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. [Illustration: Fig. 10.]