From other sources we have also found that the pit, or mine, was at the Harton Colliery and 1260 feet deep, that the pendulum at the bottom of it gained 2¼ seconds on the similar one at the top, in 24 hours; and that the surrounding country had to be extensively surveyed, the strata had to be studied, and their specific gravities ascertained.
A little unbiassed thought bestowed on this theory will at once show that it begins by violating the law of attraction discovered by Newton, when he showed that the mutually attractive forces of several bodies are the same as if they were resident in the centres of gravity of the bodies. In the case in point this means, that the attraction of the earth for the bob of the pendulum at the top of the mine was the same as if all its force was collected at its (the earth's) centre. In that position the force of the earth's attraction comprehended, most undeniably, the whole of its attractive power, including whatever might be imagined to be derived from the non-homogeneity of the earth, due to its density increasing towards the centre; and we are called upon to believe that when, virtually, the same pendulum was removed to the bottom of the mine, and a segment 1260 feet thick, at the centre as good as cut off from the earth and—as far as the pendulum was concerned—hung up on a peg in a laboratory, the diminished quantity of its matter had a greater attractive force, a very little beyond the centre—non-homogeneity again included—than the whole when the sphere was intact. This we cannot do, because all that we can see in the placing of the pendulum at the bottom of the mine, is that the position of the bob has divided the earth into two sections, one of which has a tendency to pull it up towards the surface, and the other to pull it down towards its centre of gravity; and because the mass of the smaller segment is so insignificant that its entire removal to the laboratory peg, not only could not produce the reverse action, on which the theory is based, but could not be measured by any stretch of human invention or ingenuity; it is far beyond the reach of mathematics and human comprehension of quantity.
The difficulty of belief is increased when we reflect that, were the pendulum taken down towards the centre of the earth, the number of its vibrations in a given time ought gradually to decrease as it approached the centre, and would cease altogether when that point was reached. And we feel confident that no mathematician could calculate where the theoretical acceleration of the vibrations would cease, and the inevitable retardation commence; where the theory would come to an end and the law of attraction begin to assert its rights, simply because he does not know how the non-homogeneity is distributed in the earth. No man can tell, even yet, how the mean density of 5·66 is made up throughout the earth, and without that any theory founded on its non-homogeneity is out of place.
But to follow up our assertion of non-commensurability. Taking the diameter of the earth at 8000 miles, and its mean specific gravity at 5·66, its mass would be represented by 1,517,391,000,000 cubic miles of water. On the other hand, supposing the earth to be a true sphere, the volume of a segment of it cut off from one side, at one quarter of a mile deep—not 1260, but 1320 feet—would be 785·35 cubic miles in volume, and if we suppose its specific gravity to be 2·5—greater most probably than the average of all the strata in the neighbourhood of the Harton Colliery—its mass would be represented by 1963·38 cubic miles of water. Then, if we divide the mass of the section below the pendulum, that is, 1,517,391,000,000 minus the mass of the one above it, 1963·38, viz. 1,517,390,998,036·62 by the mass of 1963·38 just mentioned, we find that the proportion they bear to each other is as 1 to 772,846,315. This being so, we are asked to believe that by removing 1/772,846,315th part of the mass of the earth from one side of it, its force of attraction at the centre will not only not be decreased, but will be so increased that it will cause a pendulum, suspended at the centre of the flat left by the removal of the segment, to vibrate 86,402·25 times in twenty-four hours instead of 86,400 times as it did when suspended at the surface before the segment was removed; that is, that the vibrations will be increased by 1/38,400th part. Again we cannot do so. Had we been asked to believe that the removal of so small a fraction as 1/772,846,315th had decreased the earth's attraction at its centre, so much as to produce a diminution of 1/38,400th part in the number of vibrations of the pendulum, we could not have done so; how much less then can we believe that the central attractive force had increased so much as to produce an augmentation of the vibrations in the same proportions? But more in this strain presently.
We have no doubt whatever that Sir George B. Airy and his assistants satisfied themselves that the pendulum at the bottom of the mine gained 2¼ seconds in twenty-four hours over the one at the top, but they may have been deceived by their over-enthusiastic adoption of what seemed to be a very grandly scientific theory, or by some unperceived changes in the temperature in the pendulums, caused by varying ventilation in the mine or the varying weather outside of it, or by the insidious manifestations of the "sympathetic electric control between clocks at the top and bottom of a mine," called in to assist at the experiments. An error of 1/38,400th part of the time the sympathetic electricity would take to travel from the top to the bottom of the shaft would be sufficient to make the experiments of no value whatever; not to speak of the small errors that may have been made in surveying the surrounding country, calculating the specific gravities of the strata—for we are told that all this had to be done-and applying the elements thus obtained to the solution of the problem they had in hand. We have read of the difficulties met with by Mr. Francis Baily when he began to revise the Cavendish Experiment—some twelve or fifteen years before the final Harton Colliery experiments were made, and suppose it possible that they met with similar difficulties without being aware of it. And 1/38,400th part is such a very small fractional difference in the vibrations in twenty-four hours, of the pendulums of the two separate clocks, that—taking into consideration the circumstances under which it was found—it would hardly be looked upon as reliable at the present day, when the clocks of astronomical observatories are placed in the deepest cellars or even caves available, so as to free them as much as possible from variations of temperature.
Having referred to the difficulties met with by Mr. Baily, we believe it worth while to transcribe Professor C. Piazzi Smythe's account of them, given in his work already referred to at page 22; because it not only has a very direct bearing on what we have been saying of changes of temperature, but is exceedingly interesting, and probably very rarely to be met with in other works. It is as follows:—
"Nearly forty years after Cavendish's great work, his experiment was repeated by Professor Reich of Freyberg, in Saxony, with a result of 5·44; and then came the grander repetition of the late Mr. Francis Baily, representing therein the Royal Astronomical Society, and, in fact, the British Government and the British Nation.
"With exquisite care did that well-versed and methodical observer proceed to his task, and yet his observations did not prosper.
"Week after week, and month after month, unceasing measures were recorded; but only to show that some disturbing element was at work, overpowering the attraction of the larger on the smaller balls.
"What could it be?