account for even one hundred millions of years' heat. Gravitation could not supply even one-half that amount. There must be some other and greater source than that of gravitation. There is, however, as is indicated, an obvious source from which far more energy may have been derived than could have been obtained from gravitation.

The method of determining the rate of sub-aërial denudation enables us also to arrive at a rough estimate of the actual mean thickness of the stratified rocks of the globe. It will be seen from Chapter XXII. that the mean thickness is far less than is generally supposed.

The physical cause of the submergence of the land during the glacial epoch, and the influence of change in the obliquity of the ecliptic on climate, are next considered. In Chapter XXVI. I have given the reasons which induce me to believe that coal is an inter-glacial formation.

The next two chapters-the one on the path of the ice in north-western Europe, the other on the north of England ice-sheet-are reprints of papers which appeared a few years ago in the Geological Magazine. Recent observations have confirmed the truth of the views advanced in these two chapters, and they are rapidly 'gaining acceptance among geologists.

I have given, at the conclusion, a statement of the molecular theory of glacier motion-a theory which I have been led to modify considerably on one particular point.

There is one point to which I wish particularly to direct attention-viz., that I have studiously avoided introducing into the theories propounded anything of a hypothetical nature. There is not, so far as I am aware, from beginning to end of this volume, a single hypothetical element: nowhere have I attempted to give a hypothetical explanation. The conclusions are in every case derived either from facts or from what I believe to be admitted principles. In short, I have aimed to prove that the theory of secular changes of climate follows, as a necessary consequence, from the admitted principles of physical science.

CHAPTER II,

OCEAN-CURRENTS IN RELATION TO THE DISTRIBUTION

OF HEAT OVER THE GLOBE.

The absolute Heating-power of Ocean-currents.-Volume of the Gulf-stream.Absolute Amount of Heat conveyed by it.-Greater Portion of Moisture in inter-tropical Regions falls as Rain in those Regions.-Land along the Equator tends to lower the Temperature of the Globe.-Influence of Gulf-stream on Climate of Europe.-Temperature of Space.-Radiation of a Particle.-Professor Dove on Normal Temperature.-Temperature of Equator and Poles in the Absence of Ocean-currents.-Temperature of London, how much due to Ocean-currents.

The absolute Heating-power of Ocean-currents.-There is perhaps no physical agent concerned in the distribution of heat over the surface of the globe the influence of which has been so much underrated as that of ocean-currents. This is, no doubt, owing to the fact that although their surface-temperature, direction, and general influence have obtained considerable attention, yet little or nothing has been done towards determining the absolute amount of heat or of cold conveyed by them or the resulting absolute increase or decrease of temperature.

The modern method of determining the amount of heateffects in absolute measure is, doubtless, destined to cast new light on all questions connected with climate, as it has done, and is still doing, in every department of physics where energy, under the form of heat, is being studied. But this method has hardly as yet been attempted in questions of meteorology; and owing to the complicated nature of the phenomena with which the meteorologist has generally to deal, its application will very often prove practically impossible. Nevertheless, it is particularly suitable to all questions relating to the direct

thermal effects of currents, whatever the nature of these currents may happen to be.

In the application of the method to an ocean-current, the two most important elements required as data are the volume of the stream and its mean temperature. But although we know something of the temperature of most of the great oceancurrents, yet, with the exception of the Gulf-stream, little has been ascertained regarding their volume.

The breadth, depth, and temperature of the Gulf-stream have formed the subject of extensive and accurate observations by the United States Coast Survey. In the memoirs and charts of that survey cross-sections of the stream at various places are given, showing its breadth and depth, and also the temperature of the water from the surface to the bottom. We are thus enabled to determine with some precision the mean temperature of the stream. And knowing its mean velocity at any given section, we have likewise a means of determining the number of cubic feet of water passing through that section in a given time. But although we can obtain with tolerable accuracy the mean temperature, yet observations regarding the velocity of the water at all depths have unfortunately not been made at any particular section. Consequently we have no means of estimating as accurately as we could wish the volume of the current. Nevertheless, since we know the surface-velocity of the water at places where some of the sections were taken, we are enabled to make at least a rough estimate of the volume.

From an examination of the published sections, I came to the conclusion some years ago that the total quantity of water conveyed by the stream is probably equal to that of a stream fifty miles broad and 1,000 feet deep,† flowing at the rate of

* Phil. Mag. for February, 1867, p. 127.

The Gulf-stream at the narrowest place examined by the Coast Survey, and where also its velocity was greatest, was found to be over 30 statute miles broad and 1,950 feet deep. But we must not suppose that this represents all the warm water which is received by the Atlantic from the equator; a great mass flows into the Atlantic without passing through the Straits of Florida.

four miles an hour, and that the mean temperature of the entire mass of moving water is not under 65° at the moment of leaving the Gulf. But to prevent the possibility of any objections being raised on the grounds that I may have over-estimated the volume of the stream, I shall take the velocity to be two miles instead of four miles an hour. We are warranted, I think, in concluding that the stream before it returns from its northern journey is on an average cooled down to at least 40°,* consequently it loses 25° of heat. Each cubic foot of water, therefore, in this case carries from the tropics for distribution upwards of 1,158,000 foot-pounds of heat. According to the above estimate of the size and velocity of the stream, which in Chapter XI. will be shown to be an under-estimate, 2,787,840,000,000 cubic feet of water are conveyed from the Gulf per hour, or 66,908,160,000,000 cubic feet daily. Consequently the total quantity of heat thus transferred per day amounts to 77,479,650,000,000,000,000 foot-pounds.

This estimate of the volume of the stream is considerably less by one-half than that given both by Captain Maury and by Sir John Herschel. Captain Maury considers the Gulf-stream equal to a stream thirty-two miles broad and 1,200 feet deep, flowing at the rate of five knots an hour.† This gives 6,165,700,000,000 cubic feet per hour as the quantity of water conveyed by this stream. Sir John Herschel's estimate is still greater. He considers it equal to a stream thirty miles broad and 2,200 feet deep, flowing at the rate of four miles an hour. This makes the quantity 7,359,900,000,000 cubic feet per hour. Dr. Colding, in his elaborate memoir on the Gulf-stream, estimates the volume at 5,760,000,000,000 cubic feet per hour, while Mr. Laughton's estimate is nearly double that of mine.

It is probable that a large proportion of the water constituting the south eastern branch of the Gulf-stream is never cooled down to 40°; but, on the other hand, the north-eastern branch, which passes into the arctic regions, will be cooled far below 40°, probably below 30°. Hence I cannot be over-estimating the extent to which the water of the Gulf-stream is cooled down in fixing upon 40° as the average minimum temperature.

"Physical Geography of the Sea," § 24, 6th edition.
"Physical Geography," § 54.

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. 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 footpounds 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,† 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

* Trans. of Roy. Soc. of Edin., vol. xxi., p. 57. Phil. Mag., § 4, vol. ix., p. 36. "Smithsonian Contributions to Knowledge," vol. ix.