attraction, as they did; conic-section form, etc. but the phenomena did not so far indicate the cause of this gravity, and it was both unnecessary and improper to Book 2 largely concerns motion through resisting frame hypotheses of things not implied by the phenomena: media and also hydrostatics and the properties of such hypotheses “have no place in experimental compressible fluids, the effects of air resistance on philosophy”, in contrast to the proper way in which pendulums along with Newton’s account of experiments “particular propositions are inferred from the phenomena that he carried out, to try to find out some characteristics and afterwards rendered general by induction”. of air resistance in reality by observing the motions of pendulums under different conditions. Newton compares Contrary to the deductive approach of Descartes and the resistance offered by a medium against motions of Leibniz, Newton holds an inductive approach to scientific bodies of different shapes, attempts to derive the speed of inquiry. Phenomena should first be observed, and then sound, and gives accounts of experimental tests of the general rules should be searched for, and not vice versa. It result. is this approach, states Newton, that has led to the discovery of “the laws of motion and gravitation”. Book 3, subtitled “De mundi systemate” (On the system of the world) is an exposition of many consequences Newton also underlined his criticism of the vortex of universal gravitation, especially its consequences for theory of planetary motions, of Descartes, pointing to its

VOL. 80, NOS. 3–4 73 incompatibility with the highly eccentric orbits of comets, and the other two books somewhat later. The complete which carry them “through all parts of the heavens work, published by Halley at his own financial indifferently”. risk, appeared in July 1687. Newton’s religious views are found in the General Social and Economic Background of Newton’s Scholium. It has been claimed that the text implies that Emergence Newton was an anti-Trinitarianist heretic. With no comments explicitly addressing the subject of the Holy Trinity, several Let us now discuss where is the source of Newton’s parts of the text seem to raise anti-Trinitarianist positions creative genius? What determined the content and the indirectly, most notably. direction of his work? It is to be remembered that human thoughts and ideas are conditioned by the limits of time, Publication space and the social environment. However great a genius man may be his power of thinking can by no means Early in his career, Newton was reluctant to publish supersede the limits of objective condition. his work. The publication of The Principia was the result of Halley’s visit to Newton in 1684. At that time Halley The remarkable development of natural science was working on planetary motions, but faced some during the 16th and 17th centuries was the result of the problems. He visited Newton to discuss the problems. disintegration of the feudal economy, the development of When Halley asked Newton’s opinion on the problem of mercantile capital and of heavy (mining and metallurgical) planetary motions Newton surprised Halley by saying that industry and the development of private property. Trade he had already made the derivations some time ago; but and manufacture created the bourgeoisie. This period began that he could not find the papers. Halley then had to in the mid-17th century and continued to the end of the wait for Newton to ‘find’ the results, but in November 1684 18th. Newton’s activities fall within the second period in Newton sent Halley an amplified version of whatever the history of the development of private property. previous work Newton had done on the subject. This took Consequently, we shall first discuss the historical demands the form of a 9-page manuscript, “De motu corporum in presented by the emergence. Three prominent spheres that gyrum” (Of the motion of bodies in an orbit). This tract were of decisive importance to the social and economic contained the nucleus that Newton developed and expanded system were communications, industry and war. The to form the Principia. Halley was at that time a Fellow physical problems presented by the development of and Council member of the Royal Society in London. The transport, industry and mining were all fundamentally contents of “De motu corporum in gyrum” so excited mechanical problems. The development of the productive Halley by their mathematical and physical originality and forces in the age of mercantile capital presented science far-reaching implications for astronomical theory, that he with a number of practical tasks and urgently demanded immediately went to visit Newton again, in November their solution. Official science, based in the mediaeval 1684, to ask Newton to let the Royal Society have more universities, not only made no attempt to solve these of such work. The results of their meetings clearly helped problems, but actively opposed the development of the to stimulate Newton with the enthusiasm needed to take natural sciences. his investigations of mathematical problems much further In the 15th to the 17th centuries the universities were in this area of physical science, and he did so in a period the scientific centres of feudalism. They were not only the of highly concentrated work that lasted at least until mid- bearers of feudal traditions, but the active defenders of 1686. On April 21, 1686 Halley read to the Royal those traditions. Society his Discourse concerning Gravity and its Properties, in which he states “that his worthy countryman Throughout the medieval period European scholars Mr. has an incomparable treatise of motion had relied heavily on the teachings of Aristotle (384-322 almost ready for the press,” and that the law of the inverse B.C.) and the works of a few Christian philosophers. In square “is the principle on which Mr. Newton has made order to develop industry, the bourgeoisie required a science out all the phenomena of the celestial motions so easily that would investigate the properties of material bodies and and naturally, that its truth is past dispute.” Royal Society the manifestations of the forces of nature. Hitherto science decided to publish the book and entrusted Halley to had been the humble servant of the church and had not undertake the business of looking after it, and printing The been allowed to go beyond the limits set by the church. Principia at his own charge.The first of the three constituent The bourgeoisie had need of science, and they came into books was sent to Halley for the printer in spring 1686, conflict with the feudal church. The intellectual community

74 SCIENCE AND CULTURE, MARCH-APRIL, 2014 began to challenge firmly held academic and religious The Principia established mathematics as the language of beliefs. In the late 15th century there was a rediscovery science. Mathematics became a means of knowing about and popularization of ancient philosophers, such as Plato the universe. (427- 347 B.C.). Nicolaus Copernicus (1473-1543) had We thus see that the rising bourgeoisie brought natural moved the Earth away from the center of the universe with science into its service, into the service of the developing the heliocentric theory for which he presented evidence in productive forces. Being the most progressive class at that his book De revolutionibus orbium coelestium (On the time, it demanded the most progressive science. The revolutions of the heavenly spheres) published in 1543. English Revolution gave a mighty stimulus to the The structure was completed when (1571- development of the productive forces. This objective and 1630) wrote the book Astronomia nova (A new astronomy) material condition is the source of Newton’s creative genius. in 1609, setting out the evidence that planets move in elliptical orbits with the sun at one focus, and that planets Conclusion do not move with constant speed along this orbit. To these two laws he added a third a decade later, in his Even after 325 years of publication of The Principia, book ”Harmonices Mundi” (Harmonies of the world). Newton is remembered because his inventions laid the foundation of modern science. He tried to solve the The foundation of modern dynamics was set out in scientific problems of his time with great perseverance and Galileo’s book ”Dialogo sopra i due massimi sistemi del devotion. Even then he said, “I do not know what I may mondo” (Dialogue on the two main world systems) where appear to the world, but to myself I seem to have been the notion of was implicit and used. In addition, only a boy playing on the sea-shore, and diverting myself Galileo’s experiments with inclined planes had yielded in now and then finding a smoother pebble or a prettier precise mathematical relations between elapsed time and shell than ordinary, whilst the great ocean of truth lay all acceleration, velocity or distance for uniform and uniformly undiscovered before me.” He was so great that he said, “If accelerated motion of bodies. I have seen further than others, it is by standing upon the Newton had studied these books, or, in some cases, shoulders of giants.”  secondary sources based on them, and taken notes entitled Quaestiones quaedam philosophicae (Questions References about philosophy) during his days as an undergraduate. 1. G E Smith, ”Newton’s Philosophiae Naturalis Principia René Descartes work, Principia Philosophiae (1644), Mathematica”, The Stanford Encyclopedia of Philosophy (Winter attempted to put the whole universe on a mathematical 2008 Edition), E N Zalta (ed.). foundation, reducing the study of everything to that of 2. R S Westfall, Never at Rest: A Biography of Isaac Newton, Cambridge University Press (1980), at p.404. mechanics. Descartes had stressed the importance of 3. I. Bernard Cohen, Introduction to Newton’s Principia (Harvard mathematics, and on this point Newton agreed. Newton University Press), (1971). initially turned to the mathematical deduction of Descartes 4. John Herivel, The background to Newton’s Principia; a study of as an escape from Aristotle. However, the more he Newton’s dynamical researches in the years 1664–84 (Oxford, considered Descartes ideas the more he disagreed. Newton Clarendon Press), (1965). combined the works of Copernicus, Kepler and Galileo. 5. Boris Hessen, The Social and Economic Roots of Newton’s The work that resulted was his Principia Mathematica. Principia, www.russelldale.com/phil-material/V1_Hessen.pdfý

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