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

by James Croll

Of course we are at present simply considering the earth as an absorber and radiator of heat, without taking into account the effects of distribution of sea and land and other modifying causes, and are assuming that everything is the same in both hemispheres, with the exception that the winter of the one hemisphere is longer than that of the other.

What, then, is the amount of heat stored up by the one hemisphere and lost by the other? Is it such an amount as to sensibly affect climate?

The experiments and observations which have been made on underground temperature afford us a means of making at least a rough estimate of the amount. And from these it will be seen that the influence of an excess of seven or eight days in the length of the southern winter over the northern could hardly produce an effect that would be sensible.

Observations were made at Edinburgh by Professor J. D. Forbes on three different substances; viz., sandstone, sand, and trap-rock. By calculation, we find from the data afforded by those observations that the total quantity of heat accumulated in the ground during the summer above the mean temperature was as follows:—In the sandstone-rock, a quantity sufficient to raise the temperature of the rock 1° C. to a depth of 85 feet 6 inches; in the sand a quantity sufficient to raise the temperature 1° C. to a depth of 72 feet 6 inches; and in the trap-rock a quantity only sufficient to raise the temperature 1° C. to a depth of 61 feet 6 inches.

Taking the specific heat of the sandstone per unit volume, as determined by Regnault, at ·4623, and that of sand at ·3006, and trap at ·5283, and reducing all the results to one standard, viz., that of water, we find that the quantity of heat stored up in the sandstone would, if applied to water, raise its temperature 1° C. to a depth of 39 feet 6 inches; that stored up in the sand would raise the temperature of the water 1° C. to a depth of 21 feet 8 inches, and that stored up in the trap would raise the water 1° C. to the depth of 32 feet 6 inches. We may take the mean of these three results as representing pretty accurately the quantity stored up in the general surface of the country. This would be equal to 31 feet 3 inches depth of water raised 1° C. The quantity of heat lost by radiation during winter below the mean was found to be about equal to that stored up during summer.

The total quantity of heat per square foot of surface received by the equator from sunrise till sunset at the time of the equinoxes, allowing 22 per cent. for the amount cut off in passing through the atmosphere, is 1,780,474 foot-pounds. In the latitude of Edinburgh about 938,460 foot-pounds per square foot of surface is received, assuming that not more than 22 per cent. is cut off by the atmosphere. At this rate a quantity of heat would be received from the sun in two days ten hours (say, three days) sufficient to raise the temperature of the water 1° C. to the required depth of 31 feet 3 inches. Consequently the total quantity of heat stored up during summer in the latitude of Edinburgh is only equal to what we receive from the sun during three days at the time of the equinoxes. Three days’ sunshine during the middle of March or September, if applied to raise the temperature of the ground, would restore all the heat lost during the entire winter; and another three days’ sunshine would confer on the ground as much heat as is stored up during the entire summer. But it must be observed that the total duration of sunshine in winter is to that of summer in the latitude of Edinburgh only about as 4 to 7. Here is a difference of two months. But this is not all; the quantity of heat received during winter is scarcely one-third of that received during summer; yet, notwithstanding this enormous difference between summer and winter, the ground during winter loses only about six days’ sun-heat below the maximum amount possessed by it in summer.

But if what has already been stated is correct, this loss of heat sustained by the earth during winter is not chiefly owing to radiation during the longer absence of the sun, but to the decrease in the quantity of heat received in consequence of his longer absence combined with the obliquity of his rays during that season. Now in the case of the two hemispheres, although the southern winter is longer than the northern, yet the quantity of heat received by each is the same. But supposing it held true, which it does not, that the loss of heat sustained by the earth in winter is as much owing to radiation resulting from the excess in the length of the winter nights over those of the summer as to the deficiency of heat received in winter from that received in summer, three days’ heat would then in this case be the amount lost by radiation in consequence of this excess in the length of the winter nights. The total length of the winter nights to those of the summer is, as we have seen, about as 7 to 4. This is a difference of nearly 1200 hours. But the excess of the south polar winter over the north amounts to only about 184 hours. Now if 1200 hours give a loss of three days’ sun-heat, 184 hours will give a loss of scarcely 5½ hours.

It is no doubt true that the two cases are not exactly analogous; but it is obvious that any error which can possibly arise from regarding them as such cannot materially alter the conclusion to which we have arrived. Supposing the effect were double, or even quadruple, what we have concluded it to be, still it would not amount to a loss of two days’ heat, which could certainly have little or no influence on climate.

But even assuming all the preceding reasoning to be incorrect, and that the southern hemisphere, in consequence of its longer winter, loses heat to the extravagant extent of 168 hours, supposed by Adhémar, still this could not materially affect climate. The climate is influenced by the mere temperature of the surface of the ground, and not by the quantity of heat or cold that may be stored up under the surface. The climate is determined, so far as the ground is concerned, by the temperature of the surface, and is wholly independent of the temperature which may exist under the surface. Underground temperature can only affect climate through the surface. If the surface could, for example, be kept covered with perpetual snow, we should have a cold and sterile climate, although the temperature of the ground under the snow was actually at the boiling-point. Let the ground to a depth of, say 40 or 50 feet, be deprived of an amount of heat equal to that received from the sun in 168 hours. This could produce little or no sensible effect on climate; for, owing to the slow conductivity of the ground for heat, this loss would not sensibly affect the temperature of the surface, as it would take several months for the sun’s heat to penetrate to that depth and restore the lost heat. The cold, if I may be allowed to use the expression, would come so slowly out to the surface that its effect in lowering the temperature of the surface would scarcely be sensible. And, again, if we suppose the 168 hours’ heat to be lost by the mere surface of the ground, the effect would certainly be sensible, but it would only be so for a few days. We might in this case have a week’s frozen soil, but that would be all. Before the air had time to become very sensibly affected by the low temperature of the surface the frozen soil would be thawed.

The storing up of heat or cold in the ground has in reality very little to do with climate. Some physicists explain, for example, why the month of July is warmer than June by referring it to the fact that by the month of July the ground has become possessed of a larger accumulation of heat than it possessed in June. This explanation is evidently erroneous. The ground in July certainly possesses a greater store of heat than it did in June; but this is not the reason why the former month is hotter than the latter. July is hotter than June because the air (not the ground) has become possessed of a larger store of heat than it had in June. Now the air is warmer in July than in June because, receiving little increase of temperature from the direct rays of the sun, it is heated chiefly by radiation from the earth and by contact with its warm surface. Consequently, although the sun’s heat is greater in June than it is in July, it is near the middle of July before the air becomes possessed of its maximum store of heat. We therefore say that July is hotter than June because the air is hotter, and consequently the temperature in the shade is greater in the former month than in the latter.