When the artist executes a portrait, he does it from one point of sight, which we may suppose fixed, and corresponding with that which is seen with his _left_ eye. If he takes another portrait of the same person, occupying exactly the same position, from another point of sight, two and a half inches to the right of himself, as seen with his _right_ eye, the two pictures will differ only in this, that each point in the head, and bust, and drapery, will, in the second picture, _be carried farther to the left of the artist_ on the plane of representation. The points which project most, or are most distant from that plane, will be carried farther to the left than those which project less, the extent to which they are carried being proportional to the amount of their projection, or their distance from the plane. But since the painter cannot discover from the original or left-eye plane picture the degree of prominence of the leading points of the head, the bust, and the drapery, he must work by guess, and submit his empirical touches, step by step, to the judgment of the stereoscope. In devoting himself to this branch of the art he will doubtless acquire much knowledge and dexterity from experience, and may succeed to a very considerable extent in obtaining pictures in relief, if he follows certain rules, which we shall endeavour to explain. If the given portrait, or picture of any kind, is not of the proper size for the stereoscope, it must be reduced to that size, by taking a photographic copy of it, from which the right-eye picture is to be drawn. [Illustration: FIG. 50.] In order to diminish the size of the diagram, let us suppose that the plane on which the portrait is taken touches the back of the head, and is represented in section by AB, Fig. 50. We must now assume, under the guidance of the original, a certain form of the head, whose breadth from ear to ear is EE″, N being the point of the nose in the horizontal section of the head, E″NEN′, passing through the nose N, and the lobes EE″ of the two ears. Let L, R be the left and right eyes of the person viewing them, and LN the distance at which they are viewed, and let lines be drawn from L and R, through L, N, E and E″, meeting the plane AB on which the portrait is taken in _e′_, E‴, _n_, N′, _e_, and E′. The breadth, E‴_e′_, and the distances of the nose from the ears N′E′, N′E‴, being given by measurement of the photograph suited to the stereoscope, the distances NN′, EE′, E″E‴ may be approximately obtained from the known form of the human head, either by projection or calculation. With these data, procured as correctly as we can, we shall, from the position of the nose _n_, as seen by the right eye R, have the formula LR × NN′ N′_n_ = ———————— NL. The distance of the _right_ ear _e′_, from the right-eye picture, will be, _ne′_ = _e′_N - N′_n_; LR × EE′ and as E′_e_ = ————————— EL.