In Fig. 8, where there is no ice-cap, the centre of gravity of the earth coincides with the centre of the concentric layers of the fluid interior. In Fig. 9, where there is an ice-cap placed on one pole, the concentric layer F1 being denser than layer F, is attracted towards the cap more forcibly than F, and consequently sinks to a certain depth in F. Again, F2 being denser than F1, it also sinks to a certain extent in F1. And again F3, the mass at the centre, being denser than F2, it also sinks in F2. All this being combined with the effects of the ice-cap, and the displaced ocean outside the shell, the centre of gravity of the entire globe will no longer be at C, but at C1, a considerable distance nearer to the side of the shell on which the cap rests than C, and also a considerable distance nearer than it would have been had the interior of the globe been solid. There are here three causes tending to shift the centre of gravity, (1) the ice-cap, (2) the displaced ocean, and (3) the displaced materials in the interior. Two of the three causes mutually re-act on each other in such a way as to increase each other's effect. Thus the more the ocean is drawn in the direction of the ice-cap, the more effect it has in drawing the heavier materials in the interior in the same direction; and in turn the more the heavier materials in the interior are drawn towards the cap, the greater is the displacement of the earth's centre of gravity, and of course, as a consequence, the greater is the displacement of the ocean. It may be observed also that, other things being equal, the thinner the solid crust or shell is, and the greater the difference in the density of the fluid materials in the interior, the greater will be the extent of the displacement of the ocean, because the greater will be the displacement of the centre of gravity.

It follows that if we knew (1) the extent of the general submergence of the glacial epoch, and (2) the present amount of ice on the southern hemisphere, we could determine whether or not the earth is fluid in the interior.

CHAPTER XXV.

THE INFLUENCE OF THE OBLIQUITY OF THE ECLIPTIC ON CLIMATE AND ON THE LEVEL OF THE SEA.

The direct Effect of Change of Obliquity on Climate.-Mr. Stockwell on the maximum Change of Obliquity.-How Obliquity affects the Distribution of Heat over the Globe.-Increase of Obliquity diminishes the Heat at the Equator and increases that at the Poles.-Influence of Change of Obliquity on the Level of the Sea. When the Obliquity was last at its superior Limit. -Probable Date of the 25-foot raised Beach.--Probable Extent of Rise of Sea-level resulting from Increase of Obliquity.-Lieutenant-Colonel Drayson's and Mr. Belt's Theories.-Sir Charles Lyell on Influence of Obliquity.

The direct Effect of Change in the Obliquity of the Ecliptic on Climate. There is still another cause which, I feel convinced, must to a very considerable extent have affected climate during past geological ages. I refer to the change in the obliquity of the ecliptic. This cause has long engaged the attention of geologists and physicists, and the conclusion' generally come to is that no great effect can be attributed to it. After giving special attention to the matter, I have been led to the very opposite conclusion. It is quite true, as has been urged, that the changes in the obliquity of the ecliptic cannot sensibly affect the climate of temperate regions; but it will produce a slight change on the climate of tropical latitudes, and a very considerable effect on that of the polar regions, especially at the poles themselves. We shall now consider the matter briefly.

It was found by Laplace that the obliquity of the ecliptic will oscillate to the extent of 1° 22′ 34′′ on each side of 23° 28', the obliquity in the year 1801.* This point has lately been

* Lieutenant-Colonel Drayson ("Last Glacial Epoch of Geology") and also Mr. Belt (Quart. Journ. of Science, October, 1874) state that Leverrier has late'y investigated the question as to the extent of the variation of the plane of the

examined by Mr. Stockwell, and the results at which he has arrived are almost identical with those of Laplace. "The mean value of the obliquity," he says, "of both the apparent and fixed ecliptics to the equator is 23° 17′ 17" The limits

of the obliquity of the apparent ecliptic to the equator are 24° 35′ 58′′ and 21° 58′ 36′′; whence it follows that the greatest and least declinations of the sun at the solstices can never differ from each other to any greater extent than 2° 37′ 22′′." *

This change will but slightly affect the climate of the temperate regions, but it will exercise a very considerable influence on the climate of the polar regions. According to Mr. Meech,† if 365-24 thermal days represent the present total annual quantity of heat received at the equator from the sun, 151-59 thermal days will represent the quantity received at the poles. Adopting his method of calculation, it turns out that when the obliquity of the ecliptic is at the maximum assigned by Laplace the quantity received at the equator would be 363.51 thermal days, and at the poles 160.04 thermal days. The equator would therefore receive 1.73 thermal days less heat, and the poles 8.45 thermal days more heat than at present.

ecliptic, and has arrived at results differing considerably from those of Laplace; viz., that the variation may amount to 4° 52', whereas, according to Laplace, it amounts to only 1° 21'. I fear they are comparing things that are totally different; viz., the variation of the plane of the ecliptic in relation to its mean position with its variation in relation to the equator. Laplace estimated that the plane of the ecliptic would oscillate to the extent of 4° 53′ 33′′ on each side of its mean position, a result almost identical with that of Leverrier, who makes it 4° 51′ 42′′. But neither of these geometricians ever imagined that the ecliptic could change in relation to the equator to even one-third of that amount.

Laplace demonstrated that the change in the plane of the ecliptic affected the position of the equator, causing it to vary along with it, so that the equator could never possibly recede further than 1° 22′ 34" from its mean position in relation to the ecliptic ("Mécanique Céleste," vol. ii., p. 856, Bowditch's Trans lation; see also Laplace's memoir, "Sur les Variations de l'Obliquité de l'Écliptique," Connaissance des Temps for 1827, p. 234), and I am not aware that Leverrier has arrived at a different conclusion.

Memoir on the Secular Variations of the Elements of the Orbits of the Planets, "Smithsonian Contributions to Knowledge,” vol. xvii. "Smithsonian Contributions to Knowledge," vol. ix.

When the obliquity was at a maximum, the poles would therefore be receiving 19 rays for every 18 they are receiving at present. The poles would then be receiving nearly as much heat as latitude 76° is receiving at present.

The increase of obliquity would not sensibly affect the polar winter. It is true that it would slightly increase the breadth of the frigid zone, but the length of the winter at the poles would remain unaffected. After the sun disappears below the horizon his rays are completely cut off, so that a further descent of 1° 22′ 34′′ would make no material difference in the climate. In the temperate regions the sun's altitude at the winter solstice would be 1° 22′ 34′′ less than at present. This would slightly increase the cold of winter in those regions. Rut the increase in the amount of heat received by the polar regions would materially affect the condition of the polar summer. What, then, is the rise of temperature at the poles which would result from the increase of 8.45 thermal days in the total amount received from the sun?

An increase of 8.45 thermal days, or 1-18th of the total quantity received from the sun, according to the mode of calculation adopted in Chap. II. would produce, all other things being equal, a rise in the mean annual temperature equal to 14° or 15°.

According to Professor Dove* there is a difference of 7°.6 between the mean annual temperature of latitude 76° and the

"Distribution of Heat on the Surface of the Globe," p. 14.

pole; the temperature of the former being 9°.8, and that of the latter 20.2. Since it follows that when the obliquity of the ecliptic is at a maximum the poles would receive about as much heat per annum as latitude 76° receives at present, it may be supposed that the temperature of the poles at that period ought to be no higher than that of latitude 76° at the present time. A little consideration will, however, show that this by no means follows. Professor Dove's Tables represent correctly the mean annual temperature corresponding to every tenth degree of latitude from the equator to the pole. But it must be observed that the rate at which the temperature diminishes from the equator to the pole is not proportionate to the decrease in the total quantity of heat received from the sun as we pass from the equator to the pole. Were the mean annual temperature of the various latitudes proportionate to the amount of direct heat received, the equator would be much warmer than it actually is at present, and the poles much colder. The reason of this, as has been shown in Chapter II., is perfectly obvious. There is a constant transferrence of heat from the equator to the poles, and of cold from the poles to the equator. The warm water of the equator is constantly flowing towards the poles, and the cold water at the poles is constantly flowing to the equator. The same is the case in regard to the aërial currents. Consequently a great portion of the direct heat of the sun goes, not to raise the temperature of the equator, but to heat the poles. And, on the other hand, the cold materials at the poles are transferred to the equator, and thus lower the temperature of that part of the globe to a great extent. The present difference of temperature between lat. 76° and the pole, determined according to the rate at which the temperature is found to diminish between the equator and the pole, amounts to only about 7° or 8°. But were there no mutual transferrence of warm and cold materials between the equatorial and polar regions, and were the temperature of each latitude to depend solely upon the direct rays of the sun, the difference would far exceed that amount.