Fig. 96.
“If we now place ([fig. 96]) two lights in front of the screen AB, at such distances that the two shadows a′ and b′ should have equal intensities, it is evident that if the eye be placed at P, the shadow b′ must appear more intense than the shadow a′, and that the reverse will take place if the eye be at Q. But the difference which is then observed, arises not only from the difference in the brightness of the parts surrounding the shadows, but also from a difference in the intensity of the shadows themselves; for the shadow b′ is illuminated by b, and radiates much more towards Q than towards P; and, on the contrary, the shadow a′, which is illuminated by a, radiates much more towards P than towards Q. We perceive also why the differences of the tints increase with the separation of the two shadows, and why they become very small when the shadows touch each other; it is because, in proportion as the shadows are farther apart, each of them is illuminated more obliquely, and a greater quantity of light is radiated (by reflection) in the regular direction. When they touch each other, on the contrary, they are illuminated almost perpendicularly, and consequently the shadows radiate light almost equally on either side.
“Those anomalies of a like kind which are observed when the shadows are viewed through a translucent body, such as paper or linen, may be referred to a similar cause. We know, in fact, that, in looking through a translucent medium, we always, more or less, distinctly perceive the luminous body behind it, and, also, that there is a very large proportion of the rays which traverse the body, which stray but a little from the direction which they would follow if the substance were absolutely transparent. Consequently, the space which surrounds the shadow is more luminous in proportion as we come nearer to the direction of the shadow; and as the absolute intensity of the shadows diminishes as we come nearer to the direction of the rays which light them, those two effects concur to increase the intensity of that shadow to which the eye is nearer.
“As the dispersion by reflection is much more complete than by refraction, the variations of which we have just spoken are much greater with a transparent screen, through which the shadows are viewed, than with an opaque screen (from which they are reflected).
“This, then, is the mode of observing which has appeared to me the best, and by means of which we may obtain very great precision in measuring the intensity of two lights. I view, first, the two shadows in such a manner that both of them may be seen in succession from either side of the body which produces them, and at equal distances. For this purpose I use a good opera-glass. I alter the distance of the flames until in those two positions I perceive the differences (of the intensity in the shadows) to be in opposite directions. The distances of the lamps may then be considered as very nearly in the proper proportion for producing equal shadows, and to make them exactly so, the differences, which are observed on either side (of the centre line between them), should be equal; and, of course, the two shadows themselves, seen at one moment from either side of the opaque body, should be perfectly equal also.[85] These three observations, which mutually serve to verify or correct each other, will lead, with a little practice, to very great precision in the result. We may, also, by using a narrow screen, bring the shadows sufficiently near to touch each other; the variations of the tints then become very small by any change of our position, and we may, in this case, rest content with observing them from one point. To get rid of large penumbrae which are always an obstacle in forming a right estimate of the tints of the shadows, I place the opaque body very near the screen.
[85] I prefer to view the exterior portions of both shadows from the central line itself, in which case the opaque rod stands between them, because, in this manner, I obtain a more correct comparison by the direct contrast of the surfaces than by successive views of them, however quickly taken.
Fig. 97.
“When we wish to make a great many observations, it is very convenient to mark divisions on the table (which carries the lights), in order to read off, by means of them, the distance of the lamps from the shadows which they illuminate. By this means, each observation need not occupy more than two minutes. I generally use a table CC DD ([fig. 97]), about two mètres long (6 feet 6 inches), by 80 centimètres wide (2 feet 8 inches). At one end I place the screen AB, covered with white paper, dull (or not glazed), and kept in a vertical plane by two small pieces P and Q. Through the point M, the centre of the opaque body, I draw two lines Mf and Mg, equally inclined to the central line x y, whose extremities b′, a′ are the axes of the two shadows. These lines must be inclined in such a manner that the distance of the shadows may be a little less than the diameter of the opaque body, or so that they may actually touch each other, according to the mode of observing which you wish to follow. These lines M f, M g I divide into decimètres and centimètres, starting from the points a′, b′ and over these lines I place the centres of the flames; the distance between the shadows remains always the same, whatever may be the distance of the lamps: to determine the distance of each lamp from the shadow which it illuminates, we ought, strictly speaking, to take the distance of the centre of the flame b from the point a′; but as the distance from the point b to the point a′ differs little from the distance between the points b and b′, we assume the latter for the former, without causing any sensible error. That distance may be obtained very conveniently by taking the half of the sum of the distances of the two extremities z and z′ of the diameter of the pedestal of the lamp. When the burner is not placed over the centre of the pedestal, we may suspend from it a small plummet, whose point will touch some division and indicate the distance between the centre of the burner and the shadow.