The Library Magazine of Select Foreign Literature / All volumes

by Various

Now, before applying this result to the case of the moon, we must take into account two considerations:—First, the probability that when the moon was formed she was not nearly so hot as the earth when it first took planetary shape; and secondly, the different densities of the earth and moon.

The original heat of every member of the solar system, including the sun, depended on the gravitating energy of its own mass. The greater that energy, the greater the heat generated either by the process of steady contraction imagined in Laplace's theory, or by the process of meteoric indraught imagined in the aggregation theory. To show how very different are the heat-generating powers of two very unequal masses, consider what would happen if the earth drew down to its own surface a meteoric mass which had approached the earth under her own attraction only. (The case is of course purely imaginary, because no meteor can approach the earth which has not been subjected to the far greater attractive energy of the sun, and does not possess a velocity far greater than any which the earth herself could impart). In this case such a mass would strike the earth with a velocity of about seven miles per second, and the heat generated would be that due to this velocity only. Now, when a meteor strikes the sun full tilt after a journey from the star depths under his attraction, it reaches his surface with a velocity of nearly three hundred and sixty miles per second. The heat generated is nearly fifty times greater than in the imagined case of the earth. The moon being very much less than the earth, the velocity she can impart to meteoric bodies is still less. It amounts, in fact, to only about a mile per second. The condensing energy of the moon in her vaporous era was in like manner far less than that of the earth, and consequently far less heat was then generated. Thus, although we might well believe on a priori grounds, even if not assured by actual study of the lunar features, that the moon when first formed as a planet had a surface far hotter than molten iron, we must yet believe that, when first formed, the moon had a temperature very much below that of our earth at the corresponding stage of her existence.

On this account, then, we must consider that the moon started in planetary existence in a condition as to heat which our earth did not attain till many millions, probably hundreds of millions of years after the epoch of her first formation as a planet.

As regards the moon's substance, we have no means of forming a satisfactory opinion. But we shall be safe in regarding quantity of matter in the moon as a safer basis of calculation than volume, in comparing the duration of her various stages of development with those of our own earth. When, in the August number of this Magazine, I adopted a relation derived from the latter and less correct method, it was because the more correct method gave the result most favourable to the argument I was then considering. The same is indeed the case now. Yet it will be better to adopt the more exact method, because the consideration relates no longer to a mere side issue, but belongs to the very essence of my reasoning.

The moon has a mass equal to about one eighty-first part of the earth's. Her diameter being less than the earth's, about as two to seven, the duration of each stage of her cooling would be in this degree less than the corresponding duration for the earth, if her density were the same as the earth's, in which case her mass would be only one forty-ninth part of the earth's. But her mass being so much less, we must assume that her amount of heat at any given stage of cooling was less in similar degree than it would have been had her density been the same as the earth's. We may, in fact, assume that the moon's total supply of heat would be only one eighty-first of the earth's if the two bodies were at the same temperature throughout.[63] But the surface of the moon is between one-thirteenth and one-fourteenth of the earth's. Since, then, the earth at any given stage of cooling parted with her heat between thirteen and fourteen times as fast as the moon, but had about eighty-one times as much heat to part with (for that stage), it follows that she would take about six times as long (six times thirteen and a-half is equal to eighty-one) to cool through that particular stage as the moon would.

If we take this relation as the basis of our estimate of the moon's age, we shall find that, even if the moon's existence as a planet began simultaneously with the earth's instead of many millions of years earlier, even if the moon was then as hot as the earth instead of being so much cooler that many millions of years would be required for the earth to cool to the same temperature—making, I say, these assumptions, which probably correspond to the omission of hundreds of millions of years in our estimate of the moon's age, we shall still find the moon to be hundreds of millions of years older than the earth.

Nay, we may even take a position still less favourable to my argument. Let us overlook the long ages during which the two orbs were in the vaporous state, and suppose the earth and moon to be simultaneously in that stage of planetary existence when the surface has a temperature of two thousand degrees Centigrade.

From Bischoff's experiments on the cooling of rocks, it appears to follow that some three hundred and twenty millions of years must have elapsed between the time when the earth's surface was at this temperature and the time when the surface temperature was reduced to two hundred degrees Centigrade, or one hundred and eighty degrees Fahrenheit above the boiling point. The earth was for that enormous period a mass (in the main) of molten rock. In the moon's case this period lasted only one-sixth of three hundred and twenty million years, or about fifty-three million years, leaving two hundred and sixty-seven million years' interval between the time when the moon's surface had cooled down to two hundred degrees Centigrade and the later epoch when the earth's surface had attained that temperature.

I would not, however, insist on these numerical details. It has always seemed to me unsafe to base calculations respecting suns and planets on experiments conducted in the laboratory. The circumstances under which the heavenly bodies exist, regarding these bodies as wholes, are utterly unlike any which can be produced in the laboratory, no matter on what scale the experimenter may carry on his researches. I have often been amused to see even mathematicians of repute employing a formula based on terrestrial experiments, physical, optical, and otherwise, as though the formula were an eternal omnipresent reality, without noting that, if similarly applied to obtain other determinations, the most stupendously absurd results would be deduced. It is as though, having found that a child grows three inches in the fifth year of his age, one should infer not only that that person but every other person in every age and in every planet, nay, in the whole universe, would be thirty inches taller at the age of fifteen than at the age of five, without noticing that the same method of computation would show everyone to be more than fifteen feet taller at the age of sixty-five. It may well be that, instead of three hundred and twenty millions of years, the era considered by Bischoff lasted less than a hundred millions of years. Or quite as probably it may have lasted five or six hundred millions of years. And again, instead of the corresponding era of the moon's past history having lasted one sixth of the time required to produce the same change in the earth's condition, it may have lasted a quarter, or a third, or even half that time, though quite as probably it may have lasted much less than a sixth. But in any case we cannot reasonably doubt that the moon reached the stage of cooling through which the earth is now passing many millions of years ago. We shall not probably err very greatly in taking the interval as at least two hundred millions of years.

But I could point out that in reality it is a matter of small importance, so far as my present argument is concerned, whether we adopt Bischoff's period or a period differing greatly from it. For if instead of about three hundred millions the earth required only thirty millions of years to cool from a surface temperature of two thousand degrees Centigrade to a temperature of two hundred degrees, we must assume that the rate of cooling is ten times greater than Bischoff supposed. And we must of course extend the same assumption to the moon. Now, since the sole question before us is to what degree the moon has cooled, it matters nothing whether we suppose the moon has been cooling very slowly during many millions of years since she was in the same condition as the earth at present, or that the moon has been cooling ten times as quickly during a tenth part of the time, or a hundred times as quickly during one-hundredth part of the time.