When by means of any of these instruments we have succeeded in forming a single image of the two pictures, we have only, as I have already explained, placed the one picture above the other, in so far as the stereoscope is concerned. It is by the subsequent action of the two eyes that we obtain the desired relief. Were we to unite the two pictures when transparent, and take a copy of the combination by the best possible camera, the result would be a blurred picture, in which none of the points or lines of the one would be united with the points or lines of the other; but were we to look at the combination with both eyes the blurred picture would start into relief, the eyes uniting in succession the separate points and lines of which it is composed. Now, since, in the stereoscope, when looked into with two eyes, we see the picture in relief with the same accuracy as, in ordinary binocular vision, we see the same object in relief by uniting on the retina two pictures exactly the same as the binocular ones, the mere statement of this fact has been regarded as the theory of the stereoscope. We shall see, however, that it is not, and that it remains to be explained, more minutely than we have done in Chapter III., both how we see objects in relief in ordinary binocular vision, and how we see them in the same relief by uniting ocularly, or in the stereoscope, two dissimilar images of them. Before proceeding, however, to this subject, we must explain the manner in which half and quarter lenses unite the two dissimilar pictures. [Illustration: FIG. 17.] In Fig. 17 is shewn a semi-lens MN, with its section M′N′. If we look at any object successively through the portions AA′A″ in the semi-lens MN, corresponding to _aa′a″_ in the section M′N′, which is the same as in a quarter-lens, the object will be magnified equally in all of them, but it will be more displaced, or more refracted, towards N, by looking through A′ or _a′_ than through A or _a_, and most of all by looking through A″ or _a″_, the refraction being greatest at A″ or _a″_, less at A′ or _a′_, and still less at A or _a_. By means of a semi-lens, or a quarter of a lens of the size of MN, we can, with an aperture of the size of A, obtain three different degrees of displacement or refraction, without any change of the magnifying power. If we use a thicker lens, as shewn at M′N′_nm_, keeping the curvature of the surface the same, we increase the refracting angle at its margin N′_n_, we can produce any degree of displacement we require, either for the purposes of experiment, or for the duplication of large binocular pictures.