planes, is the same at any instant as if the other vibration did not exist; so that each vibration subsists independently of the other, and the result will be a compound elliptical vibration. We have here supposed the coexisting vibrations to take place in separate planes, in order that their independence may be more distinctly recognised. When the two vibrations are in the same plane, it is obvious that the resulting vibration will be also in that plane; and that its amplitude will be the sum of the amplitudes of the component vibrations when their directions conspire, and their difference when they are opposed. suppose (76) Let us transfer this to the case of Light:-Let us that two sets of waves start at the same time from two near luminous origins (which, for simplicity, we shall assume to be of equal intensity), and that a distant particle of ether is thrown into vibration by both at the same time. Then, supposing that these two vibrations are performed in the same plane, it follows from what has been said, that, when their directions conspire, they will be added together, and the resulting space of vibration will be double of either; and that, on the contrary, they will counteract one another, and the resulting vibration will be reduced to nothing, when their directions are opposed. It is evident, further, that the directions of the vibrations will conspire, and therefore the space of vibration be doubled, when the two waves arrive in the same phase; and that, on the contrary, their directions will be opposed, and the resulting vibration reduced to no thing, when they arrive in Al n' n B m A" " m n' state of rest being represented by the ordinate, or perpendicu lar, at the corresponding point of the horizontal or mean line. Then, if the undulation A'B' be superposed upon AB, the corresponding points of each being in the same phase, it is evident that the distances by which the particle at any point is removed from its state of rest by each, mn and m'n', will be added together, and the space of vibration doubled. Whereas, if the undulations A"B" and AB, whose corresponding points are in opposite phases, be superposed, the distances from the position of rest, mn and m"n", lie on opposite sides of the mean line, and when added together destroy one another. Thus the space of vibration is doubled, when the waves arrive at the same point in the same phase: it is annihilated, when they arrive in opposite phases. Now the intensity of the light is as the square of the amplitude of vibration; the intensity, therefore, is quadrupled in the former case, and destroyed in the latter. We have here taken, for the sake of illustration, two of the most important cases, those, namely, in which the coexisting undulations are in complete accordance, or complete discordance. When this is not the case, and the waves meet in some intermediate stage of the vibratory movement, the position of the maximum will be altered, as well as its magnitude; and the rules for the composition of the coexisting vibrations bear a close analogy to the well-known rule for the composition of forces. (76) We learn, then, as a result of the wave-theory, that two lights may either augment each other's effects; or they may partially, or even wholly, destroy one another, and thus, by their union, produce complete darkness. Before we proceed to examine more particularly this indication of theory, we may observe that it is altogether analogous to what is known to take place in other cases of vibratory motion. If two waves of water arrive at the same point at the same instant, in such a manner that the crest of one wave coincides with that of the other, their effects will be added together, and the water at that point will be raised into a wave, whose height is the sum of the heights of the conspiring waves. If, on the other hand, the crest of one wave coincides with the sinus, or depression of the other, the height of the resultant wave will be the difference of the components; and, when these are equal, the resultant wave will entirely disappear. We have a magnificent example of these effects in the well-known phenomena of the spring and neap tides; the tidal wave in the former case being the sum of the waves caused by the action of the Sun and Moon, and in the latter, their difference. The peculiarity of the tides in the port of Batsha furnishes a still more striking instance of the principle of interference. The tidal wave reaches this port by two distinct channels, which are so unequal in length, that the time of arrival by one passage is exactly six hours longer than by the other. It follows from this that when the crest of the tidal wave, or the high water, reaches the port by one channel, it is met by the low water coming through the other; and when these opposite effects are also equal, they completely neutralize each other. At particular seasons, therefore, when the morning and evening tides are equal, there is no tide whatever in the port of Batsha; while at other seasons there is but one tide in the day, whose height is the difference of the heights of the ordinary morning and evening tides. Analogous phenomena take place in sound, and produce the coincidences or beats in music. These effects occur when the condensed part of the aërial pulse, arising from one origin of sound, coincides with the rarified part of that proceeding from the other. They are often heard during the playing of large organ, and give rise to the swelling and falling sounds which are heard, especially among the lower notes of the in strument. (77) The interference of the aerial pulses may be exhibited to the eye. Let a compound tube be taken, consisting of two equal and similar branches terminating in a common trunk. It is evident, then, that if the air be thrown into the same state of vibration at the extremities of the two branches,-the particles going and returning simultaneously in both,—a double vibration will be propagated to the extremity of the main trunk, and may be rendered sensible by the agitation of the particles of sand on a stretched membrane. If, on the other hand, the air be in opposite states of vibration at the extremities of the branches, these will neutralize one another in the trunk, and the membrane, and the sand, will be quiescent. The conditions here described are attained, by bringing the ends of the branches over the parts of a vibrating plate which are in similar, or in opposite states of vibration. When the length of the tube is such that it is in unison with the vibrating plate, it will utter a distinct sound in the one case, while in the other it will be silent. The alternate augmentation and intermission of sound observed by Young, when a tuning-fork is turned round its axis at a short distance from the ear, are easily referred to the same principles. (78) That two lights, then, should produce darkness, is a result of the same kind as that two sounds should cause silence, or that two waves should make a dead level. But we are not left to analogy alone for the proof of this remarkable consequence of the wave-theory of light. The phenomenon itself has been established by the most direct and convincing experiments; and we shall soon see that it is observed in a multitude of cases where its existence was at first little suspected. This important law-now known under the name of the interference of light-was for the first time distinctly stated and established by Young, although some facts connected with it were known to Grimaldi. The latter writer had even explicitly asserted that "an illuminated body may be rendered darker by the addition of light," and adduced a simple experiment in proof of it. Grimaldi's experiment was as follows. Let the Sun's light be admitted into a darkened chamber through two small and equal apertures of a circular form. Two diverging cones of light will be thus produced; and each of these cones will be surrounded by a penumbra in which the illumination is only partial. Now let these two beams be received on a screen at some distance, where the penumbras of the two cones overlap. It will be then observed, that although the greater part of this doubly illuminated space is brighter than the penumbra of one cone alone, yet the boundaries of the overlapping portions are much darker than the other parts of the penumbras which do not overlap; and if one of the beams be intercepted by an obstacle, this dark part will recover the brightness of the rest. Thus darkness may be produced by adding light; and, on the other hand, by withdrawing a portion of the light we may augment the illumination. (79) This interesting experiment assumed a more distinct and decisive character in the hands of Young. If the two apertures be reduced to a very small size, and brought close together, and if the original light be homogeneous, we shall observe a series of alternate bright and dark bands, formed at those points where the waves proceeding from the two origins conspire, or are opposed. That these alternations of light and darkness are caused by the mutual action of the two beams, is proved by the fact, that if one of the beams be intercepted, the whole system of bands will disappear, and the light which remains become of uniform intensity. By withdrawing one of the lights, then, the dark intervals recover their brightness; so that darkness, in this case, must have been produced by the action of one light on the other. |