[Footnote 10: Keith Johnston's 'Africa' in Stanford's Compendium.]
[Footnote 11: Chambers's Encyclopaedia, Art. 'Deserts.']
Now, as it is admitted that our dense atmosphere, however dry and clear, absorbs and reflects some considerable portion of the solar heat, we shall certainly underestimate the radiation from the moon's surface during its long night if we take as the basis of our calculation a lowering of temperature amounting to 100° F. during twelve hours, as not unfrequently occurs with us. Using these data—with Stefan's law of decrease of radiation as the 4th power of the temperature—a mathematical friend finds that the temperature of the moon's surface would be reduced during the lunar night to nearly 200° F. absolute (equal to-258° F.).
More Rapid Loss of Heat by the Moon.
Although such a calculation as the above may afford us a good approximation to the rate of loss of heat by Mars with its very scanty atmosphere, we have now good evidence that in the case of the moon the loss is much more rapid. Two independent workers have investigated this subject with very accordant results—Dr. Boeddicker, with Lord Rosse's 3-foot reflector and a Thermopile to measure the heat, and Mr. Frank Very, with a glass reflector of 12 inches diameter and the Bolometer invented by Mr. Langley. The very striking and unexpected fact in which these observers agree is the sudden disappearance of much of the stored-up heat during the comparatively short duration of a total eclipse of the moon—less than two hours of complete darkness, and about twice that period of partial obscuration.
Dr. Boeddicker was unable to detect any appreciable heat at the period of greatest obscuration; but, owing to the extreme sensitiveness of the Bolometer, Mr. Very ascertained that those parts of the surface which had been longest in the shadow still emitted heat "to the amount of one per cent. of the heat to be expected from the full moon." This however is the amount of radiation measured by the Bolometer, and to get the temperature of the radiating surface we must apply Stefan's law of the 4th power. Hence the temperature of the moon's dark surface will be the [fourth root of (1 over 100)] = 1 over 3.2 [A] of the highest temperature (which we may take at the freezing-point, 491° F. abs.), or 154° F. abs., just below the liquefaction point of air. This is about 50° lower than the amount found by calculation from our most rapid radiation; and as this amount is produced in a few hours, it is not too much to expect that, when continued for more than two weeks (the lunar night), it might reach a temperature sufficient to liquefy hydrogen (60° F. abs.), or perhaps even below it.
[Note A: LaTex markup $\root 4 \of {1 \over 100} = {1 \over 3.2}$ ]
Theory of the Moon's Origin.
This extremely rapid loss of heat by radiation, at first sight so improbable as to be almost incredible, may perhaps be to some extent explained by the physical constitution of the moon's surface, which, from a theoretical point of view, does not appear to have received the attention it deserves. It is clear that our satellite has been long subjected to volcanic eruptions over its whole visible face, and these have evidently been of an explosive nature, so as to build up the very lofty cones and craters, as well as thousands of smaller ones, which, owing to the absence of any degrading or denuding agencies, have remained piled up as they were first formed.
This highly volcanic structure can, I think, be well explained by an origin such as that attributed to it by Sir George Darwin, and which has been so well described by Sir Robert Ball in his small volume, Time and Tide. These astronomers adduce strong evidence that the earth once rotated so rapidly that the equatorial protuberance was almost at the point of separation from the planet as a ring. Before this occurred, however, the tension was so great that one large portion of the protuberance where it was weakest broke away, and began to move around the earth at some considerable distance from it. As about 1/50 of the bulk of the earth thus escaped, it must have consisted of a considerable portion of the solid crust and a much larger quantity of the liquid or semi-liquid interior, together with a proportionate amount of the gases which we know formed, and still form, an important part of the earth's substance.