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.”