It is not easy to answer the question which I am sometimes asked, “Is
the moon very big?” I would meet that question by another, “Is a cat a
big animal?” The fact is, there is no such thing as absolute bigness or
smallness. The cat is no doubt a small animal when compared with the
tiger, but I think a mouse would probably tell you that the cat was
quite a big animal--rather too big, indeed, in the mouse’s opinion. And
the tiger himself is small compared with an elephant, while the mouse
is large as compared with a fly.
When we talk of the bigness or the smallness of a body, we must always
consider what we are going to compare it with. It is natural in
speaking of the moon to compare it with our own globe, and then we can
say that the moon is a small body.
The relative sizes of the earth and the moon may be illustrated by
objects of very much smaller dimensions. Both a tennis ball and a
football are no doubt familiar objects to everybody. If the earth be
represented by the football, then the moon would be about as large as
the lawn-tennis ball. But this proportion is not quite accurate, so
I will suggest to you an instructive way of making a better pair of
models of the earth and the moon. In fact, experiments somewhat similar
to those I describe have been actually going on in every kitchen in the
land during this festive season. For have not globes and balls of all
sorts and sizes been made of plum-pudding, and it will only require a
little care on the part of the cook to make a pair of luscious spheres
that shall fairly set forth the sizes of the earth and the moon. There
is first to be a nice little round plum-pudding, three inches in
diameter. It is just a little bigger than a cricket ball. It should,
however, only make its appearance at a bachelor’s table. Were it set
down before a hearty circle on Christmas Day, dire disappointment would
result. One boy of sound constitution could eat it all. Perhaps it
would weigh about three-quarters of a pound. This little globe is to
represent the moon.
[Illustration: FIG. 32.--Relative Sizes of the Earth and Moon.]
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.