media. Now as double-refracting crystals have two refractive indices, of different magnitudes, there will be two images, at different distances from the surface. In Iceland spar, the ordinary index is greater than the extraordinary, and therefore the ordinary image is nearer than the other. The reverse is the case in positive crystals, such as quartz, in which the extraordinary index is the greater. (72) The refractions being equal at the two parallel surfaces of the rhomb, whether the refraction be ordinary or extraordinary, the two rays will emerge parallel to the incident ray, and therefore parallel to one another; and the distance between them will be proportional to the thickness of the crystal. But if the surfaces be inclined, so as to form a prism, the deviation of the two rays will be different, and they will emerge inclined to one another; consequently the separation will increase with the distance. Such a separation is of use in many experiments. In order to render the divergence of the emergent pencils greatest, the prism should be cut with its edge parallel to the optic axis; so that the refraction may take place in a plane perpendicular to the axis. In this case the ordinary and extraordinary refractions differ by the greatest amount, and therefore the difference of the deviations of the two pencils is greatest. A double-refracting prisin, so cut, is usually achromatized by a prism of glass, with its refracting angle turned in the opposite way. ton. A better arrangement has been suggested by WollasTwo prisms of the same substance, and of equal refracting angles, are cut in such a manner, that in one the refracting edge is parallel to the optic axis, and in the other perpendicular to it. They are then united, with their refracting angles turned in opposite directions, so as to form a parallelopiped ; and the effect of this arrangement is to double the separation of the images produced by either singly. By this duplication the weak double refraction of rock crystal is rendered very sensible. (73) An achromatic prism of this kind is employed in the double image micrometer, an ingenious and valuable instrument invented by Rochon. It consists of a telescope, in which a prism, such as we have described, is introduced between the object-glass and its principal focus; and thus two images are formed in the principal focus, whose interval is greater or less, according to the distance of the prism from that point. When the instrument is used, the prism is moved until the two images appear in contact, and its distance from the focus is then read on a graduated scale. The two angles in this case having the same subtense, the visual angle of the object is to the deviation produced by the prism, as the distance of the prism from the focus is to the focal length. Now the divergence of the two rays is constant for a given prism, and may be determined either by calculation or experiment; consequently, the visual angle is deduced from the preceding proportion. this instrument Arago has determined the apparent diameters of the planets with great precision. By The same instrument has been also employed in war, to determine the distance of an inapproachable object. Thus, if it be required to ascertain the distance of the walls of a besieged town, in order to know whether they are within the range of shot, it is only necessary to measure by this instrument the angle subtended by a man, or any other object whose height is known approximately. The height of the object, divided by the tangent of the angle, is the distance required. CHAPTER V. INTERFERENCE OF LIGHT. (74) HAVING Considered the mode of propagation of a luminous wave, and the modifications which it undergoes on encountering the surface of a new medium, we may now proceed to inquire what will be the effect, when two series of waves are propagated simultaneously from two near luminous origins. It is obvious that when two waves-one proceeding from each source-arrive at any instant at the same point of space, the particle of ether there will be thrown into vibration by both; and we are to consider what will be the result of this compound vibration. Now, it is demonstrated by analysis, that when two small vibrations are communicated at the same time to a material point, each of them will subsist independently of the other; and the motion of the point will, in consequence, be the resultant of the motions due to each vibration considered separately. This principle is denominated the superposition of small motions. Its nature may be made clear by a simple instance. Let a pendulous body receive an impulse in any plane passing through the point of suspension: it will then, of course, vibrate in that plane. Now, at the lowest point of the arc of vibration, let a second impulse be given to the moving body, in a direction perpendicular to the plane in which it already vibrates. This impulse, if communicated to the body at rest, would cause it to vibrate in a plane at right angles to the former, and through an arc depending on the magnitude of the impulse. Now it will be found, on trial, that the distance of the body from the vertical, measured in either of these 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. (76) Let us transfer this to the case of Light :-Let us suppose 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 A m 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 |