a _hollow_, or the converse of relief, their places must be exchanged. [Illustration: FIG. 22.] In order to find the height MN, or rather the depth of the cone in Fig. 22, let D, _d_, C, _c_, represent the same quantities as before, and we shall have D_d_ MP = ——————— C - _d_ D_d′_ NP = ——————— , and C - _d′_ D_d′_ D_d_ OP = ——————— - —————— C - _d′_ C - _d_ When D, C, _d_, _d′_ have the same values as before, we shall have MN = 18·7 feet! When C = _d_, MP will be infinite. We have already explained how the two binocular pictures are combined or laid upon one another in the lenticular stereoscope. Let us now see how the relief is obtained. The two plane pictures _abcd_, ABCD, in Fig. 18, are, as we have already explained, combined or simply laid upon one another by the lenses LL, L′L′, and in this state are shewn by the middle circles at A_a_B_b_, C_c_D_d_. The images of the bases AB, _ab_ of the cone are accurately united in the double base AB, _ab_, but the summits of the conical frustum remain separate, as seen at C′D′, _c′d′_. It is now the business of the eyes to unite these, or rather to make them appear as united. We have already seen how they are brought into relief when the summits are refracted so as to pass one another, as in Fig. 18. Let us therefore take the case shewn in Fig. 20, where the summits CD, _cd_ are more distant than the bases AB, _ab_. The union of these figures is instantly effected, as shewn in Fig. 23, by converging the optic axes to points _m_ and _n_ successively, and thus uniting C and _c_ and D and _d_, and making these points of the summit plane appear at _m_ and _n_, the points of convergence of the axes L_m_, R_m_, and L_n_, R_n_. In like manner, every pair of points in the summit plane, and in the sides A_m_, B_n_ of the frustum, are converged to points corresponding to their distance from the base AB of the original solid frustum, from which the plane pictures ABCD, _abcd_, were taken. We shall, therefore, see in relief the frustum of a cone whose section is A_mn_B. [Illustration: FIG. 23.] The theory of the stereoscope may be expressed and illustrated in the following manner, without any reference to binocular vision:— 1. When a drawing of any object or series of objects is executed on a plane surface from _one point of sight_, according to the principles of geometrical perspective, every point of its surface that is visible from the point of sight will be represented on the plane.