Representations of geometrical solids, were, as we have already seen, the only objects which for many years were employed in the reflecting stereoscope. The figures thus used are so well known that it is unnecessary to devote much space to their consideration. For ordinary purposes they may be drawn by the hand, and composed of squares, rectangles, and circles, representing quadrangular pyramids, truncated, or terminating in a point, cones, pyramids with polygonal bases, or more complex forms in which raised pyramids or cones rise out of quadrangular or conical hollows. All these figures may be drawn by the hand, and will produce solid forms sufficiently striking to illustrate the properties of the stereoscope, though not accurate representations of any actual solid seen by binocular vision. If one of the binocular pictures is not equal to the other in its base or summit, and if the lines of the one are made crooked, it is curious to observe how the appearance of the resulting solid is still maintained and varied. The following method of drawing upon a plane the dissimilar representations of solids, will give results in the stereoscope that are perfectly correct:— [Illustration: FIG. 43.] Let L, R, Fig. 43, be the left and right eye, and A the middle point between them. Let MN be the plane on which an object or solid whose height is CB is to be drawn. Through B draw LB, meeting MN in _c_; then if the object is a solid, with its apex at B, C_c_ will be the distance of its apex from the centre C of its base, as seen by the left eye. When seen by the right eye R, C_c′_ will be its distance, _c′_ lying on the left side of C. Hence if the figure is a cone, the dissimilar pictures of it will be two circles, in one of which its apex is placed at the distance C_c_ from its centre, and in the other at the distance C_c′_ on the other side of the centre. When these two plane figures are placed in the stereoscope, they will, when combined, represent a raised cone when the points _c_, _c′_ are nearer one another than the centres of the circles representing the cone’s base, and a _hollow_ cone when the figures are interchanged. If we call E the distance between the two eyes, and _h_ the height of the solid, we shall have E AB:_h_ = ——— : C_c_, 2 _h_E 5_h_ and C_c_ = ————, or ————, 2AB 4AB which will give us the results in the following table, E being 2½, and AC 8 inches:— Height of object. BC = _h_ AB = AC - _h_ C_c_ Inches. 1 7 0.179 2 6 0.4166 3 5 0.75 4 4 1.25 5 3 2.083 6 2 3.75 7 1 8.75 8 0 Infinite.