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 é, 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

The distance of the right ear e, from the right-eye picture, will be,

The distance of the left ear e, in the right-eye picture, from the nose n, will be

In order to simplify the diagram we have made the original, or left-eye picture, a front view, in which the nose is in the middle of the face, and the line joining the ears parallel to the plane of the picture.

When the position of the nose and the ears has been thus approximately obtained, the artist may, in like manner, determine the place of the pupils of the two eyes, the point of the chin, the summit of the eyebrows, the prominence of the lips, and the junction of the nose with the teeth, by assuming, under the guidance of the original picture, the distance of these different parts from the plane of projection. In the same way other leading points in the figure and drapery may be found, and if these points are deter

mined with tolerable accuracy the artist will be able to draw the features in their new place with such correctness as to give a good result in the stereoscope.

In drawing the right-eye picture the artist will, of course, employ as the groundwork of it a faint photographic impression of the original, or left-eye picture, and he may, perhaps, derive some advantage from placing the original, when before the camera, at such an inclination to the axis of the lens as will produce the same diminution in the horizontal distance between any two points in the head, at a mean distance between N and N', as projected upon the plane AB. The line N'E", for example, which in the left-eye photograph is a representation of the cheek NE", is reduced, in the right-eye photograph, to ne, and, therefore, if the photograph on AB, as seen by the right eye, were placed so obliquely to the axis of the lens that N'e was reduced to ne, the copy obtained in the camera would have an approximate resemblance to the right-eye picture required, and might be a better groundwork for the right-eye picture than an accurate copy of the photograph on AB, taken when it is perpendicular to the axis of the lens.

In preparing the right-eye picture, the artist, in place of using paint, might use very dilute solutions of aceto-nitrate of silver, beginning with the faintest tint, and darkening these with light till he obtained the desired effect, and, when necessary, diminishing the shades with solutions of the hypo-sulphite of soda. When the picture is finished, and found satisfactory, after examining its relief in the stereoscope, a negative picture of it should be obtained in the camera, and positive copies taken, to form, with the original photographs, the pair of binocular portraits required.

CHAPTER XVL

ON CERTAIN FALLACIES OF SIGHT IN THE VISION OF
SOLID BODIES.

IN a preceding chapter I have explained a remarkable fallacy of sight which takes place in the stereoscope when we interchange the binocular pictures, that is, when we place the right-eye picture on the left side, and the left-eye picture on the right side. The objects in the foreground of the picture are thus thrown into the background, and, vice versa, the same effect, as we have seen, takes place when we unite the binocular pictures, in their usual position, by the ocular stereoscope, that is, by converging the optic axes to a point between the eye and the pictures. In both these cases the objects are only the plane representations of solid bodies, and the change which is produced by their union is not in their form but in their position. In certain cases, however, when the object is of some magnitude in the picture, the form is also changed in consequence of the inverse position of its parts. That is, the drawings of objects that are naturally convex will appear concave, and those which are naturally concave will appear convex.

In these phenomena there is no mental illusion in their production. The two similar points in each picture, if they are nearer to one another than other two similar

points, must, in conformity with the laws of vision, appear nearer the eye when combined in the common stereoscope. When this change of place and form does not appear, as in the case of the human figure, previously explained, it is by a mental illusion that the law of vision is controlled.

The phenomena which we are about to describe are, in several respects, different from those to which we have referred. They are seen in monocular as well as in binocular vision, and they are produced in all cases under a mental illusion, arising either from causes over which we have no control, or voluntarily created and maintained by the observer. The first notice of this class of optical illusion was given by Aguilonius in his work on optics, to which we have already had occasion to refer.1 After proving that convex and concave surfaces appear plane when seen at a considerable distance, he shews that the same surfaces, when seen at a moderate distance, frequently appear what he calls converse, that is, the concave convex, and the conThis conversion of forms, he says, is often seen in the globes or balls which are fixed on the walls of fortifications, and he ascribes the phenomena to the circumstance of the mind being imposed upon from not knowing in what direction the light falls upon the body. He states that a concavity differs from a convexity only in this respect, that if the shadow is on the same side as that from which the light comes it is a concavity, and if it is on the opposite side, it is a convexity. Aguilonius observes also, that in pictures imitating nature, a similar mistake is committed as to the form of surfaces. He supposes that a circle is drawn upon a table and shaded on one side so as 1 See Chap. i. p. 15.

vex concave.