As to the absence of air and water from the moon, some have supposed that they once existed, but, in the course of ages, have disappeared, either by absorption, partly mechanical and partly chemical, into the interior rocks, or by escaping into space on account of the slight force of gravity on the moon, which appears to be insufficient to enable it to retain, permanently, such volatile gases as oxygen, hydrogen, and nitrogen. This leads us to consider the force of the moon's attraction at its surface. We have seen that spherical bodies attract as if their whole mass were collected at their centres. We also know that the force of attraction varies directly as the mass of the attracting body and inversely as the square of the distance from its centre. Now the mass of the moon is one-eightieth that of the earth, so that, upon bodies situated at an equal distance from the centres of both, the moon's attraction would be only one-eightieth of the earth's. But the diameter of the moon is not very much more than one quarter that of the earth, and for the sake of round numbers let us call it one quarter. It follows that an object on the surface of the moon is four times nearer the centre of attraction than is an object on the surface of the earth, and since the force varies inversely as the square of the distance the moon's attraction upon bodies on its surface is relatively sixteen times as great as the earth's. But the total force of the earth's attraction is eighty times greater than the moon's. In order, then, to find the real relative attraction of the moon at its surface we must divide 80 by 16, the quotient, 5, showing the ratio of the earth's force of attraction at its surface to that of the moon at _its_ surface. In other words, this calculation shows that the moon draws bodies on its surface with only one-fifth the force with which the same bodies would be drawn on the earth's surface. The weight of bodies of equal mass would, therefore, be only one-fifth as great on the moon as on the earth. But the real difference is greater than this, for we have used round numbers, which exaggerated the size of the earth as compared with that of the moon. If we employ the fractional numbers which show the actual ratio of the moon's radius (half-diameter) to that of the earth, we shall find that the weight of the same body would be only about one-sixth as great on the moon as on the earth. It has been thought that this relative lack of weight on the moon may account for the gigantic proportions assumed by its craters, since the same elective force would throw volcanic matter to a much greater height and distance there than on our planet.