My readers may well think that the results of these notes are somewhat scanty, but if that nation is happy which has no history, surely universities and colleges are to be congratulated whose records of punishment are so few. To sum up the matter, the general effect left on my mind is that most of the common offences were due only to youthful exuberance of spirits and not to deliberate mischief making; and that the rules and sanctions, judged by the standard of their time, have been neither harsh nor unreasonable, and have usually been approved by public opinion in the University.
[225]
]CHAPTER XIII.
NEWTON’S PRINCIPIA.
Newton’s Principia is one of the few scientific books which has sensibly affected the methods of scientific research and the ideas of men about the universe. It is on this aspect of the subject I propose, in this paper, to make a few remarks. The work itself is a classic in the history of mathematics: the exposition of the subject, the enunciation of the principle of prime and ultimate ratios, the creation of mechanics as a science resting on experiments, and the theory of universal gravitation with concrete applications to the solar system, make it a masterpiece. Here I avoid all technicalities, and confine myself to a general description of its genesis and contents and the reason why its publication affected scientific thought and methods.
Newton’s exposition arose from an investigation of the cause of the motion of the planets round the sun, and this in due course led to the enunciation and establishment of the Newtonian theory of attraction. The origin of this theory has been often told, but will bear repetition. The fundamental idea occurred to Newton in 1665 or 1666, shortly after he had taken his degree at Cambridge, when, as he [226] ]wrote later, “I was in the prime, of my age for invention, and minded Mathematicks and Philosophy more than at any time since.” His reasoning was as follows. He knew that gravity extended to the highest hills, he saw no reason why it should cease to act at greater heights, accordingly he believed that it would be found in operation as far as the moon, and he suspected that it might be the force which retained that body in its path round the earth.
This hypothesis he verified thus. If a stone is allowed to fall near the surface of the earth, the attraction of the earth causes it to move through sixteen feet in one second: also Kepler’s Laws, if accurate and applicable, involve the conclusion that the attraction of the earth on a distant body varies inversely as the square of its distance from the earth. Now the radius of the earth and the distance of the moon were known to Newton, and therefore, on this hypothesis, he could find the magnitude of the earth’s attraction on the moon. Further, assuming that the moon moved in a circle, he could calculate the force required to retain it in its orbit. At this time his estimate of the radius of the earth was inaccurate, and, when he made the calculation, he found that this force was rather greater than the earth’s attraction on the moon. The discrepancy did not shake his faith in his theory, but he conjectured that the moon’s motion was also [227] ]affected by other influences, such for example, as the effect of a resisting medium which might itself be in motion as supposed by Descartes in his hypothetical vortices.
In 1679 Newton knew with approximate correctness the value of the radius of the earth. He repeated his calculations, and found the results to be in accordance with his former hypothesis. He then proceeded to the general theory of the motion of a particle under a force directed to a fixed point, and showed that the vector to the particle would sweep over equal areas in equal times. He also proved that, if a particle describes an ellipse under a force directed to a focus, the law must be that of the inverse square of the distance from the focus, and conversely, that the orbit of a particle projected in free space under the influence of such a force must be a conic. The application to the solar system was obvious, since Kepler had shown that the planets describe ellipses with the sun in one focus, and that the vectors from the sun to them sweep over equal areas in equal times. This investigation was made for his own satisfaction and was not published at the time. In it he treated the solar bodies as if they were particles, and he must have realized that the results could be taken as being only approximately correct.
In 1684 the subject of the planetary orbits was [228] ]discussed in London by Halley, Hooke, and Wren. They were aware that, if Kepler’s conclusions were correct, the attraction of the sun or earth on a distant external particle must vary inversely as the square of the distance, but they could not determine the orbit of a particle subjected to the action of a central force of this kind. It was suggested that Newton might be able to assist them. Accordingly in August, Halley went to Cambridge for a talk on the subject, and then found that Newton had solved the problem some five years previously, and that the path was necessarily a conic. At Halley’s request Newton wrote out the substance of his argument, and sent it to London.
Halley at once realized the importance of the communication, and later in the autumn returned to Cambridge to urge Newton to prosecute the theory further. He found that Newton had already done something in the matter, the results being contained in a manuscript which he saw. Probably this reference is to the holograph manuscript, still preserved in the University Library at Cambridge, of Newton’s lectures in the Michaelmas Term, which served as the basis of his memoir sent to the Royal Society a few months later. The great value of these investigations was recognized, and Newton was persuaded to attack the more general problem. His results are given in the Principia.
[229]
]As yet Newton had dealt with the problem as if the sun and the planets might be regarded as heavy masses concentrated at their centres. Clearly at the best this was only an approximation, though considering the enormous distances involved it was not unreasonable. In January or February, 1685, he considered the question of the attraction of bodies of finite size, and found, to his surprise and gratification, that a sphere or spherical shell attracts an external particle as if condensed into a heavy mass at its centre. Hence the results he had already proved for the relative motion of particles were true for the solar system, save for small errors due partly to the fact that the bodies were not perfectly spherical and partly to disturbances caused by the planets attracting one another. It was no longer a question of rough approximation: the problem was reducible to mathematical analysis, subject to the introduction of minute corrections, which, given the necessary observations, could be calculated very closely. This was a new discovery of first-rate importance, and initiated the modern theory of attractions.
The first book of the Principia was finished before the summer of 1685. It deals with the motion of particles or bodies in free space either in known orbits or under the action of known forces. In it the law of attraction is generalized into the [230] ]statement that every particle of matter attracts every other particle with a force which varies directly as the product of their masses and inversely as the square of the distance between them. Thus gravitation was brought into the domain of Science.