In the preceding diagram we have not shewn the refraction at the second surface of the lenses, nor the parallelism of the rays when they enter the eye,—facts well known in elementary optics.
CHAPTER V.
ON THE THEORY OF STEREOSCOPIC VISION.
Having, in the preceding chapter, described the ocular, the reflecting, and the lenticular stereoscopes, and explained the manner in which the two binocular pictures are combined or laid upon one another in the last of these instruments, we shall now proceed to consider the theory of stereoscopic vision.
Fig. 19.
In order to understand how the two pictures, when placed the one above the other, rise into relief, we must first explain the manner in which a solid object itself is, in ordinary vision, seen in relief, and we shall then shew how this process takes place in the two forms of the ocular stereoscope, and in the lenticular stereoscope. For this purpose, let abcd, [Fig. 19], be a section of the frustum of a cone, that is, a cone with its top cut off by a plane cedg, and having aebg for its base. In order that the figure may not be complicated, it will be sufficient to consider how we see, with two eyes, l and r, the cone as projected upon a plane passing through its summit cedg. The points l, r being the points of sight, draw the lines ra, rb, which will cut the plane on which the projection is to be made in the points a, b, so that ab will represent the line ab, and a circle, whose diameter is ab, will represent the base of the cone, as seen by the right eye r. In like manner, by drawing la, lb, we shall find that a′b′ will represent the line ab, and a circle, whose diameter is a′b′, the base aebg, as seen by the left eye. The summit, cedg, of the frustum being in the plane of projection, will be represented by the circle cedg. The representation of the frustum abcd, therefore, upon a plane surface, as seen by the left eye l, consists of two circles, whose diameters are ab, cd; and, as seen by the right eye, of other two circles, whose diameters are ab, cd, which, in [Fig. 20], are represented by ab, cd, and ab, cd. These plane figures being also the representation of the solid on the retina of the two eyes, how comes it that we see the solid and not the plane pictures? When we look at the point b, [Fig. 19], with both eyes, we converge upon it the optic axes lb, rb, and we therefore see the point single, and at the distances lb, rb from each eye. When we look at the point d, we withdraw the optic axes from b, and converge them upon d. We therefore see the point d single, and at the distances ld, rd from each eye; and in like manner the eyes run over the whole solid, seeing every point single and distinct upon which they converge their axes, and at the distance of the point of convergence from the observer. During this rapid survey of the object, the whole of it is seen distinctly as a solid, although every point of it is seen double and indistinct, excepting the point upon which the axes are for the instant converged.
Fig. 20.
From these observations it is obvious, that when we look with both eyes at any solid or body in relief, we see more of the right side of it by the right eye, and more of the left side of it by the left eye. The right side of the frustum abcd, [Fig. 19], is represented by the line db, as seen by the right eye, and by the shorter line db′, as seen by the left eye. In like manner, the left side ac is represented by ca′, as seen by the left eye, and by the shorter line ca′, as seen by the right eye.
When the body is hollow, like a wine glass, we see more of the right side with the left eye, and more of the left side with the right eye.