Another plum-pudding is to be constructed which shall represent the earth ([Fig. 32]). We must, however, beg the cook to observe the proportions. The width of the earth, or the diameter, to use the proper word, is about four times the diameter of the moon. Hence, as the small plum-pudding was three inches across, the large one must have a diameter of twelve inches. This will be a family pudding of truly satisfactory dimensions; perhaps the cook will be a little surprised to find the alarming quantity of materials that will be required to complete a sphere of plum-pudding a foot in diameter.
These models having been duly made, and boiled, and placed on the table, we are now to propose the following problem:—
“If one schoolboy could eat the small plum-pudding, how many boys would be required to dispose of the large one?”
The hasty person, who does not reflect, will at once dash out the answer, “Four!” He will say, “It is quite plain that, since one of the puddings has four times the diameter of the other, it must be four times as big; and therefore, as one boy is able to eat the small pudding, four boys will be adequate for the large one.” But the hasty person will, as usual, be quite wrong. His argument would be sound if it were merely two pieces of sugar-stick that he was comparing; no doubt there is only four times as much material in a piece twelve inches long as there is in a piece three inches long. But the plum-puddings have breadth and depth, which are in the same proportions as the length, and the consequence is that the large plum-pudding is far more than four times as big as the small one. No four boys, however admirable their capacities, would be equal to the task of consuming it. Nor even if four more boys were called in to help would the dish be cleared. Twenty boys, forty boys, fifty boys would not be enough. It would take sixty-four boys to demolish the magnificent plum-pudding one foot in diameter.
If the cook will try the experiment, she will find that by taking the materials sufficient for sixty-four small plum-puddings all of the same size, and mixing them together, she will, no doubt, make a large plum-pudding, but its diameter will only be four times that of the small puddings.
As a matter of fact, the moon is 2160 miles in diameter, and the earth is 7918 miles. These numbers are so nearly 2000 and 8000 respectively, that for simplicity I have spoken of the earth as having a diameter four times as great as the moon. If we want to be very accurate, we ought to determine the ratio of the two quantities from the figures just given. Our illustration of the plum-puddings must, therefore, be a little modified. The earth is not quite so much as sixty-four times as big as the moon; but this figure is sufficiently accurate for our present purpose.
Another interesting question may be proposed, namely: How much land is there on the moon? We might state the answer in acres or in square miles; but it will, perhaps, be more instructive to make a comparison between the moon and the earth.
Here also I shall use an illustration; and we shall again consider two globes which are respectively three inches and twelve inches in diameter. The globes I use this time are hollow balls of india-rubber. These will represent the earth and the moon with sufficient accuracy, and the relative surfaces of these two globes is what I want to find. There are different ways in which the comparison might be made. I might, for instance, paint the two globes and see the quantity of paint that each requires. If I did this, I should find that the great globe took just sixteen times as much paint as the small one. We can adopt a simpler plan. The india-rubber in one of these balls has the same thickness as in the other, as they are each hollow, so that the quantity which is required for each ball may be taken to represent its surface. By simply weighing the two balls, I perceive that the large one is sixteen times as heavy as the small one. You notice here the difference between the comparative weights of two hollow balls and two solid ones of the same material. Had these globes been of solid india-rubber, the large one would have weighed sixty-four times as much as the small one, just as in the case of the plum-puddings; but being hollow, the ratio of their weights is only the square of the ratio of their diameters—that is to say, four times four, or sixteen.
We are thus taught that if the moon were exactly one-fourth of the diameter of the earth, its surface would be one-sixteenth part of that of the earth. It would, no doubt, have made our subject a little easier and simpler if the moon had been created somewhat smaller than it is. As, however, the universe has not been solely constructed for the purpose of these talks about Star-land, we must take things as we find them. This proportion is not four; it is more nearly 3⅔, and the relative surfaces of the two bodies is the square of 11/3, or about 13½. In other words, the entire extent of the surface of our globe is about thirteen and a half times that of the moon.
The face of the full moon, being half the entire extent of the surface, is, therefore, about one-twenty-seventh part of the earth’s surface—continents, oceans, seas, and islands all taken together. The British Empire and the Russian Empire are each of them as large as the face of the full moon.