The intensity of light decreases as the observer recedes from the luminous body, in proportion to the square of his distance. Suppose a beam of light to proceed from a radiant at F, and we shall have the rays which, of course, move in straight lines, gradually receding from each other, as _b_, _b′_, _b″_, _b‴_, and _c_, _c′_, _c″_, _c‴_, so that the section of the beam will increase with the distances F _b_, and F _c_; and the same number of rays, being thus spread over spaces continually increasing, will illuminate the surfaces with a less intensity. This decrease of intensity will, therefore, be in the inverse ratio of the extent of the transverse parallel sections of the luminous cones at _b_ and _c_, which, we know, increase as the square of their distances from the apex of the cone at F. Hence we conclude, that the _intensity of any section of a divergent beam of light decreases as the square of its distance from the radiant_. This law furnishes us with a simple measure of the comparative intensity of lights. If we suppose two lights so placed that they may separately illuminate adjacent portions of a vertical screen of paper, we may, by repeatedly comparing the luminousness of those surfaces, and moving one of the lights farther from, or nearer to the screen, at length cause the separate portions of the paper to become equally luminous. This arrangement, however, has many practical difficulties, which I shall not wait to specify; but shall at once indicate a more simple and equally correct mode of obtaining the same result, by means of the shadows cast by the lights from an opaque rod, in a vertical position at O (fig. 94), placed between them, and a screen covered with white paper on which the shadows fall. It is obvious that the light at F would cause the object O to cast a shadow at SS, while the light at F′ would cast a shadow at S′S′. But while the shadow at S would still receive light from F′, S′ would receive light from F, so that those two shadows are, in fact, the only portions of the screen which are each illuminated only by one of the lights, while every other portion of its surface receives light from both the radiants at F and F′. If we suppose F to be the weaker light, we can bring it nearer the screen, until the shadow S′S′, shall become similar in appearance to the shadow SS; and we shall have the ratio of the intensity of the light at F to that of the light at F′, as (FS′)² is to (F′S)², which distances must be measured with the greatest exactness. Such is the mode commonly used in estimating the comparative intensities of two lights; but there are various precautions which are needful in order to prevent errors in comparing the deepness of the shadows, and to insure the greatest attainable accuracy in the estimate of the power of the lights, which I shall endeavour briefly to describe. [Illustration: Fig. 94.] ~More accurate comparison of the intensity of Lights.~