The luminous rays, in fact, form in the objective a double truncated cone whose upper base is equal to the diaphragm, and the lower one to the diameter of the lenses. If the aperture be equal to any diameter whatever of one of the cones, the result will be the same; but, for the same period of exposure, it will evidently prove advantageous to approach the diaphragm. The ratio of the apertures that give the same results at the optical center or behind the objective is as that of the diaphragm employed to that of the back lens. If the diaphragm is one centimeter and the lenses four centimeters, an aperture of one centimeter in one case and of four in the other will give the same result. We shall see further along that it is advantageous to employ apertures equal to several times the diameter of the diaphragm or lens. Now, from what we have just said, an aperture, equal for example to four times the diaphragm, will be only 4 centimeters, while the corresponding aperture behind the lens must be 16. The dimensions of the first will be practical, and those of the second will give too cumbersome and too fragile an apparatus. But why must the aperture be larger than the diaphragm employed? This is what we are going to demonstrate. Let us make the aperture equal to the diameter of the objective, and see what occurs at the different periods of the exposure. For the sake of clearness, we shall suppose the velocity uniform. It is evident, _a priori_, that a perfect apparatus will be the one that will allow the light to act during the entire exposure with a maximum of intensity. Is it thus, when the aperture is equal to the diameter of the objective? Evidently not. Let us consult Fig. 2. We here see the shutter progressively uncovering the objective. The light will increase from A to C up to the moment when the objective is entirely uncovered, and will then immediately decrease up to B. The objective has operated with a maximum of light for only a short time. We are far from the ideal result in which the maximum of light, CD, should exist during the entire exposure, and form the upper plane precisely equal to AB. [Illustration: Fig. 2.] If we cannot obtain such a result in practice, we must nevertheless aproximate to it. We shall do so by increasing the shutter. Up to C' the apparatus will operate as before, but from C' to D' the aperture will be complete, and from D' to B' will decrease as has been said. Let us give A'B' the same value as AB, that is to say, let us increase the velocity in the second case in order that the time of exposure shall be the same; we shall at once see that in the first case the object will be completely uncovered for only a very short time, while in the second the exposure will be perfect for a very appreciable period.