Illustrations of the Huttonian Theory of the Earth

by John Playfair

[194] The time requisite for taking away by waste and erosion two feet from the surface of all our continents, and depositing it at the bottom of the sea, cannot be reckoned less than 200 years. The fraction 1/12855068184, reduced to parts of a day, is 1/148554 of a second; so that it would require 200 years to shorten the length of the day, by the above fraction of a second; and therefore it would require 148554 times 200 years, or 29710800 years, to diminish it an entire second. The accumulated effect, however, of all the diminutions during that period, would amount to much more: and if we had any perfectly uniform standard to compare the motion of the earth with, its difference from that standard would increase as the squares of the time, and the total acceleration would amount to one second in 77080 years. Whatever relation this bears to the age of the globe itself, it exceeds more than ten times the age of any historical record.

Though Frisius concludes, as is stated here, that the acceleration produced in the diurnal motion of the earth, is far too inconsiderable to become the object of astronomical observation, he makes a supposition difficult to be reconciled with this conclusion, namely, that the acceleration has had a sensible effect on the figure of the earth, or rather of the sea, having increased the centrifugal force, and thereby accumulated the waters under the equator, in the present, more than in former ages. Such an accumulation, he thinks agreeable to certain appearances that have been observed respecting the ancient level of the sea. These appearances will be afterwards considered: it is sufficient to remark here, that though the fraction, expressing the increment of the centrifugal force, must be double that which expresses the acceleration, it must be too small to have any perceptible effect in elevating the sea, except after an immense interval of time; and the compensations which arise from other causes, probably must prevent it from becoming sensible in any length of time whatsoever.

377. The instance just given may serve as one of many, to shew what confidence is to be placed in that indigested mass of facts and quotations which Mr Kirwan, without discrimination, and without discussion, has brought together from all quarters. He has no intention, I believe, to deceive his readers; but we may judge, from this specimen, of the precautions he has taken against being deceived himself.

In some respects, the result of Frisi's investigation must be considered as imperfect. If there were no relative motion in the parts of our globe, but that by which things descend from a higher to a lower level, a continual acceleration of its rotation, though extremely slow, would take place, as above computed. But as, in the interior of the earth, there are undoubtedly motions of a tendency opposite to those on the surface, and directed from the centre towards the circumference, they must produce a retardation in the diurnal revolution; and from this must arise an inequality, not uniformly progressive in the same direction, but periodical, and confined within certain limits, as the causes are by which it is produced.[195]

[195] 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.

378. Mr Kirwan's second objection is founded on the misapprehension of a well-known fact in the natural history of the earth. "Rivers," says this author, "do not carry into the sea the spoils which they bring from the land, but employ them in the formation of deltas of low alluvial land at their mouths, according to what Major Rennell has proved." The fact of the formation of deltas from the spoils which the rivers carry from the higher grounds, is perfectly ascertained; and the detail into which Major Rennell has entered in the passage referred to by Mr Kirwan, does credit to the acuteness and accuracy of that excellent geographer. But it is not there asserted, that rivers employ all the materials which they carry with them, in the formation of those deltas, and deliver none of them into the sea. On the contrary, they carry from the delta itself mud and earth, which they can deposit no where but in the sea; and it is this circumstance chiefly that limits the increase of those alluvial lands, and makes them either cease to increase, or makes them increase very slowly after a certain period, though the supply of earth from the higher grounds remains nearly the same. To make Mr Kirwan's argument conclusive, it would be necessary to prove, that all the mud carried down by the Nile or the Ganges, was deposited on the low lands before these rivers enter the sea; a thing so obviously absurd, that nothing but his haste to obtain a conclusion unfavourable to the Plutonic system, could have prevented him from perceiving it[196].