If we assume that the southern ice-cap extends on an average down to lat. 70°, we shall have an area equal to 1/33·163 of the entire surface of the globe. The proportion of land to that of water, taking into account the antarctic continent, is as 526 to 1272. The southern ice-cap will therefore be equal to 1/23·46 of the area covered by water. The density of ice to that of water being taken at ·92 to 1, it follows that 25 feet 6 inches of ice melted from off the face of the antarctic continent would raise the level of the ocean one foot. If 470 feet were melted off—and this is by no means an extravagant supposition, when we reflect that for every 18 pounds of ice presently melted an additional pound or two pounds, or perhaps more, would then be melted, and that for many ages in succession—the water thus produced from the melted ice would raise the level of the sea 18 feet 5 inches. The removal of the 470 feet of solid ice— which must be but a very small fraction of the total quantity of ice lying upon the antarctic continent—would shift the earth’s centre of gravity about 7 feet to the north of its present position. The shifting of the centre of gravity would cause the sea to sink on the southern hemisphere and rise on the northern. And the quantity of water thus transferred from the southern hemisphere to the northern would carry the centre of gravity about one foot further, and thus give a total displacement of the centre to the extent of about 8 feet. The sea would therefore rise about 8 feet at the North Pole, and in the latitude of Edinburgh about 6 feet 7 inches. This, added to the rise of 18 feet 5 inches, occasioned by the melting of the ice, would give 25 feet as the total rise in the latitude of Scotland 11,700 years ago.
Each square foot of surface at the poles 11,700 years ago would be receiving 18,223,100 foot-pounds more of heat annually than at present. If we deduct 22 per cent. as the amount absorbed in passing through the atmosphere, we have 14,214,000 foot-pounds. This would be sufficient to melt 2·26 feet of ice. But if 50, instead of 22, per cent. were cut off, 1·45 cubic feet would be melted. In this case the 470 feet of ice would be melted, independently of the effects of eccentricity, in about 320 years. And supposing that only one-fourth part of the extra heat reached the ground, 470 feet of ice would be removed in about 640 years.
As to the exact time that the obliquity was at a maximum, previous to that of 11,700 years ago, our uncertainty is still greater. If we are permitted to assume that the ecliptic passes from its maximum to its minimum state and back to its maximum again with anything like uniformity, at the rate assigned by Leverrier and others, the obliquity would not be far from a maximum about 60,000 years ago. Taking the rate of precession at 50″·21129, and assuming it to be uniform—which it probably is not—the winter solstice would be in the aphelion about 61,300 years ago.[231] In short, it seems not at all improbable that at the time the solstice-point was in the aphelion, the obliquity of the ecliptic would not be far from its maximum state. But at that time the value of the eccentricity was 0·023, instead of 0·0187, its value at the last period. Consequently the rise of the sea would probably be somewhat greater than it was 11,700 years ago. Might not this be the period of the 40-foot beach? In this case 11,000 or 12,000 years would be the age of the 25-foot beach, and 60,000 years the age of the 40-foot beach.
About 22,000 years ago, the winter solstice was in the perihelion, and as the eccentricity was then somewhat greater than it is at present, the winters would be a little warmer and the climate more equable than it is at the present day. This perhaps might be the period of the submarine forests and lower peat-beds which underlie the Carse clays, Scrobicularia mud, and other deposits belonging to the age of the 25-foot beach. At any rate, it is perfectly certain that a condition of climate at this period prevailed exceedingly favourable to the growth of peat. It follows also that at this time, owing to a greater accumulation of ice on the southern hemisphere, the sea-level would be a few feet lower than at present, and that forests and peat may have then grown on places which are now under the sea-level.
For a few thousand years before and after 11,700 years ago, when the winter solstice was evidently not far from the aphelion, and the sea standing considerably above its present level, would probably, as we have already stated, be the time when the Carse clays and other recent deposits lying above the present level of the river were formed. And it is also a singular fact that the condition of things at that period must have been exceedingly favourable to the formation of such estuarine deposits; for at that time the winter temperature of our island, as has been already shown, would be considerably lower than at present, and, consequently, during that season, snow, to a much larger extent than now, would fall instead of rain. The melting of the winter’s accumulation of snow on the approach of summer would necessarily produce great floods, similar to what occur in the northern parts of Asia and America at the present day from this very same cause. The loose upper soil would be carried down by those floods and deposited in the estuaries of our rivers.
The foregoing is a rough and imperfect sketch of the history of the climate and the physical conditions of our globe for the past 60,000 years, in so far as physical and cosmical considerations seem to afford us information on the subject, and its striking agreement with that derived from geological sources is an additional evidence in favour of the opinion that geological and cosmical phenomena are physically related by a bond of causation.
Lieutenant-Colonel Drayson’s Theory of the Cause of the Glacial Epoch.—In a paper read before the Geological Society by Lieutenant-Colonel Drayson, R.A., on the 22nd February, 1871,[232] that author states, that after calculating from the recorded positions of the pole of the heavens during the last 2,000 years, he finds the pole of the ecliptic is not the centre of the circle traced by the pole of the heavens. The pole of the heavens, he considers, describes a circle round a point 6° distant from the pole of the ecliptic and 29° 25′ 47″ from the pole of the heavens, and that about 13,700 years b.c. the angular distance of the two poles was 35° 25′ 47″. This would bring the Arctic Circle down to latitude 54° 34′ 13″ N. I fear that this is a conclusion that will not be generally accepted by those familiar with celestial mechanics. But, be this as it may, my present object is not to discuss the astronomical part of Colonel Drayson’s theory, but to consider whether the conclusions which he deduces from his theory in regard to the cause of the glacial epoch be legitimate or not. Assuming for argument’s sake that the obliquity of the ecliptic can possibly reach to 35° or 36°, so as to bring the Arctic Circle down to the centre of England, would this account for the glacial epoch? Colonel Drayson concludes that the shifting of the Arctic Circle down to the latitude of England would induce here a condition of climate similar to that which obtains in arctic regions. This seems to be the radical error of the theory. It is perfectly true that were the Arctic Circle brought down to latitude 54° 35′ part of our island would be in the arctic regions, but it does not on that account follow that our island would be subjected to an arctic climate.
The polar regions owe their cold not to the obliquity of the ecliptic, but to their distance from the equator. Indeed were it not for obliquity those regions would be much colder than they really are, and an increase of obliquity, instead of increasing their cold, would really make them warmer. The general effect of obliquity, as we have seen, is to diminish the amount of heat received in equatorial and tropical regions, and to increase it in the polar and temperate regions. The greater the obliquity, and, consequently, the farther the sun recedes from the equator, the smaller is the quantity of heat received by equatorial regions, and the greater the amount bestowed on polar and temperate regions. If, for example, we represent the present amount of heat received from the sun at the equator on a given surface at 100 parts, 42·47 parts will then represent the amount received at the poles on the same given surface. But were the obliquity increased to 35° the amount received at the equator would be reduced to 94·93 parts, and that at the poles increased to 59·81; being an increase at the poles of nearly one half. At latitude 60° the present quantity is equal to 57 parts; but about 63 parts would be received were the obliquity increased to 35°. It therefore follows that although the Arctic Circle were brought down to the latitude of London so that the British islands would become a part of the arctic regions, the mean temperature of these islands would not be lowered, but the reverse. The winters would no doubt be colder than they are at present, but the cold of winter would be far more than compensated for by the heat of summer. It is not a fair representation of the state of things, merely to say that an increase of obliquity tends to make the winters colder and the summers hotter, for it affects the summer heat far more than it does the winter cold. And the greater the obliquity the more does the increase of heat during summer exceed the decrease during winter. This is obvious because the greater the obliquity the greater the total annual amount of heat received.
If an increase of obliquity tended to produce an increase of ice in temperate and polar regions, and thus to lead to a glacial epoch, then the greater the obliquity the greater would be the tendency to produce such an effect. Conceive, then, the obliquity to go on increasing until it ultimately reached its absolute limit, 90°, and the earth’s axis to coincide with the plane of the ecliptic. The Arctic Circle would then extend to the equator. Would this produce a glacial epoch? Certainly not. A square foot of surface at the poles would then be receiving as much heat per annum as a square foot at the equator at present, supposing the sun remained on the equator during the entire year. Less heat, however, would be reaching the equatorial regions than now. At present, as we have just seen, the annual quantity of heat received at either pole is to that received at the equator as 42·47 to 100; but at the period under consideration the poles would be actually obtaining one-half more heat than the equator. The amount received per square foot at the poles, to that received per square foot at the equator, would be in the ratio of half the circumference of a circle to its diameter, or as 1·5708 to 1. But merely to say that the poles would be receiving more heat per annum than the equator is at present, does not convey a correct idea of the excessive heat which the poles would then have to endure; for it must be borne in mind that the heat reaching the equator is spread over the whole year, whereas the poles would get their total amount during the six months of their summer. Consequently, for six months in the year the poles would be obtaining far more than double the quantity of heat received at present by the equator during the same length of time, and more than three times the quantity then received by the equator. The amount reaching the pole during the six months to that reaching the equator would be as 3·1416 to 1.
At the equator twelve hours’ darkness alternates with twelve hours’ sunshine, and this prevents the temperature from rising excessively high; but at the poles it would be continuous sunshine for six months without the ground having an opportunity of cooling for a single hour. At the summer solstice, when the sun would be in the zenith of the pole, the amount of heat received there every twenty-four hours would actually be nearly three-and-a-quarter times greater than that presently received at the equator. Now what holds true with regard to the poles would hold equally true, though to a lesser extent, of polar and temperate regions. We can form but a very inadequate idea of the condition of things which would result from such an enormous increase of heat. Nothing living on the face of the globe could exist in polar regions under so fearful a temperature as would then prevail during summer months. How absurd would it be to suppose that this condition of things would tend to produce a glacial epoch! Not only would every particle of ice in polar regions be dissipated, but the very seas around the pole would be, for several months in the year, at the boiling point.