Note 195 — Note xix. § 117.

Even in the descent of bodies from a higher to a lower level at the surface of the earth, the whole tendency is not to increase the velocity of the earth's rotation, and many compensations take place, which, when the matter is considered only in general, are necessarily overlooked. This will appear evident, if we reflect, that it is not simply the approach of a body towards the centre of the earth, or its removal from that centre, which tends to disturb the rotation of the earth; but its approach to the axis of the earth, or its removal from that axis. The velocity with which a particle of matter revolves, whether on the surface, or in the interior of the globe, is proportional to its distance from the axis of rotation; and therefore, when a body comes nearer to the axis, it loses a part of the motion which it had before; which part, of consequence, is communicated to the whole mass of the earth, and therefore tends to increase the velocity with which it revolves. The contrary happens when a body recedes from the axis; for it then receives an addition to its velocity, which, of course, is taken away from the rotatory motion of the earth.

Hence, bodies moving in a horizontal plane, may increase or diminish the swiftness of the diurnal motion, according as they move towards the poles or towards the equator; and those which descend from a higher to a lower level, disturb the earth's rotation, much more in consequence of their horizontal, than of their perpendicular motion. The Ganges, for instance, though its source is probably elevated no less than 7000 feet above the level of the sea, tends to retard the earth's rotation, by bringing its waters, and the mud contained in them, from the parallel of 31° to that of 22°, and so increasing their distance from the earth's axis by more than 1/12 th part. Had the Ganges flowed towards the north, as the Nile does, its effect would have been just the contrary.

In the same manner, a stone descending from the top of a mountain, may accelerate or retard the earth's rotation, according to the direction in which it descends. If it descend on the side of the elevated pole, it will then produce acceleration, because its distance from the axis will be diminished; but if it descend on the side of the depressed pole, and if the direction in which it is moved, be over a line less inclined, than a line drawn from the same point to the depressed pole, it will then produce a retardation, because its distance from the axis will be increased.

Let us suppose, for example, that the top of Mount Blanc is in latitude 45° 49′, and that its height is 2450 toises above the level of the sea. The point at which a line drawn from the top of this mountain, parallel to the earth's axis, will meet the superficies of the sea, (supposing that superficies continued inland from the Mediterranean), must be about 2382 toises in horizontal distance, or about 2½ minutes south of the summit, that is, in the parallel of 45° 46½′; and if this parallel be continued all round the globe, the points of the earth's surface between it and the equator, are all more distant from the earth's axis than the top of Mount Blanc is; whereas all the points to the north of it are nearer to that axis. A stone, therefore, from the top of Mount Blanc, if carried any where to the south of the above parallel, will retard the earth's diurnal motion; but if carried any where to the north of the same line, will accelerate that motion.

The same quantity of matter, however, carried an equal distance toward the pole, and toward the equator, from any point, will lose more velocity in the former case than it will gain in the latter, as easily follows from the nature of circle. Therefore, supposing an equal dispersion of the detritus of a mountain in all directions, the parts that go toward the pole will most disturb the diurnal motion; and hence a balance on their side, or in favour of acceleration, as already observed.