For this purpose it is assumed as a principle, that the same quantity of light, diverging in all directions from a luminous body, remains undiminished in all distances from the centre of divergency. Thus we must suppose, that the quantity of light falling on every body, is the same as would have fallen on the places occupied by the shadow; and if there were any doubt of the truth of the supposition, it might be confirmed by some simple experiment. Therefore, it follows, that, since the shadow of a square inch of any surface occupies at twice the distance of the surface from the luminous point the space of four square inches, the intensity of the light diminishes as the square of the distance increases. If, consequently, we remove two sources of light to such distances from an object that they may illuminate it in equal degrees, we may conclude that their original intensities are inversely as the squares of the distances. Hence, if two lights of unequal illuminating powers shine upon the same surface at equal obliquities, and an opake body be interposed between them and the illuminated surface, the two shadows produced, must differ in blackness or intensity in the same degree. For the shadow formed by intercepting the greater light, will be illuminated by the smaller light only, and reversely the other shadow will be illuminated by the greater light: that is to say, the stronger light will be attended with the deeper shadow. Now it is easy, by removing the stronger light to a greater distance, to render the shadow which it produces at the common surface equal to that afforded by the less. Experiments of this kind may be conveniently made by fastening a sheet of white paper against the wall of a room; the two lights, of whatever nature they are, intended to be compared, must then be placed so that the ray of light from each shall fall with nearly the same angle of incidence upon the middle of the paper. In this situation, if a book or other object be held to intercept part of the light which would have fallen on the paper, the two shadows may be made to appear as in this figure; [Illustration]