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

by James Croll

Adhémar’s Explanation.—It has long been known that on the southern hemisphere the temperature is lower and the accumulation of ice greater than on the northern. This difference has usually been attributed to the great preponderance of sea on the southern hemisphere. M. Adhémar, on the other hand, attempts to explain this difference by referring it to the difference in the amount of heat lost by the two hemispheres in consequence of the difference of seven days in the length of their respective winters. As the northern winter is shorter than the summer, he concludes that there is an accumulation of heat on that hemisphere, while, on the other hand, the southern winter being longer than the summer, there is therefore a loss of heat on the southern hemisphere. “The south pole,” he says, “loses in one year more heat than it receives, because the total duration of its night surpasses that of its day by 168 hours; and the contrary takes place for the north pole. If, for example, we take for unity the mean quantity of heat which the sun sends off in one hour, the heat accumulated at the end of the year at the north pole will be expressed by 168, while the heat lost by the south pole will be equal to 168 times what the radiation lessens it by in one hour, so that at the end of the year the difference in the heat of the two hemispheres will be represented by 336 times what the earth receives from the sun or loses in an hour by radiation.”[48]

Adhémar supposes that about 10,000 years hence, when our northern winter will occur in aphelion and the southern in perihelion, the climatic conditions of the two hemispheres will be reversed; the ice will melt at the south pole, and the northern hemisphere will become enveloped in one continuous mass of ice, leagues in thickness, extending down to temperate regions.

This theory seems to be based upon an erroneous interpretation of a principle, first pointed out, so far as I am aware, by Humboldt in his memoir “On Isothermal Lines and Distribution of Heat over the Globe.”[49] This principle may be stated as follows:—

Although the total quantity of heat received by the earth from the sun in one revolution is inversely proportional to the minor axis of the orbit, yet this amount, as was proved by D’Alembert, is equally distributed between the two hemispheres, whatever the eccentricity may be. Whatever extra heat the southern hemisphere may at present receive from the sun daily during its summer months owing to greater proximity to the sun, is exactly compensated by a corresponding loss arising from the shortness of the season; and, on the other hand, whatever daily deficiency of heat we in the northern hemisphere may at present have during our summer half-year, in consequence of the earth’s distance from the sun, is also exactly compensated by a corresponding length of season.

But the surface temperature of our globe depends as much upon the amount of heat radiated into space as upon the amount derived from the sun, and it has been thought by some that this compensating principle holds true only in regard to the latter. In the case of the heat lost by radiation the reverse is supposed to take place. The southern hemisphere, it is asserted, has not only a colder winter than the northern in consequence of the sun’s greater distance, but it has also a longer winter; and the extra loss of heat from radiation during winter is not compensated by its nearness to the sun during summer, for it gains no additional heat from this proximity. And in the same way it is argued that as our winter in the northern hemisphere, owing to the less distance of the sun, is not only warmer than that of the southern hemisphere, but is also at the same time shorter, so our hemisphere is not cooled to such an extent as the southern. And thus the mean temperature of the winter half-year, as well as the intensity of the sun’s heat, is affected by a change in the sun’s distance.

Although I always regarded this cause of Humboldt’s to be utterly inadequate to produce such effects as those attributed to it by Adhémar, still, in my earlier papers[50] I stated it to be a vera causa which ought to produce some sensible effect on climate. But shortly afterwards on a more careful consideration of the whole subject, I was led to suspect that the circumstance in question can, according to theory, produce little or no effect on the climatic condition of our globe.

As there appears to be a considerable amount of misapprehension in reference to this point, which forms the basis of Adhémar’s theory, I may here give it a brief consideration.[51]

The rate at which the earth radiates into space the heat received from the sun depends upon the temperature of its surface; and the temperature of its surface (other things being equal) depends upon the rate at which the heat is received. The greater the rate at which the earth receives heat from the sun, the greater will therefore be the rate at which it will lose that heat by radiation. Now the total quantity of heat received during winter by the southern hemisphere is exactly equal to that received during winter by the northern. But as the southern winter is longer than the northern, the rate at which the heat is received, and consequently the rate of radiation, during that season must be less on the southern hemisphere than on the northern. Thus the southern hemisphere loses heat during a longer period than the northern, and therefore the less rate of radiation (were it not for a circumstance presently to be noticed) would wholly compensate for the longer period, and the total quantity of heat lost during winter would be the same on both hemispheres. The southern summer is shorter than the northern, but the heat is more intense, and the surface of the ground kept at a higher temperature; consequently the rate of radiation into space is greater.

When the rate at which a body receives heat is increased, the temperature of the body rises till the rate of radiation equals the rate of absorption, after which equilibrium is restored; and when the rate of absorption is diminished, the temperature falls till the rate of radiation equals that of absorption.

But notwithstanding all this, owing to the slow conductivity of the ground for heat, more heat will pass into it during the longer summer of aphelion than during the shorter one of perihelion; for the amount of heat which passes into the ground depends on the length of time during which the earth is receiving heat, as well as upon the amount received. In like manner, more heat will pass out of the ground during the longer winter in aphelion than during the shorter one in perihelion. Suppose the length of the days on the one hemisphere (say the northern) to be 23 hours, and the length of the nights, say one hour; while on the other hemisphere the days are one hour and the nights 23 hours. Suppose also that the quantity of heat received from the sun by the southern hemisphere during the day of one hour to be equal to that received by the northern hemisphere during the day of 23 hours. It is evident that although the surface of the ground on the southern hemisphere would receive as much heat from the sun during the short day of one hour as the surface of the northern hemisphere during the long day of 23 hours, yet, owing to the slow conductivity of the ground for heat, the amount absorbed would not be nearly so much on the southern hemisphere as on the northern. The temperature of the surface during the day, it is true, would be far higher on the southern hemisphere than on the northern, and consequently the rate at which the heat would pass into the ground would be greater on that hemisphere than on the northern; but, notwithstanding the greater rate of absorption resulting from the high temperature of the surface, it would not compensate for the shortness of the day. On the other hand, the surface of the ground on the southern hemisphere would be colder during the long night of 23 hours than it would be on the northern during the short night of only one hour; and the low temperature of the ground would tend to lessen the rate of radiation into space. But the decrease in the rate of radiation would not compensate fully for the great length of the night. The general and combined result of all those causes would be that a slight accumulation of heat would take place on the northern hemisphere and a slight loss on the southern. But this loss of heat on the one hemisphere and gain on the other would not go on accumulating at a uniform rate year by year, as Adhémar supposes.