The singular fallacy in vision which thus takes place is best seen in a picture where a number of separate articles are placed upon a table, and in other cases where the judgment of the spectator is not called upon to resist the optical effect. Although the nose of the human face should retire behind the ears yet no such effect is produced, as all the features of the face are connected with each other, but if the nose and ears had been represented separately in the position which they occupy in the human head, the nearer features would have retired behind the more remote ones, like the separate articles on a table.
We shall have occasion to resume this subject in our concluding chapter on the fallacies which take place in viewing solids, whether raised or hollow, and whether seen by direct or inverted vision.
CHAPTER XV.
ON THE PRODUCTION OF STEREOSCOPIC PICTURES
FROM A SINGLE PICTURE.
Those who are desirous of having stereoscopic relievos of absent or deceased friends, and who possess single photographic portraits of them, or even oil paintings or miniatures, will be anxious to know whether or not it is possible to obtain from one plane picture another which could be combined with it in the stereoscope; that is, if we consider the picture as one seen by either eye alone, can we by any process obtain a second picture as seen by the other eye? We have no hesitation in saying that it is impossible to do this by any direct process.
Every picture, whether taken photographically or by the eye, is necessarily a picture seen by one eye, or from one point of sight; and, therefore, a skilful artist, who fully understands the principle of the stereoscope, might make a copy of any picture as seen by the other eye, so approximately correct as to appear in relief when united with the original in the stereoscope; but the task would be a very difficult one, and if well executed, so as to give a relievo without distortion, the fortune of the painter would be made.
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.
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