It was a portion of Newton’s assertion in his great discovery, that all the bodies of the universe attract each other with forces which are as the quantity of matter in each: that is, for instance, the sun attracts the satellites of any planet just as much as he attracts the planet itself, in proportion to the quantity of matter in each; and the planets attract one another just as much as they attract the sun, according to the quantity of matter.
To prove this part of the law exactly is a matter which requires careful experiments; and though proved experimentally by Newton, has been considered in our time worthy of re-examination by the great astronomer Bessel. There was some ground for doubt; for the mass of Jupiter, as deduced from the perturbations of Saturn, was only 1⁄1070 of the mass of the sun; the mass of the same planet as deduced from the perturbations of Juno and Pallas was 1⁄1045 of that of the Sun. If this difference were to be confirmed by accurate observations and calculations, it would follow that the attractive power exercised by Jupiter upon the minor planets was greater than that exercised upon [550] Saturn. And in the same way, if the attraction of the Earth had any specific relation to different kinds of matter, the time of oscillation of a pendulum of equal length composed wholly or in part of the two substances would be different. If, for instance, it were more intense for magnetized iron than for stone, the iron pendulum would oscillate more quickly. Bessel showed[47] that it was possible to assume hypothetically a constitution of the sun, planets, and their appendages, such that the attraction of the Sun on the Planets and Satellites should be proportional to the quantity of matter in each; but that the attraction of the Planets on one another would not be on the same scale.
[47] Berlin Mem. 1824.
Newton had made experiments (described in the Principia, Book iii., Prop. vi.) by which it was shown that there could be no considerable or palpable amount of such specific difference among terrestrial bodies, but his experiments could not be regarded as exact enough for the requirements of modern science. Bessel instituted a laborious series of experiments (presented to the Berlin Academy in 1832) which completely disproved the conjecture of such a difference; every substance examined having given exactly the same coefficient of gravitating intensity as compared with inertia. Among the substances examined were metallic and stony masses of meteoric origin, which might be supposed, if any bodies could, to come from other parts of the solar system.
CHAPTER IV.
Verification and Completion of the Newtonian Theory.
Tables of the Moon and Planets.
THE Newtonian discovery of Universal Gravitation, so remarkable in other respects, is also remarkable as exemplifying the immense extent to which the verification of a great truth may be carried, the amount of human labor which may be requisite to do it justice, and the striking extension of human knowledge to which it may lead. I have said that it is remarked as a beauty in the first fixation of a theory that its measures or elements are established by means of a few [551] data; but that its excellence when established is in the number of observations which it explains. The multiplicity of observations which are explained by astronomy, and which are made because astronomy explains them, is immense, as I have noted in the text. And the multitude of observations thus made is employed for the purpose of correcting the first adopted elements of the theory. I have mentioned some of the examples of this process: I might mention many others in order to continue the history of this part of Astronomy up to the present time. But I will notice only those which seem to me the most remarkable.
In 1812, Burckhardt’s Tables de la Lune were published by the French Bureau des Longitudes. A comparison of these and Burg’s with a considerable number of observations, gave 9⁄100ths of a second as the mean error of the former in the Moon’s longitude, while the mean error of Burg’s was 18⁄100ths. The preference was therefore accorded to Burckhardt’s.