CHAPTER V.

REASON WHY THE SOUTHERN HEMISPHERE IS COLDER THAN THE NORTHERN.

Adhémar’s Explanation.—Adhémar’s Theory founded upon a physical Mistake in regard to Radiation.—Professor J. D. Forbes on Underground Temperature.—Generally accepted Explanation.—Low Temperature of Southern Hemisphere attributed to Preponderance of Sea.—Heat transferred from Southern to Northern Hemisphere by Ocean-current the true Explanation.—A large Portion of the Heat of the Gulf-stream derived from the Southern Hemisphere.

_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.

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.

It is therefore, I presume, quite apparent that Adhémar’s theory fails to explain why the southern hemisphere is colder than the northern.

_The generally accepted Explanation._—The difference in the mean temperature of the two hemispheres is usually attributed to the proportion of sea to land in the southern hemisphere and of land to sea in the northern hemisphere. This, no doubt, will account for the greater _annual range_ of temperature on the northern hemisphere, but it seems to me that it will not account for the excess of _mean_ temperature possessed by that hemisphere over the southern.

The general influence of land on climate is to exaggerate the variation of temperature due to the seasons. On continents the summers are hotter and the winters colder than on the ocean. The days are also hotter and the nights colder on land than on sea. This is a result which follows from the mere physical properties of land and water, independently of currents, whether of ocean or of air. But it nevertheless follows, according to theory (and this is a point which has been overlooked), that the mean annual temperature of the ocean ought to be greater than that of the land in equatorial regions as well as in temperate and polar regions. This will appear obvious for the following reasons:—(1) The ground stores up heat only by the slow process of conduction, whereas water, by the mobility of its particles and its transparency for heat-rays, especially those from the sun, becomes heated to a considerable depth rapidly. The quantity of heat stored up in the ground is thus comparatively small, while the quantity stored up in the ocean is great. (2) The air is probably heated more rapidly by contact with the ground than with the ocean; but, on the other hand, it is heated far more rapidly by radiation from the ocean than from the land. The aqueous vapour of the air is to a great extent diathermanous to radiation from the ground, while it absorbs the rays from water and thus becomes heated. (3) The air radiates back a considerable portion of its heat, and the ocean absorbs this radiation from the air more readily than the ground does. The ocean will not reflect the heat from the aqueous vapour of the air, but absorbs it, while the ground does the opposite. Radiation from the air, therefore, tends more readily to heat the ocean than it does the land. (4) The aqueous vapour of the air acts as a screen to prevent the loss by radiation from water, while it allows radiation from the ground to pass more freely into space; the atmosphere over the ocean consequently throws back a greater amount of heat than is thrown back by the atmosphere over the land. The sea in this case has a much greater difficulty than the land has in getting quit of the heat received from the sun; in other words, the land tends to lose its heat more rapidly than the sea. The consequence of all these circumstances is that the ocean must stand at a higher mean temperature than the land. A state of equilibrium is never gained until the rate at which a body is receiving heat is equal to the rate at which it is losing it; but as equal surfaces of sea and land receive from the sun the same amount of heat, it therefore follows that, in order that the sea may get quit of its heat as rapidly as the land, it _must stand at a higher temperature_ than the land. The temperature of the sea must continue to rise till the amount of heat thrown off into space equals that received from the sun; when this point is reached, equilibrium is established and the temperature remains stationary. But, owing to the greater difficulty that the sea has in getting rid of its heat, the mean temperature of equilibrium of the ocean must be higher than that of the land; consequently the mean temperature of the ocean, and also of the air immediately over it, in tropical regions should be higher than the mean temperature of the land and the air over it.

The greater portion of the southern hemisphere, however, is occupied by water, and why then, it may be asked, is this water hemisphere colder than the land hemisphere? Ought it not also to follow that the sea in inter-tropical regions should be warmer than the land under the same parallels; yet, as we know, the reverse is actually found to be the case. How then is all this to be explained, if the foregoing reasoning be correct? We find when we examine Professor Dove’s charts of mean annual temperature, that the ocean in inter-tropical regions has a mean annual temperature below the normal, and the land a mean annual temperature above the normal. Both in the Pacific and in the Atlantic the mean temperature sinks to 2°·3 below the normal, while on the land it rises 4°·6 above the normal. The explanation in this case is obviously this: the temperature of the ocean in inter-tropical regions, as we have already seen, is kept much lower than it would otherwise be by the enormous amount of _heat_ that is being constantly carried away from those regions into temperate and polar regions, and of _cold_ that is being constantly carried from temperate and polar regions to the tropical regions by means of ocean-currents. The same principle which explains why the sea in inter-tropical regions has a lower mean annual temperature than the land, explains also why the southern hemisphere has a lower mean annual temperature than the northern. The temperature of the southern hemisphere is lowered by the transference of heat by means of ocean-currents.

_Heat transferred from the Southern to the Northern Hemisphere by Ocean-currents the true Explanation._—The great ocean-currents of the globe take their rise in three immense streams from the Southern Ocean, which, on reaching the tropical regions, become deflected in a westerly direction and flow along the southern side of the equator for thousands of miles. Perhaps more than one half of this mass of moving water returns into the Southern Ocean without ever crossing the equator, but the quantity which crosses over to the northern hemisphere is enormous. This constant flow of water from the southern hemisphere to the northern in the form of surface currents must be compensated by _under currents_ of equal magnitude from the northern hemisphere to the southern. The currents, however, which cross the equator are far higher in temperature than their compensating under currents; consequently there is a constant transference of heat from the southern hemisphere to the northern. Any currents taking their rise in the northern hemisphere and flowing across into the southern are comparatively trifling, and the amount of heat transferred by them is also trifling. There are one or two currents of considerable size, such as the Brazilian branch of the great equatorial current of the Atlantic, and a part of the South Equatorial Drift-current of the Pacific, which cross the equator from north to south; but these cannot be regarded as northern currents; they are simply southern currents deflected back after crossing over to the northern hemisphere. The heat which these currents possess is chiefly obtained on the southern hemisphere before crossing over to the northern; and although the northern hemisphere may not gain much heat by means of them, it, on the other hand, does not lose much, for the heat which they give out in their progress along the southern hemisphere does not belong to the northern hemisphere.

But, after making the fullest allowance for the amount of heat carried across the equator from the northern hemisphere to the southern, we shall find, if we compare the mean temperature of the currents from south to north with that of the great compensating under currents and the one or two small surface currents, that the former is very much higher than the latter. The mean temperature of the water crossing the equator from south to north is probably not under 65°, that of the under currents is probably not over 39°. But to the under currents we must add the surface currents from north to south; and assuming that this will raise the mean temperature of the entire mass of water flowing south to, say, 45°, we have still a difference of 20° between the temperature of the masses flowing north and south. Each cubic foot of water which crosses the equator will in this case transfer about 965,000 foot-pounds of heat from the southern hemisphere to the northern. If we had any means of ascertaining the volume of those great currents crossing the equator, we should then be able to make a rough estimate of the total amount of heat transferred from the southern hemisphere to the northern; but as yet no accurate estimate has been made on this point. Let us assume, what is probably below the truth, that the total amount of water crossing the equator is at least double that of the Gulf-stream as it passes through the Straits of Florida, which amount we have already found to be equal to 66,908,160,000,000 cubic feet daily. Taking the quantity of heat conveyed by each cubic foot of water of the Gulf-stream as 1,158,000 foot-pounds, it is found, as we have seen, that an amount of heat is conveyed by this current equal to all the heat that falls within 32 miles on each side of the equator. Then, if each cubic foot of water crossing the equator transfers 965,000 foot-pounds, and the quantity of water be double that of the Gulf-stream, it follows that the amount of heat transferred from the southern hemisphere to the northern is equal to all the heat falling within 52 miles on each side of the equator, or equal to all the heat falling on the southern hemisphere within 104 miles of the equator. This quantity taken from the southern hemisphere and added to the northern will therefore make a difference in the amount of heat possessed by the two hemispheres equal to all the heat which falls on the southern hemisphere within somewhat more than 208 miles of the equator.

_A large Portion of the Heat of the Gulf-stream derived from the Southern Hemisphere._—It can be proved that a very large portion of the heat conveyed by the Gulf-stream comes from the southern hemisphere. The proof is as follows:—

If all the heat came from the northern hemisphere, it could only come from that portion of the Atlantic, Caribbean Sea, and Gulf of Mexico which lies to the north of the equator. The entire area of these seas, extending to the Tropic of Cancer, is about 7,700,000 square miles. But this area is not sufficient to supply the current passing through the “Narrows” with the necessary heat. Were the heat which passes through the Straits of Florida derived exclusively from this area, the following table would then represent the relative quantity per unit surface possessed by the Atlantic in the three zones, assuming that one half of the heat of the Gulf-stream passes into the arctic regions and the other half remains to warm the temperate regions[52]:—

From the equator to the Tropic of Cancer 773 From the Tropic of Cancer to the Arctic Circle 848 From the Arctic Circle to the North Pole 610

These figures show that the Atlantic, from the equator to the Tropic of Cancer, would be as cold as from the Tropic of Cancer to the North Pole, were it not that a large proportion of the heat possessed by the Gulf-stream is derived from the southern hemisphere.