Climate and Time in Their Geological Relations / A Theory of Secular Changes of the Earth's Climate

by James Croll

Fig. 5.

We shall now consider the result when the earth is taken at its actual density, which is generally believed to be about 5·5. The density of ice being ·92, the density of the cap to that of the earth will therefore be as 1 to 6.

Fig. 6.

Let Fig. 6 represent the earth with an ice-cap on the northern hemisphere, whose thickness is, say, 6,000 feet at the pole. The centre of gravity of the earth without the cap is at c. When the cap is on, the centre of gravity is shifted to o, a point a little more than 500 feet to the north of c. Had the cap and the earth been of equal density, the centre of gravity would have been shifted to o′ the centre of the figure, a point situated, of course, 3,000 feet to the north of c. Now it is very approximately true that the ocean will tend to adjust itself as a sphere around the centre of gravity, o. Thus it would of course sink at the south pole and rise to the same extent at the north, in any opening or channel in the ice allowing the water to enter.

Let the ice-cap be now transferred over to the southern hemisphere, and the condition of things on the two hemispheres will in every particular be reversed. The centre of gravity will then lie to the south of c, or about 1,000 feet from its former position. Consequently the transference of the cap from the one hemisphere to the other will produce a total submergence of about 1,000 feet.

It is, of course, absurd to suppose that an ice-cap could ever actually reach down to the equator. It is probable that the great ice-cap of the glacial epoch nowhere reached even halfway to the equator. Our cap must therefore terminate at a moderately high latitude. Let it terminate somewhere about the latitude of the north of England, say at latitude 55°. All that we have to do now is simply to imagine our cap, up to that latitude, becoming converted into the fluid state. This would reduce the cap to less than one-half its former mass. But it would not diminish the submergence to anything like that extent. For although the cap would be reduced to less than one-half its former mass, yet its influence in displacing the centre of gravity would not be diminished to that extent. This is evident; for the cap now extending down to only latitude 55°, has its centre of gravity much farther removed from the earth’s centre of gravity than it had when it extended down to the equator. Consequently it now possesses, in proportion to its mass, a much greater power in displacing the earth’s centre of gravity.

There is another fact which must be taken into account. The common centre of gravity of the earth and cap is not exactly the point around which the ocean tends to adjust itself. It adjusts itself not in relation to the centre of gravity of the solid mass alone, but in relation to the common centre of gravity of the entire mass, solid and liquid. Now the water which is pulled over from the one hemisphere to the other by the attraction of the cap will also aid in displacing the centre of gravity. It will co-operate with the cap and carry the true centre of gravity to a point beyond that of the centre of gravity of the earth and cap, and thus increase the effect.

It is of course perfectly true that when the ice-cap does not extend down to the equator, as in the latter supposition, and is of less density than the globe, the ocean will not adjust itself uniformly around the centre of gravity; but the deviation from perfect uniformity is so trifling, as will be seen from the appended note of Sir William Thomson, that for all practical purposes it may be entirely left out of account.