Having now taken a rapid general view of observation and experiment, of the faculty of sound theorizing, let us enter the presence of two great masters of research and invention, beginning with a man who united the loftiest powers as a mathematician, a physicist, and a generalizer.
How Newton Discovered the Law of Gravitation.
How Sir Isaac Newton discovered the law of gravitation is thus told in his Life by Sir David Brewster:—“It was either in 1665 or 1666 that Newton’s mind was first directed to the subject of gravity. He appears to have left Cambridge some time before August 8, 1665, when the college was dismissed on account of the plague, and it was, therefore, in the autumn of that year, and not in that of 1666, that the apple is said to have fallen from the tree at Woolsthorpe, and suggested to Newton the idea of gravity. When sitting alone in the garden, and speculating on the power of gravity, it occurred to him that, as the same power by which the apple fell to the ground was not sensibly diminished at the greatest distance from the centre of the earth to which we can reach, neither at the summits of the loftiest spires, nor on the tops of the highest mountains, it might extend to the moon and retain her in her orbit, in the same manner as it bends into a curve the path of a stone or a cannon ball, when projected in a straight line from the surface of the earth. If the moon was thus kept in her orbit by gravitation, or, in other words, its attraction, it was equally probable, he thought, that the planets were kept in their orbits by gravitating towards the sun. Kepler had discovered the great law of the planetary motions, that the squares of their periodic times were as the cubes of their distances from the sun, and hence Newton drew the important conclusion that the force of gravity, or attraction, by which the planets were retained in their orbits, varied as the square of their distances from the sun. Knowing the force of gravity at the earth’s surface, he was, therefore, led to compare it with the force exhibited in the actual motion of the moon, in a circular orbit; but having assumed that the distance of the moon from the earth was equal to sixty of the earth’s semi-diameters, he found that the force by which the moon was drawn from its rectilinear path in a second of time was only 13.9 feet, whereas at the surface of the earth it was 16.1 in a second. This great discrepancy between his theory and what he then considered to be the fact, induced him to abandon the subject, and pursue other studies with which he had been occupied.
“It does not distinctly appear at what time Newton became acquainted with the more accurate measurement of the earth, executed by Picard in 1670, and was thus led to resume his investigations. Picard’s method of measuring his degree, and the precise result which he obtained, were communicated to the Royal Society, January 11, 1672, and the results of his observations and calculations were published in the Philosophical Transactions for 1675. But whatever was the time when Newton became acquainted with Picard’s measurement, it seems to be quite certain that he did not resume his former thoughts concerning the moon until 1684. Pemberton tells us, that ‘some years after he laid aside’ his former thoughts, a letter from Dr. Hooke put him on inquiring what was the real figure in which a body, let fall from any high place, descends, taking the motion of the earth round its axis into consideration, and that this gave occasion to his resuming his former thoughts concerning the moon, and determining, from Picard’s recent measures, that ‘the moon appeared to be kept in her orbit purely by the power of gravity.’ But though Hooke’s letter of 1679 was the occasion of Newton’s resuming his inquiries, it does not fix the time when he employed the measures of Picard. In a letter from Newton to Hailey, in 1686, he tells him that Hooke’s letters in 1679 were the cause of his ‘finding the method of determining the figures, which, when I had tried in the ellipsis, I threw the calculations by, being upon other studies; and so it rested for about five years, till, upon your request, I sought for the papers.’ Hence Mr. Rigaud considers it clear, that the figures here alluded to were the paths of bodies acted upon by a central force, and that the same occasion induced him to resume his former thoughts concerning the moon, and to avail himself of Picard’s measures to correct his calculations. It was, therefore, in 1684, that Newton discovered that the moon’s deflection in a minute was sixteen feet, the same as that of bodies at the earth’s surface. As his calculations drew to a close, he is said to have been so agitated that he was obliged to desire a friend to finish them.”
Michael Faraday’s Method of Working.
With no mathematics beyond simple arithmetic, Michael Faraday displayed powers of experiment and generalization so extraordinary that in these respects he stands at the same height as Newton himself. In the life of Michael Faraday, by Dr. J. H. Gladstone, we are given his account of the great physicist’s method of working:—
“The habit of Faraday was to think out carefully beforehand the subject on which he was working, and to plan his mode of attack. Then, if he saw that some new piece of apparatus was needed, he would describe it fully to the instrument maker with a drawing, and it rarely happened that there was any need of alteration in executing the order. If, however, the means of experiment existed already, he would give Anderson, his assistant, a written list of the things he would require, at least a day before—for Anderson was not to be hurried. When all was ready, he would descend into the laboratory, give a quick glance round to see that all was right, take an apron from the drawer, and rub his hands together as he looked at the preparations made for his work. There must be no tool on the table but such as he required. As he began his face would be exceedingly grave, and during the progress of an experiment all must be exceedingly quiet; but if it was proceeding according to his wish, he would commence to hum a tune, and sometimes to rock himself sideways, balancing alternately on either foot. Then, too, he would often talk to his assistant about the result he was expecting. He would put away each tool in its own place as soon as done with, or at any rate as soon as the day’s work was over, and he would not unnecessarily take a thing away from its place. No bottle was allowed to remain without its proper stopper; no open glass might stand for a night without a paper cover; no rubbish was to be left on the floor; bad smells were to be avoided if possible; and machinery in motion was not to be permitted to grate. In working, also, he was very careful not to employ more force than was wanted to produce the effect. When his experiments were finished and put away, he would leave the laboratory, and think further about them upstairs.
“It was through this lifelong series of experiments that Faraday won his knowledge and mastered the forces of nature. The rare ingenuity of his mind was ably seconded by his manipulative skill, while the quickness of his perceptions was equalled by the calm rapidity of his movements. He had indeed a passion for experimenting. This peeps out in the preface to the second edition of his ‘Chemical Manipulation,’ where he writes, ‘Being intended especially as a book of instruction, no attempts were made to render it pleasing, otherwise than by rendering it effectual; for I concluded that, if the work taught clearly what it was intended to inculcate, the high interest always belonging to a well-made or successful experiment would be sufficient to give it all the requisite charms, and more than enough to make it valuable in the eyes of those for whom it was designed.’
“He could scarcely pass a gold leaf electrometer without causing the leaves to diverge by a sudden flick from his silk handkerchief. I recollect, too, his meeting me at the entrance to the lecture theatre at Jermyn Street, when Lyon Playfair was giving the first, or one of the first lectures ever delivered in the building. ‘Let us go up here,’ said he, leading me far away from the central table. I asked him why he chose such an out-of-the-way place. ‘Oh,’ he replied, ‘we shall be able here to find out what are the acoustic qualities of the room.’
“The simplicity of the means with which he made his experiments was often astonishing, and was indeed one of the manifestations of his genius. A good instance is thus narrated by Sir Frederick Arrow:—‘When the electric light was first permanently exhibited at Dungeness, on 6th June, 1862, a committee of the Elder Brethren, of which I was one, accompanied Faraday to observe it. Before we left Dover, Faraday showed me a little common paper box and said, “I must take care of this; it’s my special photometer,”—and then, opening it, produced a lady’s ordinary black shawl pin (jet, or imitation, perhaps)—and then holding it a little way off the candle, showed me the image very distinct; and then, putting it a little further off, placed another candle near it, and the relative distance was shown by the size of the image.’