immediate or instantaneous perception of relief, but wrong in supposing that there is a complete mental fusion of the two images. Brücke is right in asserting that binocular perspective is a judgment based on the perception of double images, but wrong in supposing change of optic convergence and successive trial combinations of different parts of the two images to be a necessary part of the evidence on which judgment is based.

My own View is an attempt to bring together and reconcile what is true in both of the preceding views. This, which I conceive to be the only true and complete theory, is hinted at, but not distinctly formulated, by Helmholtz.* I have strongly insisted upon it in all my papers on this subject. I quote from one of them:† "All objects or points of objects, either beyond or nearer than the point of sight, are doubled, but differently the former homonymously, the latter heteronymously. The double images in the former case are united by less convergence, in the latter case by greater convergence, of the optic axes. Now, the observer knows instinctively and without trial, in any case of double images, whether they will be united by greater or less optic convergence, and therefore never makes a mistake, or attempts to unite by making a wrong movement of the optic axes. In other words, the eye (or the mind) instinctively distinguishes homonymous from heteronymous images, referring the former to objects beyond, and the latter to objects this side of, the point of sight." Or again: In case of double images, "each eye, as it were, knows its own image," although such knowledge does not emerge into distinct consciousness.

* "Optique Physiologique," p. 939 et seq.

"American Journal of Science and Arts," vol. ii, 1871, p. 425.

Thus, then, I conclude that the mind perceives relief instantly, but not immediately; for it does so by means of double images, as just explained. This is all that is absolutely necessary for the perception of relief; but it is probable-nay, it is certain-that the relief is made clearer by a ranging of the point of sight back and forth, and a successive combination of the different parts of the object or scene or pictures, as maintained by Brücke.

CHAPTER V.

JUDGMENT OF DISTANCE AND SIZE.

WE are now prepared to understand the modes of estimating distance and size; for these modes are founded partly on monocular and partly on binocular vision.

The eye perceives immediately direction up and down, and right and left; and therefore also outlineform and surface-contents-for these are but a combination of directions. Thus, two dimensions of space or angular diameter in all directions are directly given in sense. But this does not give size, unless distance in the line of sight, or depth of space, or third dimension is also known. Now, this third dimension is not given by sense, but is a judgment. As already stated, the direct and simple sense-impressions given by the optic nerve are light—its intensity, its color, and its direction. These can not be analyzed into any simpler clements. But size, distance, and solid form are judgments based on these direct gifts. Moreover, apparent size and estimated distance are strictly correlated with one another in such wise that a mistake in one necessarily involves a corresponding mistake in the other.

Distance. We judge of distance by means of the different forms of perspective already described on page 161: 1. By focal adjustment, or monocular per

By

spective. The eye adjusts itself for distinct vision for all distances from infinite distance to five inches. experience we know distance from the amount of effort necessary to adjust for perfect image, and therefore distinct vision. Judgments based on this are tolerably accurate from 5 inches to several yards. Beyond 20 feet it is too small to be appreciable. 2. By axial

adjustment, or binocular perspective. The greater or less amount of optic convergence necessary to produce single vision is a far more accurate mode of judging of distance than the last. It is reliable from near the root of the nose to the distance of about a quarter of a mile. Beyond this it also becomes inappreciable, for the doubling of objects is only equal to the interocular distance. 3. By mathematical perspective. By diminution of the apparent size of known objects and the convergence of parallel lines we judge of distance with great accuracy and almost without limit. 4. By aërial perspective. Change of color and brightness of all objects, in proportion to the depth of air looked through, is still another mode of judging of distance, which, though far less accurate than the last, like it extends without limit. Estimates of distance, being judgments, are liable to error. Such errors are often called deceptions of sense, but they are not so. They are errors of judgment based upon true deliverances of sense.

Size. The size of an unknown object is judged by its angular diameter, or the size of its retinal image multiplied by its estimated distance.* For example, an image a, Fig. 61, occupies a certain space on the retina.

* Hence magnification-which is only increase of retinal image-is equivalent to nearness of view. It is perfectly right to say of a telescope either that it increases the diameter of the moon five thousand times, or that it brings the moon within the distance of fifty miles. A myopic eye, therefore, magnifies every object.

Now, evidently, precisely the same image would be made by a small object at A, or a proportionally larger similar object at A', or a still larger similar one at A”. Therefore the estimated size of the object which produced the image will depend wholly upon the distance we imagine the object to be from us, this distance being of course estimated by the different forms of perspective given above. Thus, estimates of size and distance are very closely related to each other, and an error in the one will involve an error in the other. If we misjudge

FIG. 61.

A

a

the distance of an unknown object, we will to the same degree and in the same direction misjudge its size: if our estimate of distance be too great, our judgment of size will also and to the same extent be too great; if our estimate of distance be two small, so also will be our judgment of size. Contrarily, if we make a mistake as to the size of a known object-as, for example, if we mistake a boy for a man—we will also to the same extent misjudge the distance. There is a moral as well as a physical perspective. A dollar may be held so near the eye or sit so near the affections as to cover and conceal the rest of the world. But in either case we must have an eye single to the dollar. The mind's eye, too, must be binocular or we get no true moral perspective.

Very many illustrations may be given of this gencral principle, but by far the most perfect are the ex