the unpracticed and unobservant. It makes that simple and primary which is capable of analysis into simpler elements. It is therefore a popular, not a scientific theory. It cuts, but does not loose, the Gordian knot.

Brücke's Theory.-Brücke and Brewster and Prévost, by more refined observation and more careful analysis, easily perceived that there was in reality no mental fusion of two dissimilar images. Their view, most completely expressed by Brücke,* is that which has been assumed in the foregoing account and explanation of binocular phenomena. It is, that in regarding a solid object or a natural scene, or two stereoscopic pictures in a stereoscope, the eyes are in incessant unconscious motion, and the observer, by alternately greater and less convergence of the axes, combines successively the different parts of the two pictures as seen by the two eyes, and thus by running the point of sight back and forth reaches by trial a distinct perception of binocular perspective or binocular relief, or depth of space between foreground and background.

That double images are really necessary to binocular perspective, as maintained by Brücke, is abundantly proved by the experiments already given on that subject. But one additional experiment may be given here to complete the proof.

Experiment.-As I look out of my window, I see the clothes-lines of a neighboring family, about 40 feet distant. Two of these are parallel, but one about 5 or 6 feet beyond the other. The lines being horizontal, no double images are visible when the head is erect. In this position I am unable to tell which line is the farther off. But when I turn the head to one side, so that the interocular line is at right angles to the cords,

* "Archives des Sciences," tome iii, p. 142 (1858).

immediately their relative distance comes out with great distinctness.

This theory is a great advance on the preceding. It is really a scientific theory, since it is based on an analysis of our visual judgments. It is also in part a true theory, and for this reason, in anticipation of what we believe to be a more perfect theory, we have used it in the explanation of many visual phenomena in the preceding pages. But it is evidently not the whole truth, as we now proceed to show.

1. If we place one object before another in the median plane of sight, even when we look steadily and without change of optic convergence at the one or the other, we distinctly perceive the depth of space between them. Evidently no trial combination, no running of the point of sight back and forth, and successive union and disunion of the images, are necessary for the perception of binocular relief. But if it be said that change of optic convergence does indeed take place, only rapidly and unconsciously, I proceed to prove that such is not the case.

2. Dove's Experiment.-The instantaneous perception of binocular relief is demonstrated by the now celebrated experiment of Dove. If a natural object, or a scene, or two stereoscopic pictures, be viewed by the light of an electric spark or a succession of electric sparks, the perspective is perfect, even though the duration of such a spark is only of a second of time. On a dark night the relative distance of objects is perfectly perceived by the light of a flash of lightning, which according to Arago lasts only obʊ,* and according to Roodt of a second. It is inconceiva

*

Arago, "Euvres Complètes," tome iv, p. 70.

Rood, "American Journal of Science and Arts," vol. i, 1870, p. 15.

ble that there should be any change of optic convergence, any running of the point of sight back and forth, in the space of part of a second. Evidently, therefore, binocular perspective may be perceived without such change of convergence. This point is certainly one of capital importance. The instantaneous perception of relief is fatal to Brücke's theory in its pure unmodified form. I have therefore repeated Dove's experiment with care, varying it in every possibly way, so as to guard against every source of error. These experiments completely confirm Dove's result, and establish beyond doubt the instantaneous perception of binocular relief. From a large number of experiments I select a few of the most conclusive and most easily repeated. The spark apparatus used was a Ritchie's Ruhmkorff capable of producing sparks 12 inches long. A Leyden jar was introduced into the circuit to increase the brilliancy of the sparks.

Experiment 1.-I select stereoscopic pictures in which other forms of perspective are wanting, or nearly so; skeleton geometric diagrams are the best. Standing in a perfectly dark room, and viewing these in a stereoscope by the light of a succession of sparks, the perspective is perfectly distinct with two eyes, but not at all with one eye.

Experiment 2.—I select a stereoscopic card like the last, except that mathematical perspective is also strong —such, for example, as a view of the interior of a bridgeway. Of course, as in the last case, the natural perspective is instantly perceived in the stereoscope; but this might be attributed to the mathematical perspective. But now hold the card in the hand and unite the pictures with the naked eyes by squinting: the inverse perspective described on page 135 will be brought

out with perfect clearness with two eyes, but the natural perspective (mathematical) returns when we shut one eye. This experiment is conclusive, being removed from even the suspicion of the effect being the result of other forms of perspective; for in this case the binocular is opposed to all other forms of perspective, overbears them, and reverses the perspective.

So much for combination of stereoscopic pictures, whether beyond the plane of the card, as in the stereoscope, or on this side the plane of the card, as in nakedeye combination by squinting. We will next try the viewing of natural objects, eliminating as before as much as possible other forms of perspective.

Experiment 3.-Let two objects, as two brass balls, of the same size, be hung by invisible threads, one about 5 or 6 feet distant, and the other about 1 foot farther. At this distance focal adjustment is practically the same for the two balls, and thus this mode of judging of relative distance is eliminated. Let the balls be placed in the median plane of sight, or nearly so, in such wise that their relative distance may be easily detected with two eyes, but not with one. In the latter case—i. e., with one eye-they look like two balls side by side, the one a trifle larger than the other. Now, after darkening the room, try the experiment by the instantaneous flash of electric sparks. It will be found that under these conditions also the relative distance is perceived with perfect clearness with two eyes, but not with one.

It is certain, then, that binocular perspective is perceived instantly, and therefore without the trial combinations of different parts of the two images, as maintained by Brücke, Brewster, and others.

Between the two rival theories, therefore, the case stands thus: Wheatstone is right in so far as he asserts

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.