[1] The writer inherited from his father (Professor J. D. Forbes) a small box containing a bit of wood and a slip of paper, which had been presented to him by Sir David Brewster. On the paper Sir David had written these words: “If there be any truth in the story that Newton was led to the theory of gravitation by the fall of an apple, this bit of wood is probably a piece of the apple tree from which Newton saw the apple fall. When I was on a pilgrimage to the house in which Newton was born, I cut it off an ancient apple tree growing in his garden.” When lecturing in Glasgow, about 1875, the writer showed it to his audience. The next morning, when removing his property from the lecture table, he found that his precious relic had been stolen. It would be interesting to know who has got it now!
[2] It must be noted that these words, in which the laws of gravitation are always summarised in histories and text-books, do not appear in the Principia; but, though they must have been composed by some early commentator, it does not appear that their origin has been traced. Nor does it appear that Newton ever extended the law beyond the Solar System, and probably his caution would have led him to avoid any statement of the kind until it should be proved.
With this exception the above statement of the law of universal gravitation contains nothing that is not to be found in the Principia; and the nearest approach to that statement occurs in the Seventh Proposition of Book III.:—
Prop.: That gravitation occurs in all bodies, and that it is proportional to the quantity of matter in each.
Cor. I.: The total attraction of gravitation on a planet arises, and is composed, out of the attraction on the separate parts.
Cor. II.: The attraction on separate equal particles of a body is reciprocally as the square of the distance from the particles.
[3] It is said that, when working out this final result, the probability of its confirming that part of his theory which he had reluctantly abandoned years before excited him so keenly that he was forced to hand over his calculations to a friend, to be completed by him.
8. NEWTON’S SUCCESSORS—HALLEY, EULER, LAGRANGE, LAPLACE, ETC.
Edmund Halley succeeded Flamsteed as Second Astronomer Royal in 1721. Although he did not contribute directly to the mathematical proofs of Newton’s theory, yet his name is closely associated with some of its greatest successes.
He was the first to detect the acceleration of the moon’s mean motion. Hipparchus, having compared his own observations with those of more ancient astronomers, supplied an accurate value of the moon’s mean motion in his time. Halley similarly deduced a value for modern times, and found it sensibly greater. He announced this in 1693, but it was not until 1749 that Dunthorne used modern lunar tables to compute a lunar eclipse observed in Babylon 721 B.C., another at Alexandria 201 B.C., a solar eclipse observed by Theon 360 A.D., and two later ones up to the tenth century. He found that to explain these eclipses Halley’s suggestion must be adopted, the acceleration being 10” in one century. In 1757 Lalande again fixed it at 10.”
The Paris Academy, in 1770, offered their prize for an investigation to see if this could be explained by the theory of gravitation. Euler won the prize, but failed to explain the effect, and said: “It appears to be established by indisputable evidence that the secular inequality of the moon’s mean motion cannot be produced by the forces of gravitation.”
The same subject was again proposed for a prize which was shared by Lagrange[[1]] and Euler, neither finding a solution, while the latter asserted the existence of a resisting medium in space.
Again, in 1774, the Academy submitted the same subject, a third time, for the prize; and again Lagrange failed to detect a cause in gravitation.
Laplace[[2]] now took the matter in hand. He tried the effect of a non-instantaneous action of gravity, to no purpose. But in 1787 he gave the true explanation. The principal effect of the sun on the moon’s orbit is to diminish the earth’s influence, thus lengthening the period to a new value generally taken as constant. But Laplace’s calculations showed the new value to depend upon the excentricity of the earth’s orbit, which, according; to theory, has a periodical variation of enormous period, and has been continually diminishing for thousands of years. Thus the solar influence has been diminishing, and the moon’s mean motion increased. Laplace computed the amount at 10” in one century, agreeing with observation. (Later on Adams showed that Laplace’s calculation was wrong, and that the value he found was too large; so, part of the acceleration is now attributed by some astronomers to a lengthening of the day by tidal friction.)