the quantity of air now existing above each square mile of the earth's surface. For, the moon's mass being about an eighty-first part of the earth's, the mass of the lunar air must have been about an eighty-first part of the mass of our present atmosphere. But the moon's surface bears a much greater proportion to the earth's, being about a thirteenth. Whence it follows that, on the assumptions we have made, the quantity of air above each square mile of the moon's surface would be only about one sixth part of the quantity above each square mile of the earth's surface. And this air being drawn downwards only by lunar gravity, which has but about a sixth part of the energy of our terrestrial gravity, would be less compressed in the same degree on this account. One sixth of the quantity of air being thus compressed with one sixth the amount of force, it is clear that the density of the lunar air in that stage of the moon's existence would only be about one thirty-sixth of the density of our air. Similar reasoning applies to the water, except as to the compression under lunar gravity. The average quantity of water to each square mile of the moon's surface would be but about one-sixth part of the quantity there is for each square mile of the earth's surface. The relative extent of the lunar oceans would not be less in precisely the same degree, however. For, speaking generally, the bed of the ocean slopes downwards from the shore-line in such a way that more than half, or a third, or a fourth, or so on, would have to be removed to diminish the surface by a half, a third, or a fourth, or so on, respectively. We may illustrate our meaning here by considering the relation between the quantity of water in a wineglass (supposed to be cone-shaped) and the surface of the water. Suppose the wineglass full at first, and the circular surface of the water to be three square inches, then if five-sixths of the water are thrown out, so that only one-sixth remains, the surface will not be reduced to one-sixth its former extent — that is, to one-half of a square inch — but will be about nine-tenths of a square inch. It is clear that in the case of an ocean having a bottom very steeply sloping near the shore-line, and nearly level elsewhere, a large proportion of the water might be drawn off, and the ocean surface still remain almost as great as before. We may assume as a mean and sufficiently probable hypothesis that the lunar oceans had a relative surface equal to between one-half and one-third of the present relative surface of the terrestrial oceans. That is to say, our oceans covering about seventy-two hundredths of the entire surface of the earth, we may assume that the lunar oceans covered between thirty-six and twenty-four hundredths of the entire surface of the moon. It will he seen presently that some importance attaches to this question of the probable surface of the seas on the moon, a portion of the evidence for the theory we are examining depending on this relation.
Let us next consider in what way the withdrawal of the lunar oceans into the moon's interior probably took place. On this point, Frankland's presentation of the theory is undoubtedly defective. In fact, it has been the weakness of the theory in this respect, as presented in England, which has in all probability prevented it from receiving the attention here which it fairly deserves. "The cooling of the moon's mass must," said Frankland, "in accordance with all analogy, have been attended with contraction, which can scarcely be conceived as occurring without the development of a cavernous structure in the interior. Much of the cavernous structure would doubtless communicate, by means of fissures, with the surface, and thus there would be provided an internal receptacle for the ocean, from the depths of which even the burning sun of the long lunar day would be totally unable to dislodge more than traces of its vapor." And he proceeds thus to analyze the amount of space which would be rendered available for the retreat of the lunar oceans. "Assuming the solid mass of the moon to contract on cooling at the same rate as granite, its refrigeration through only 180° of the Fahrenheit thermometer (the difference between the boiling and the freezing points) would create cellular space equal to nearly fourteen and a half millions of cubic miles, which would be more than sufficient to engulf the whole of the lunar oceans, supposing them to bear the same proportion to the mass of the moon as our own oceans bear to that of the earth."
But in reality no such cavernous structure could possibly be developed in the interior of a planet like the moon. Frankland's mistake, here is similar to that made by Brewster and others, who have suggested that possibly the small mean density of the outer planets might be due to the existence of great void spaces in the interior of those bodies. So soon, however, as we make the roughest calculation of the pressures existing in the interior of
