Instead of studying how these rays spread out in every way all around M, let us only consider those which, passing out from M, fall on the square A B C D. A B C D casts a shadow, and this shadow extends, and is found to be bigger the further off from M it is measured. Suppose, at the distance from M, M E, we put a square in the path of the shadow so as just to receive the shadow on it exactly. Let E F G H be this square. As is shown by the dotted lines, this square will be four times as large as the square A B C D. So when the distance is doubled, the shadow becomes four times as big. Now those rays of light which fall on A B C D would, if they were not interrupted by it, spread out so as to exactly cover E F G H. Thus the same amount of light which falls on the small square A B C D would, if it were taken away, fall on the large square E F G H. Now since the large square is four times the size of the small square, and the same amount of rays fall on it—for it only receives those which would fall on the small square—there must be at any part of it an illumination one-quarter as strong as there would be at any point on the small square. Thus the small square, if placed in its position, would seem four times as bright as the large square. Thus, when the distance from the origin of light is doubled, the amount of light received by a surface of given area becomes one-fourth of what it was at the less distance. This is what is meant by varying inversely as the square of the distance. When the distance is doubled the intensity of the light is not simply less, but is halved and halved, and becomes one-quarter of its previous intensity. But in the case of a particle resting on a thin sheet of metal, and shaking the metal—as, for instance, a metal plate can be made to shake by a violin bow—then this law would not hold. Take the second figure. Let P be the particle, and let the influence proceeding from it fall on the rod A B lying on the plane, and let us suppose the rod to stop the vibrations from going beyond it, to receive them and to turn them back just as a body does the light. Then the “shadow” of A B would spread out away from P; and if another rod E F were put in at the distance P E, which is double of P A, then, to exactly fit the shadow, it would have to be double the length of A B; and the vibrations which fell on A B would exactly fall on E F. Now since E F is twice as long as A B, the vibrations which fall on any part of it will be one-half as intense as the vibrations which fall on a portion of matter of the same size lying where A B lies. Thus in a plane the influence or force sent out by any particle would diminish as the distance. It would not “vary inversely as the square of the distance,” but would “vary inversely as the distance.” A Picture of Our Universe. CHAPTER I.