CHAPTER IV.
THE FORM, MAGNITUDE, WEIGHT, AND DENSITY OF THE LUNAR GLOBE.
We have not hitherto had occasion to refer to what we may term the physical elements of the moon: by which we mean the various data concerning form, size, weight, density, &c. of that body, derived from observation and calculation. To this purpose, therefore, we will now devote a few pages, confining ourselves to such matters as specially bear upon the requirements of our subject, omitting such as are irrelevant to our purpose, and touching but lightly upon such as are commonly known, or are explained in ordinary elementary treatises on astronomy.
First, then, as regards the form of the moon. The form of the lunar disc, when fully illuminated, we perceive to be a perfect circle; that is to say, the measured diameters in all directions are equal; and we are therefore led to infer that the real form of the moon is that of a perfect sphere. We know that the earth and the rest of the planets of our system are spheroidal, or more or less flattened at the poles, and we also know that this flattening is a consequence of axial rotation; the extent of the flattening, or the oblateness of the spheroid, depending upon the speed of that rotation. But in the case of the moon the axial rotation is so slow that the flattening produced thereby, although it must exist, is so slight as to be imperceptible to our observation. We might therefore conclude that the moon is a perfectly spherical body, did not theory step in to show us that there is another cause by which its form is disturbed. Assuming the moon to have been once in a fluid state, it is demonstrable that the attraction of the earth would accumulate a mass of matter, like a tidal elevation, in the direction of a line joining the centres of the two bodies: and as a consequence, the real shape of the moon must be an ellipsoid, or somewhat egg-shaped body, the major axis of which is directed towards the earth. That some such phenomenon has obtained is evident from the coincidence of the times of orbital revolution and axial rotation of the lunar sphere. “It would be against all probability,” says Laplace, “to suppose that these two motions had been at their origin perfectly equal;” but it is sufficient that their primitive difference was but small, in which case the constant attraction by the earth of the protuberant part of the moon would establish the equality which at present exists.
It is, however, sufficient for all purposes with which we are concerned to regard the moon as a sphere, and the next point to be considered is its size. To determine this, two data are necessary—its apparent or angular diameter, and its distance from the earth. The first of these is obtained by measuring the angle comprised between two lines directed from the eye to two opposite “limbs” or edges of the moon. If, for instance, we were to take a pair of compasses and, placing the joint at the eye, open out the legs till the two points appear to touch two opposite edges of the moon, the two legs would be inclined at an angle which would represent the diameter of the moon, and this angle we could measure by applying a divided arc or protractor to the compasses. In practice this measurement is made by means of telescopes attached to accurately divided circles; the difference between the readings of the circle when the telescope is directed to opposite limbs of the moon giving its angular diameter at the time of the observation. But from the fact that the orbit of the moon is an ellipse, it is evident that she is at some times much nearer to us than at others, and, as a consequence, her apparent magnitude is variable: there is also a slight variation depending upon the altitude of the moon at the time of the measure; the mean diameter, however, or the diameter at mean distance from the centre of the earth has, from long course of observation, been found to be 31′ 9″.
To convert this apparent angular diameter into real linear measurement, it is necessary to know either the distance of the moon from the earth, or in astronomical language as leading to a knowledge of that distance, what is the amount of the moon’s parallax. Parallax, generally, is an apparent change of position of an object arising from change of the point of view. The parallax of a heavenly body is the angle which the earth would subtend if it were seen from that body. Supposing an observer on the moon could measure the earth’s angular diameter, just as we measure that of the moon, his measurement would represent what is called the parallax of the moon. But we cannot go to the moon to make such a measurement; nevertheless there is a simple method, explained in most treatises on astronomy, which consists in observing the moon from stations on the earth widely separated, and by which we can obtain a precisely similar result. Without detailing the process, it is sufficient for us to know that the angle which would be subtended by the earth if seen from the moon, or the moon’s parallax, is according to the latest determination, equal to 1° 54′ 5″. This value, however, varies considerably with the variations of distance due to the elliptic orbit of the moon: the number we have given represents the mean parallax, or the parallax at mean distance.
But we have to turn these angular measurements into miles. To effect this we have only to work a simple rule of three sum. It will easily be understood that, as the angular diameter of the earth seen from the moon is to the angular diameter of the moon seen from the earth, so is the diameter of the earth in miles to the diameter of the moon in miles. The diameter of the earth we know to be 7912 miles: putting this therefore in its proper place in the proportion sum, and duly working it out by the schoolboy’s rule, we get:—
1°. 54′. 5″ : 31′. 9″ :: 7912 miles. : 2160 miles.
And 2160 miles is therefore the diameter of the lunar globe.
Knowing the diameter, we can easily obtain the other elements of magnitude. According to the well-known relation of the diameter of a sphere to its area, we find the area of the moon to be 14,657,000 square miles: or half that number, 7,328,500 miles, as the area of the hemisphere at any one time presented to our view. And similarly, from the relation of the solidity of a sphere to its diameter, we find the solid contents of the moon to be 5276 millions of cubic miles of matter.
Comparing these data with corresponding dimensions of the earth, we find that the diameter of the moon is 1/3·665; the area 1/13·4245; and the volume 1/49·1865, of the respective elements of the earth. Those who prefer a graphical to a numerical comparison, may judge of the sizes of the two bodies by the accompanying illustration ([Fig. 10]). To gain an idea of their distance from each other it is necessary to suppose the two discs in the diagram to be 30 inches apart; the real distance of the moon from the earth being about 238,790 miles at its mean position.