There is no hypothesis, no theory, connected with any of the operations, unless it was the supposition that a plummet—which was naturally believed to point to the centre of the earth—should be pulled to one side by the attraction for it of a mountain in its neighbourhood, and that was found to be a fact.
Methods Employed for Finding the Density of the Earth,
And their Results.
In the case of the plummet deviating from its absolutely straight direction towards the centre of the earth, caused by their attraction, not only the mountains themselves had to be measured and virtually weighed as far as they were measurable, but the weight of the wedge or pyramid between that measurable point, in each case, and the centre of the earth had to be estimated in some way; then the centre of gravity of the whole of this mass had to be ascertained, as well as the respective distances from the centre of the earth of this centre of gravity and that of the plummet, and only after all this and a deep study of the mutual attractions of this mass and the plummet could an estimate be formed of the mass of the earth. It will thus be seen that such measurements and estimates could never be looked upon as very exact and reliable; and nevertheless they have come very near the density of 5·66 finally adopted for the earth.
In the case of the Torsion Balance experiments a very considerable advance was made in consequence, most undoubtedly, of the knowledge acquired from what had been done by Maskelyne. When it was found that the attraction of Schiehallien for the plummets was such a measurable quantity, Cavendish evidently saw that the attraction of manageable leaden balls for each other would be measurable also, and that as no calculations of any kind whatever were necessary to find the masses of the balls, the mutual attraction of large and small balls would furnish a more exact means of measuring the density of the earth, than the roundabout way of having to calculate the weight of a mountain as a beginning; and with the requisite ingenuity, invention, and labour, he found the means of applying the torsion balance, to make the experiments.
After these experiments were revised by Reich and Baily—and the density of 5·66 adopted, we believe—still another set were undertaken by J. H. Pointing, with the Chemical Balance, in which only two metal balls, one large and one small were required, which gave a density of 5·690 as shown opposite, and from its extreme simplicity may perhaps have been the most exact of all.
We have said, we think with truth, that there is no hypothesis or theory involved in any of these experiments, but only the simplest form of—we might almost say—arithmetical calculation. But there is a theory built up on hypothesis which has no foundation whatever, and about which most people, who take the trouble to study it out to the very end, will come to the conclusion that "the less said the better." This, at all events, is our opinion, and we would not have taken any notice whatever of it had it not been that up to the present day, it is published in many works on Popular Astronomy, and even in some text-books, and is looked upon in them, apparently, as an example of the transcendent height to which human science can reach.
We allude, of course, to the theory that the deeper we go down into the earth—at least to an undefined and undefinable depth—the greater is its attraction for the bob of a pendulum at that depth, and the greater the number of vibrations the pendulum is caused to make in a given time. The explanation of the theory is, that were the earth homogeneous throughout its whole volume, the pendulum ought to make the fewer vibrations, the deeper down in the earth it is placed; but as the earth is not homogeneous, it actually makes a greater number of vibrations in a given time, because the attractive force of the earth increases—up to the undefined and undefinable depth—on account of the denser matter beneath the pendulum bob more than overbalancing the loss of attraction from the lighter matter left above it. The author of the theory was the late Astronomer Royal, Sir George B. Airy, who from it endeavoured to calculate the mean density of the earth, and with that view made two experiments which are thus described by Professor C. Piazzi Smythe in his work on the Great Pyramid:—
"Another species of experiment. . . was tried in 1826 by Mr. (now Sir) George B. Airy, Astronomer Royal, Dr. Whewell, and the Rev. Richard Sheepshanks, by means of pendulum observations at the top and bottom of a deep mine in Cornwall; but the proceedings at that time failed. Subsequently, in 1855, the case was taken up again by Sir George B. Airy and his Greenwich assistants, in a mine near Newcastle. They were reinforced by the new invention of sympathetic electric control between clocks at the top and bottom of a mine, and had much better, though still unexpectedly large results—the mean density of the earth coming out, for them, 6·565."