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

by James Croll

From observations made by Sir John Herschel and by M. Pouillet on the direct heat of the sun, it is found that, were no heat absorbed by the atmosphere, about eighty-three foot-pounds per second would fall upon a square foot of surface placed at right angles to the sun’s rays.[16] Mr. Meech estimates that the quantity of heat cut off by the atmosphere is equal to about twenty-two per cent. of the total amount received from the sun. M. Pouillet estimates the loss at twenty-four per cent. Taking the former estimate, 64·74 foot-pounds per second will therefore be the quantity of heat falling on a square foot of the earth’s surface when the sun is in the zenith. And were the sun to remain stationary in the zenith for twelve hours, 2,796,768 foot-pounds would fall upon the surface.

It can be shown that the total amount of heat received upon a unit surface on the equator, during the twelve hours from sunrise till sunset at the time of the equinoxes, is to the total amount which would be received upon that surface, were the sun to remain in the zenith during those twelve hours, as the diameter of a circle to half its circumference, or as 1 to 1·5708. It follows, therefore, that a square foot of surface on the equator receives from the sun at the time of the equinoxes 1,780,474 foot-pounds daily, and a square mile 49,636,750,000,000 foot-pounds daily. But this amounts to only 1/1560935th part of the quantity of heat daily conveyed from the tropics by the Gulf-stream. In other words, the Gulf-stream conveys as much heat as is received from the sun by 1,560,935 square miles at the equator. The amount thus conveyed is equal to all the heat which falls upon the globe within thirty-two miles on each side of the equator. According to calculations made by Mr. Meech,[17] the annual quantity of heat received by a unit surface on the frigid zone, taking the mean of the whole zone, is 5·45/12th of that received at the equator; consequently the quantity of heat conveyed by the Gulf-stream in one year is equal to the heat which falls on an average on 3,436,900 square miles of the arctic regions. The frigid zone or arctic regions contain 8,130,000 square miles. There is actually, therefore, nearly one-half as much heat transferred from tropical regions by the Gulf-stream as is received from the sun by the entire arctic regions, the quantity conveyed from the tropics by the stream to that received from the sun by the arctic regions being nearly as two to five.

But we have been assuming in our calculations that the percentage of heat absorbed by the atmosphere is no greater in polar regions than it is at the equator, which is not the case. If we make due allowance for the extra amount absorbed in polar regions in consequence of the obliqueness of the sun’s rays, the total quantity of heat conveyed by the Gulf-stream will probably be nearly equal to one-half the amount received from the sun by the entire arctic regions.

If we compare the quantity of heat conveyed by the Gulf-stream with that conveyed by means of aërial currents, the result is equally startling. The density of air to that of water is as 1 to 770, and its specific heat to that of water is as 1 to 4·2; consequently the same amount of heat that would raise 1 cubic foot of water 1° would raise 770 cubic feet of air 4°·2, or 3,234 cubic feet 1°. The quantity of heat conveyed by the Gulf-stream is therefore equal to that which would be conveyed by a current of air 3,234 times the volume of the Gulf-stream, at the same temperature and moving with the same velocity. Taking, as before, the width of the stream at fifty miles, and its depth at 1,000 feet, and its velocity at two miles an hour, it follows that, in order to convey an equal amount of heat from the tropics by means of an aërial current, it would be necessary to have a current about 1¼ mile deep, and at the temperature of 65°, blowing at the rate of two miles an hour from every part of the equator over the northern hemisphere towards the pole. If its velocity were equal to that of a good sailing-breeze, which Sir John Herschel states to be about twenty-one miles an hour, the current would require to be above 600 feet deep. A greater quantity of heat is probably conveyed by the Gulf-stream alone from the tropical to the temperate and arctic regions than by all the aërial currents which flow from the equator.

We are apt, on the other hand, to over-estimate the amount of the heat conveyed from tropical regions to us by means of aërial currents. The only currents which flow from the equatorial regions are the upper currents, or anti-trades as they are called. But it is not possible that much heat can be conveyed directly by them. The upper currents of the trade-winds, even at the equator, are nowhere below the snow-line; they must therefore lie in a region of which the temperature is actually below the freezing-point. In fact, if those currents were warm, they would elevate the snow-line above themselves. The heated air rising off the hot burning ground at the equator, after ascending a few miles, becomes exposed to the intense cold of the upper regions of the atmosphere; it then very soon loses all its heat, and returns from the equator much colder than it went thither. It is impossible that we can receive any heat directly from the equatorial regions by means of aërial currents. It is perfectly true that the south-west wind, to which we owe so much of our warmth in this country, is a continuation of the anti-trade; but the heat which this wind brings to us is not derived from the equatorial regions. This will appear evident, if we but reflect that, before the upper current descends to the snow-line after leaving the equator, it must traverse a space of at least 2,000 miles; and to perform this long journey several days will be required. During all this time the air is in a region below the freezing-point; and it is perfectly obvious that by the time it begins to descend it must have acquired the temperature of the region in which it has been travelling.

If such be the case, it is evident that a wind whose temperature is below 32° could never warm a country such as ours, where the temperature does not fall below 38° or 39°. The heat of our south-west winds is derived, not directly from the equator, but from the warm water of the Atlantic—in fact, from the Gulf-stream. The upper current acquires its heat after it descends to the earth. There is one way, however, whereby heat is indirectly conveyed from the equator by the anti-trades; that is, in the form of aqueous vapour. In the formation of one pound of water from aqueous vapour, as Professor Tyndall strikingly remarks, a quantity of heat is given out sufficient to melt five pounds of cast iron.[18] It must, however, be borne in mind that the greater part of the moisture of the south-west and west winds is derived from the ocean in temperate regions. The upper current receives the greater part of its moisture after it descends to the earth, whilst the moisture received at the equator is in great part condensed, and falls as rain in those regions.

This latter assertion has been so frequently called in question that I shall give my reasons for making it. According to Dr. Keith Johnston (“Physical Atlas”) the mean rainfall of the torrid regions is ninety-six inches per annum, while that of the temperate regions amounts to only thirty-seven inches. If the greater part of the moisture of the torrid regions does not fall as rain in those regions, it must fall as such beyond them. Now the area of the torrid to that of the two temperate regions is about as 39·3 to 51. Consequently ninety-six inches of rain spread over the temperate regions would give seventy-four inches; but this is double the actual rainfall of the temperate regions. If, again, it were spread over both temperate and polar regions this would yield sixty-four inches, which, however, is nearly double the mean rainfall of the temperate and polar regions. If we add to this the amount of moisture derived from the ocean within temperate and polar regions, we should have a far greater rainfall for these latitudes than for the torrid region, and we know, of course, that it is actually far less. This proves the truth of the assertion that by far the greater part of the moisture of the torrid regions falls in those regions as rain. It will hardly do to object that the above may probably be an over-estimate of the amount of rainfall in the torrid zone, for it is not at all likely that any error will ever be found which will affect the general conclusion at which we have arrived.

Dr. Carpenter, in proof of the small rainfall of the torrid zone, adduces the case of the Red Sea, where, although evaporation is excessive, almost no rain falls. But the reason why the vapour raised from the Red Sea does not fall in that region as rain, is no doubt owing to the fact that this sea is only a narrow strip of water in a dry and parched land, the air above which is too greedy of moisture to admit of the vapour being deposited as rain. Over a wide expanse of ocean, however, where the air above is kept to a great extent in a constant state of saturation, the case is totally different.

Land at the Equator tends to Lower the Temperature of the Globe.—The foregoing considerations, as well as many others which might be stated, lead to the conclusion that, in order to raise the mean temperature of the whole earth, water should be placed along the equator, and not land, as is supposed by Sir Charles Lyell and others. For if land is placed at the equator, the possibility of conveying the sun’s heat from the equatorial regions by means of ocean-currents is prevented. The transference of heat could then be effected only by means of the upper currents of the trades; for the heat conveyed by conduction along the solid crust, if any, can have no sensible effect on climate. But these currents, as we have just seen, are ill-adapted for conveying heat.

The surface of the ground at the equator becomes intensely heated by the sun’s rays. This causes it to radiate its heat more rapidly into space than a surface of water heated under the same conditions. Again, the air in contact with the hot ground becomes also more rapidly heated than in contact with water, and consequently the ascending current of air carries off a greater amount of heat. But were the heat thus carried away transferred by means of the upper currents to high latitudes and there employed to warm the earth, then it might to a considerable extent compensate for the absence of ocean-currents, and in this case land at the equator might be nearly as well adapted as water for raising the temperature of the whole earth. But such is not the case; for the heat carried up by the ascending current at the equator is not employed in warming the earth, but is thrown off into the cold stellar space above. This ascending current, instead of being employed in warming the globe, is in reality one of the most effectual means that the earth has of getting quit of the heat received from the sun, and of thus maintaining a much lower temperature than it would otherwise possess. It is in the equatorial regions that the earth loses as well as gains the greater part of its heat; so that, of all places, here ought to be placed the substance best adapted for preventing the dissipation of the earth’s heat into space, in order to raise the general temperature of the earth. Water, of all substances in nature, seems to possess this quality to the greatest extent; and, besides, it is a fluid, and therefore adapted by means of currents to carry the heat which it receives from the sun to every region of the globe.