server, or look at some point about M. Both pictures will immediately be doubled. An image of the figure ab will advance towards P, and an image of AB will likewise advance towards P; and the instant these images are united, the frustum of a cone, which they represent, will appear in relief at MN, the place where the optic axes meet or cross each other. At first the solid figure will appear in the middle, between the two pictures from which it is formed and of the same size, but after some practice it will appear smaller and nearer the eye. Its smallness is an optical illusion, as it has the same angle of apparent magnitude as the plane figures, namely, mn L= ABL; but its position at MN is a reality, for if we look at the point of our finger held beyond м the solid figure will be seen nearer the eye. The difficulty which we experience in seeing it of the size and in the position shewn in Fig. 21, arises from its being seen along with its two plane representations, as we shall prove experimentally when we treat in a future chapter of the union of similar figures by the eye. The two images being thus superimposed, or united, we shall now see that the combined images are seen in relief in the very same way that in ordinary vision we saw the real solid, ABCD, Fig. 19, in relief, by the union of the two pictures of it on the retina. From the points A, B, C, D, a, b, c, d, draw lines to L and R, the centres of visible direction of each eye, and it will be seen that the circles AB, ab, representing the base of the cone, can be united by converging the optical axes to points in the line mn, and that the circles CD, cd, which are more distant, can be united only by converging the optic axes to points in the line op. The points A, a, for example, united by converging the axes to m, are seen at that point single; the points B, b at n single, the points c, c at o single, the points D, d at p single, the centres s, s of the base at м single, and the centres s', s' of the summit plane at N single. Hence the eyes L and R see the combined pictures at F MN in relief, exactly in the same manner as they saw in relief the original solid MN in Fig. 19. d = ss, In order to find the height MN of the conical frustum thus seen, let D = distance Op; the distance of the two points united at м; d's's', the distance of the two points united at N; and CLR=2 inches, the distance of the eyes. Then we have As the summit plane op rises above the base mn by the successive convergency of the optic axes to different points in the line oNp, it may be asked how it happens that the conical frustum still appears a solid, and the plane op where it is, when the optic axes are converged to points in the line mмn, so as to see the base distinctly? The reason of this is that the rays emanate from op exactly in the same manner, and form exactly the same image of it, on the two retinas as if it were the summit CD, Fig. 19, of the real solid when seen with both eyes. The only effect of the advance of the point of convergence from N to M is to throw the image of N a little to the right side of the optic axis of the left eye, and a little to the left of the optic axis of the right eye. The summit plane op will therefore retain its place, and will be seen slightly doubled and indistinct till the point of convergence again returns to it. It has been already stated that the two dissimilar pictures may be united by converging the optical axes to a point beyond them. In order to do this, the distance ss' of the pictures, Fig. 21, must be greatly less than the distance of the eyes L, R, in order that the optic axes, in passing through similar points of the two plane pictures, may meet at a moderate distance beyond them. In order to explain how the relief is produced in this case, let AB, CD, ab, cd, Fig. 22, be the dissimilar pictures of the frustum of a cone whose summit is CD, as seen by the right eye, and cd as seen by the left eye. From L and R, as before, draw lines through all the leading points of the pictures, and we shall have the points A, a united at m, the points B, b at n, the points c, c at o, and the points D, d at p, the points s, s at M, and the points s', s' at N, forming the cone mnop, with its base mn towards the observer, and its summit op more remote. If the cone had been formed of lines drawn from the outline of the summit to the outline of the base, it would now appear hollow, the inside of it being seen in place of the outside as before. If the pictures AB, ab are made to change places the combined picture would be in relief, while in the case shewn in Fig. 21 it would have been hollow. Hence the right-eye view of any solid must be placed on the left hand, and the left-eye view of it on the right hand, when we wish to obtain it in relief by converging the optic axes to a point between the pictures and the eye, and vice versa when we wish to obtain |