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.