He begins Book I with precise definitions of concepts we now understand as ‘mass,’ ‘inertia,’ ‘acceleration,’ and ‘centripetal force,’ followed by a SCHOLIUM defining his conceptions of time, space, and motion: “Absolute, true, and mathematical time,” “Absolute space,” “Place as a part of space which a body takes up . . . either absolute or relative,” “Absolute motion” as the “translation of a body from one absolute place into another; and relative motion, the translation from the relative place into another” (pp. 6–7). Interestingly, his motivation in adopting these absolutes was to support belief in God. As he wrote to the Reverend Richard Bentley: “When I wrote my treatise about our Systeme . . . I had an eye upon such Principles as might work wth considering men for the beleife of a Deity . . .” (Westfall, p. 441).
The evidence and arguments for these absolute conceptions seem reasonable enough at first glance, but even Newton’s justification of absolute motion in relation to absolute space appears somewhat contrived. As proof of absolute motion Newton depicts a bucket half filed with water attached to a strong, lengthy rope, the surface of the water remaining flat when the rope is unwound. But when twisted and then allowed to untwist causing the bucket to rotate, the water begins to rise at the inner sides of the vessel forming a concave shape. Newton inferred from this that the “ascent of the water shows its endeavor to recede from the axis of its motion; and the true and absolute circular motion of the water, which is here directly contrary to the relative, becomes known, and may be measured by this endeavor” (Principia, Vol. I, p. 10).
Thus, owing to Newton, space and time were considered absolute until the Michelson-Morely experiments in 1887 and Einstein’s special theory of relativity in 1905 proved that all temporal and spatial measurements, such as the simultaneity of events, were relative depending on the respective positions, velocities, and strength of the gravitational forces of the measurer and what is measured. The one exception was the constant velocity of light also regarded as the ultimate limiting velocity.
Continuing our discussion of the Principia, the definitions in the SCHOLIUM are followed by his presentation of the AXIOMS, or LAWS OF MOTION some of which continue to be valid to this day (within certain limits) followed by six COROLLARIES and another SCHOLIUM discussing Galileo’s law of free fall. This takes us to Book One, THE MOTION OF BODIES, consisting of several hundred pages of complex geometrical diagrams and discussions of the mathematical relations pertaining to the various kinds of celestial and terrestrial motions. Though his supporting diagrams are usually geometrical, he occasionally uses his theory of fluxions or differential calculus when discussing magnitudes approaching “vanishing limits” or zero: for example, when explaining Aristotle’s problem as to how there can be instantaneous velocities that imply motion in durationless intervals.
Newton explained this with his fluxions by showing how the rate of a dependent variables, such velocity or distance, can vanish as the independent variable, such as time becomes zero as in the differential equation ds/dt, where s stands for speed, d for distance and t for time. He also used his fluxions when he demonstrates how the attractive gravitating force of the nearest massive object deflects planetary bodies from circular to elliptical orbits permitting the deduction of the exact ratios of the distances, forces, and velocities to produce Kepler’s three laws.
The second book of Volume I consists of nine sections analyzing the effects of different media on the motions of bodies along with their ratios, such as the properties of the particles in fluids affecting their fluidity as had been investigated by Boyle; the effect of air on the motion of pendulums; and how oscillating bodies in general are affected by the compression of air and the density of fluids. Though only a brief account of the scope, originality, and complexity of his investigations, it should be sufficient to convey the extraordinary range and depth of his thinking.
Turning to Volume II containing Book III of the Principia, including the subtitled THE SYSTEM OF THE WORLD (the title that was the basis of Hooke’s charge of plagiarism because it duplicated the title he had used for one of his early works and that brought on a lasting contention), Newton originally intended it to be a nonmathematical popularization of his scientific achievements, but finally presented it in his usual mathematical rigor to avoid controversy by those unable to comprehend the mathematics. As he wrote in the introductory paragraph:
In the preceding books I have laid down the principles of philosophy; principles not philosophical but mathematical: such, namely, as we may build our reasoning upon in philosophical inquiries. . . . It remains that, from the same principles, I now demonstrate the frame of the System of the World. Upon this subject I had, indeed, composed the third Book in a popular method, that it might be read by many; but afterwards, considering that such as had not sufficiently entered into the principles could not easily discern the strength of the consequences, nor lay aside the prejudices to which they had been many years accustomed, therefore, to prevent the disputes which might be raised upon such accounts, I chose to reduce the substance of this Book into the form of Propositions (in the mathematical way), which should be read by those only who had first made themselves masters of the principles in the preceding Books. . . .35
In insisting that his principles of philosophy be mathematical and not merely philosophical he was distinguishing himself from Aristotle and Descartes, but following Kepler, Galileo, Huygens, Hooke, and the future tradition of science. This is followed by his list of the four RULES OF REASONING IN PHILOSOPHY which again are nearly identical to those stated previously by Galileo.
Rule I: “We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearance.” . . . Rule II: “Therefore to the same natural effect we must, as far as possible, assign the same causes.” . . . Rule III: “The qualities of bodies, which admit neither intensification nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever.” . . . Rule IV: “In experimental philosophy we are to look upon propositions inferred by general induction from phenomena as accurately or very nearly true, notwithstanding any contrary hypotheses that may be imagined, till such time as other phenomena occur, by which they may either be made more accurate, or liable to exceptions.” (pp. 398–440)
However, he was not always consistent in following his own strict rules of reasoning. At the end of the GENERAL SCHOLIUM in Book III, he states that
hitherto I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses; for whatever is not deduced from the phenomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy. (p. 547)
Yet in the following paragraph he introduces the hypothesis of a “subtle spirit” pervading all bodies to explain gravity, motion, and all kinds of interactions in contradiction to his previous objections.
And now we might add something concerning a certain most subtle spirit which pervades and lies hid in all gross bodies; by the force and action of which spirit the particles of bodies attract one another at near distances, and cohere, if contiguous; and electric bodies operate to greater distances, as well repelling as attracting the neighboring corpuscles; and light is emitted, reflected, refracted, inflected, and heats bodies; and all sensation is excited, and the members of animal bodies move at the command of the will, namely by the vibrations of this spirit, mutually propagated along the solid filaments of the nerves, from the outward organs of sense to the brain, and from the brain to the muscles. But these are things that cannot be explained in a few words, nor are we furnished with the sufficiency of experiments which is required to an accurate determination and demonstration of the laws by which this electric and elastic spirit operates. (p. 547)
As in Volume I, the rest of the book contains numerous geomet
rical diagrams, charts, and explanations presenting and supporting his “System of the World,” which is too long and complex to be summarized here. And though I have tried to bring out the striking similarities between Galileo’s contributions and those of Newton’s, as I said previously, my intent is not to minimize the extraordinary achievements of Newton that guided scientific research during the following two centuries and whose formula F = ma is still used for most ordinary calculations in our familiar world and that stands with Einstein’s E = mc2 as the two most famous scientific formulas.
As an indication of the intense esteem the book aroused, the French mathematician of international repute, Marquis de l’Hôpital, after he had been shown a copy of Newton’s Principia,
cried out with admiration Good god what a fund of knowledge there is in that book? he then asked the Dr every particular about Sr I. even to the colour of his hair [asked] does he eat & drink & sleep. [I]s he like other men? & was surprised when the Dr told him he conversed cheerfully with his friends assumed nothing & put himself upon a level with all mankind.36
Before concluding the discussion of Newton something should be said of his later life and the publication of his final work, the Opticks. There were two incidents in this period that especially reveal his courageous character and integrity. The first involves the attempt by King James II, a Catholic who ascended the throne in 1685, to replace the Anglican religion with Catholicism. Hoping to accomplish this by enabling Catholics to acquire positions of authority at the universities, which was then prevented by their having to take “the oath of supremacy, in effect an oath to uphold the established Anglican religion,” he decided to eliminate this obstacle by using the traditional “letter mandate” to confer higher degrees on Catholics thereby exempting them from taking the oath (p. 474).
The situation came to a climax when the King proposed Alban Francis, a Benedictine Monk, to the degree of Masters of Arts at Cambridge. When John Peachell, the Vice Chancellor, decided to resist, Newton drafted a supporting letter urging “‘an honest Courage’ which would ‘save ye University’” (p. 475). The King on receiving the letter summoned Peachell, along with a faculty delegation to which Newton was elected as well as eight others, to appear before the Court of Ecclesiastical Commission headed by Lord Jeffreys. In a compromise the King proposed that Father Francis could be awarded the degree with the understanding that this would not be considered a precedent. Strongly objecting, Newton persuaded the delegation that this would be a dishonorable capitulation that could set a precedent.
However, when Peachell and the faculty delegation met with Lord Jeffreys and the Commission, Lord Jeffreys so intimidated Peachell that the latter failed to present a strong case for the delegation’s objections and as a result resigned from the university. Thus it fell to the delegation to defend the objection with Newton forcefully advocating that they should not concede, drafting five letters preparatory to the final written response, including in one that a “mixture of Papist & Protestants in ye same University can neither subsist happily nor long together” which, however, was not included (p. 479).
Not knowing whether they would face the same fate as poor Peachell, the delegation met with Lord Jeffreys and the Commission, but this time it was the latter who yielded but warned that in the future the King’s commands must be obeyed. Fortunately, the threat proved futile because eighteen months later James II was deposed by William of Orange and fled to France. But the fortitude and wise council that Newton had shown during this very threatening period did not go unnoticed or unrewarded, for when it came time for two delegates to be elected to represent the university at the convention to ratify the Glorious Revolution that deposed James II, Newton was elected as one. Then an act of Parliament led to his being one of the regular commissioners “to oversee the collection in Cambridge of aids voted to the government” (p. 480), a lucrative appointment commending his new standing.
Not only did it increase his income, but it changed his life by requiring him to move to London for a year when the convention was reconvened as Parliament. Owing to his move to London he met Christiaan Huygens and the philosopher John Locke with whom he formed a close friendship. Reading Locke’s An Essay Concerning Human Understanding one can find many indications of what must have been their mutual influence due to their preferences for a more empirical conception of knowledge, in contrast to Descartes’s rationalistic philosophy which they opposed.
As his final scholarly achievement, Newton decided to present the results of his earlier optical experiments in book form. When completed in 1694 and shown to his friend David Gregory, the latter was so impressed that he declared it “would rival the Principia.” The Royal Society was eager to publish it but was detained owing to Newton’s reluctance to have it published while Hooke was still president of the society; but when Hooke died in March 1703 and Newton was elected president the following November, he agreed to its publication by the Royal Society in 1704.
Though it did not rival the Principia, it was more accessible and widely read because it made less mathematical demands on the reader, had fewer geometrical diagrams, and was originally published in English rather than Latin. Nonetheless, because the questions it raised, especially the thirty-one Queries in Book III at the end of the book, were so original and far reaching that they generated much of the experimental research during the ensuing eighteenth century. As I. Bernard Cohen, professor of the History of Science at Harvard University, states, contrasting the Opticks with the Principia in his outstanding book Franklin and Newton:
Not primarily in the Principia, then, but in the Opticks could the eighteenth-century experimentalists find Newton’s methods for studying the properties or behavior of bodies that are due to their special composition. Hence, we need not be surprised to find that in the age of Newton—which the eighteenth century certainly was!—the experimental natural philosophers should be drawn to the Opticks rather than to the Principia. Furthermore, the Opticks was more than an account of mere optical phenomena, but contained an atomic theory of matter, ideas about electricity and magnetism, heat, fluidity, volatility, sensation, chemistry, and so on, and a theory (or hypothesis) of the actual cause of gravitation.37
The Opticks consists of three Books plus the thirty-one Queries.38 As the first three books contain a recapitulation of his optical experiments performed thirty years earlier along with some of his theories presented in the Principia, I shall confine my discussion to the Queries, especially as they represent Newton’s genius in forecasting the scientific research of the future according to his specified methodology.
For example, in Queries 6 and 8 he remarkably anticipates the early twentieth century investigations and explanations of blackbody radiation by Max Planck in 1900 and Einstein’s explanation of the photoelectric effect in 1905 in stating that the reflection of light from black bodies is due to the increased intensity of the internal vibrations of the heated particles. Having indicated in Query 6 that “Black bodies conceive heat more easily from light than those of other colours,” in Query 8 he asks “Do not all fix’d Bodies, when heated beyond a certain degree, emit Light and shine; and is not this Emission perform’d by the vibrating motion of their parts?” (p. 340; italics added). The similarity to Einstein’s explanation is especially apparent since Newton’s adoption of the corpuscular over the wave theory of light would conform to Einstein’s interpretation in terms of discrete units of energy, called photons, rather than waves. But what was most striking was his attribution of the increased heat of the black body and ejection of the light to the intensified movement of the internal particles!
In Query 12 he presents his conclusions based on what appear to be his own experiments on the physiological nature of vision. As he states: “Do not the Rays of Light in falling upon the bottom of the Eye excite Vibrations in the Tunica Retina [a retinal membrane]? Which vibrations, being propagated along the solid Fibres of the optick Nerves into the Brain, cause the Sense of seeing” (p. 345; brackets
added). He goes on to describe how the various magnitudes of the vibrations of the different rays of light produce in the brain the different colors, though he was mistaken in thinking that each of the optic nerves terminate in the same hemisphere of the brain as the location of the eyes, rather than crossing over to the opposite hemisphere.
In Query 28 he rejects metaphysical explanations as “feigning hypotheses,” affirming that “the main Business of natural Philosophy is to argue from Phænomena without feigning Hypotheses, and to deduce Causes from Effects, till we come to the very first Cause” which “certainly is not mechanical; and not only to unfold the mechanism of the world, but to resolve these and such like Questions” (p. 369). As an indication of how difficult it is for someone even as brilliant as Newton to break completely with tradition, although having insisted on his opposition to metaphysical explanations and “feigned hypotheses,” he again resorts to a transcendental explanation: “an exceedingly rare Æthereal Medium” lighter than air pervading the universe, along with God apparently as “the very first cause,” to account for all the inexplicable interactions producing natural phenomena. However, now rejecting his earlier interpretation of the ether as “spiritual,” he refers to it as an ethereal medium, though admitting that “I do not know what this Æther is” (p. 352). Despite the glaring inconsistency, the theory of a luminiferous ether filling all unoccupied space to explain the transmission of radiation such as light was generally accepted until disproved by Einstein in the early twentieth century.
In Query 31, Book III, Part I, he reaffirms the theory of particle physics consisting of the interactions of minute particles due to attractive and repulsive forces.
Have not the small Particles of Bodies certain Powers, Virtues, or Forces, by which they act at a distance, not only upon the Rays of light for reflecting, refracting, and inflecting them, but also upon one another for producing a great part of the Phænomena of Nature? For it’s well known, that Bodies act one upon another by the Attractions of Gravity, Magnetism, and Electricity; and these Instances shew the Tenor and Course of nature, and make it not improbable but that there may be more attractive Powers than these. (pp. 375–76)
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