Association at Cambridge in 1904, says: "The surface of the earth receives, we know, an amount of heat from the inside almost infinitesimal compared with that which it receives from the sun, and on the sun, therefore, we depend for our temperature."]

In order to understand the immense significance of this conclusion we must know what is meant by the whole heat or warmth; as unless we know this we cannot define what half or any other proportion of sun-heat really means. Now I feel pretty sure that nine out of ten of the average educated public would answer the following question incorrectly: The mean temperature of the southern half of England is about 48° F. Supposing the earth received only half the sun-heat it now receives, what would then be the probable mean temperature of the South of England? The majority would, I think, answer at once—About 24° F. Nearly as many would perhaps say—48° F. is 16° above the freezing point; therefore half the heat received would bring us down to 8° above the freezing point, or 40° F. Very few, I think, would realise that our share of half the amount of sun-heat received by the earth would probably result in reducing our mean temperature to about 100° F. below the freezing point, and perhaps even lower. This is about the very lowest temperature yet experienced on the earth's surface. To understand how such results are obtained a few words must be said about the absolute zero of temperature.

The Zero of Temperature.

Heat is now believed to be entirely due to ether-vibration, which produces a correspondingly rapid vibration of the molecules of matter, causing it to expand and producing all the phenomena we term 'heat.' We can conceive this vibration to increase indefinitely, and thus there would appear to be no necessary limit to the amount of heat possible, but we cannot conceive it to decrease indefinitely at the same uniform rate, as it must soon inevitably come to nothing. Now it has been found by experiment that gases under uniform pressure expand 1/273 of their volume for each degree Centigrade of increased temperature, so that in passing from 0° C. to 273° C. they are doubled in volume. They also decrease in volume at the same rate for each degree below 0° C. (the freezing point of water). Hence if this goes on to-273° C. a gas will have no volume, or it will undergo some change of nature. Hence this is called the zero of temperature, or the temperature to which any matter falls which receives no heat from any other matter. It is also sometimes called the temperature of space, or of the ether in a state of rest, if that is possible. All the gases have now been proved to become, first liquid and then (most of them) solid, at temperatures considerably above this zero.

The only way to compare the proportional temperatures of bodies, whether on the earth or in space, is therefore by means of a scale beginning at this natural zero, instead of those scales founded on the artificial zero of the freezing point of water, or, as in Fahrenheit's, 32° below it. Only by using the natural zero and measuring continuously from it can we estimate temperatures in relative proportion to the amount of heat received. This is termed the absolute zero, and so that we start reckoning from that point it does not matter whether the scale adopted is the Centigrade or that of Fahrenheit.

The Complex Problem of Planetary Temperatures.

Now if, as is the case with Mars, a planet receives only half the amount of solar heat that we receive, owing to its greater distance from the sun, and if the mean temperature of our earth is 60° F., this is equal to 551° F. on the absolute scale. It would therefore appear very simple to halve this amount and obtain 275.5° F. as the mean temperature of that planet. But this result is erroneous, because the actual amount of sun heat intercepted by a planet is only one condition out of many that determine its resulting temperature. Radiation, that is loss of heat, is going on concurrently with gain, and the rate of loss varies with the temperature according to a law recently discovered, the loss being much greater at high temperatures in proportion to the 4th power of the absolute temperature. Then, again, the whole heat intercepted by a planet does not reach its surface unless it has no atmosphere. When it has one, much is reflected or absorbed according to complex laws dependent on the density and composition of the atmosphere. Then, again, the heat that reaches the actual surface is partly reflected and partly absorbed, according to the nature of that surface—land or water, desert or forest or snow-clad—that part which is absorbed being the chief agent in raising the temperature of the surface and of the air in contact with it. Very important too is the loss of heat by radiation from these various heated surfaces at different rates; while the atmosphere itself sends back to the surface an ever varying portion of both this radiant and reflected heat according to distinct laws. Further difficulties arise from the fact that much of the sun's heat consists of dark or invisible rays, and it cannot therefore be measured by the quantity of light only.

From this rough statement it will be seen that the problem is an exceedingly complex one, not to be decided off-hand, or by any simple method. It has in fact been usually considered as (strictly speaking) insoluble, and only to be estimated by a more or less rough approximation, or by the method of general analogy from certain known facts. It will be seen, from what has been said in previous chapters, that Mr. Lowell, in his book, has used the latter method, and, by taking the presence of water and water-vapour in Mars as proved by the behaviour of the snow-caps and the bluish colour that results from their melting, has deduced a temperature above the freezing point of water, as prevalent in the equatorial regions permanently, and in the temperate and arctic zones during a portion of each year.

Mr. Lowell's Mathematical Investigation of the Problem.

But as this result has been held to be both improbable in itself and founded on no valid evidence, he has now, in the London, Edinburgh, and Dublin Philosophical Magazine of July 1907, published an elaborate paper of 15 pages, entitled A General Method for Evaluating the Surface-Temperatures of the Planets; with special reference to the Temperature of Mars, by Professor Percival Lowell; and in this paper, by what purports to be strict mathematical reasoning based on the most recent discoveries as to the laws of heat, as well as on measurements or estimates of the various elements and constants used in the calculations, he arrives at a conclusion strikingly accordant with that put forward in the recently published volume. Having myself neither mathematical nor physical knowledge sufficient to enable me to criticise this elaborate paper, except on a few points, I will here limit myself to giving a short account of it, so as to explain its method of procedure; after which I may add a few notes on what seem to me doubtful points; while I also hope to be able to give the opinions of some more competent critics than myself.

Mr. Lowell's Mode of Estimating the Surface-temperature of Mars.

The author first states, that Professor Young, in his General Astronomy (1898), makes the mean temperature of Mars 223.6° absolute, by using Newton's law of heat being radiated in proportion to temperature, and 363° abs. (=-96° F.) by Dulong and Petit's law; but adds, that a closer determination has been made by Professor Moulton, using Stefan's law, that radiation is as the /4th power of the temperature, whence results a mean temperature of-31° F. These estimates assume identity of atmospheric conditions of Mars and the Earth.

But as none of these estimates take account of the many complex