tively distinguishes between homonymous and heteronymous images, referring the one to a position beyond, and the other to a position on this side the point of sight.

This last point is so important in the theory of binocular perspective, and so at variance with the accepted view on this subject that I must dwell upon it a moment. It is now generally admitted that Wheatstone's idea of a complete mental combination of dissimilar pictures or images is not true, either in stereoscopic experiments or in natural vision; but the theory which has displaced Wheatstone's, and which is now generally held, though certainly true, is, I believe, still imperfect. According to Brücke, Brewster, Prevost and others, the highest authorities on this subject, binocular perspective is wholly the result of rapid changes of convergence, or what I have called ranging of the eyes back and forth from foreground to background and vice versa.t I think, however, close attention to our visual perceptions will confirm the popular notion that we distinctly perceive depth of space or the relative distance of objects while gazing steadily at one point, even in those cases in which we are unassisted in our judgment by any other form of perspective. This is accounted for on the principle just announced, viz: that the eye instinctively distinguishes between homonymous and heteronymous images, referring the former to objects beyond and the latter to objects on this side the point of sight, or in other words, each eye knows its own images. It is true we are not usually conscious of making this distinction, but the same is true of the rapid changes of convergence and many other visual phenomena upon which judgments are based. The observation of Dove mentioned by Claparède‡ that stereoscopic relief is distinctly perceived by the light of an electric spark, and the undeniable fact that such relief is distinctly perceived by the light of a flash of lightning, cannot be explained by the usual theory. According to Wheatstone's well-known experiments in 1835, the duration of an electric spark from a Leyden jar is 55 (000042) of a second.§ The later experi

24

*Mr. Townes in the elaborate paper 66 on the physiology of vision" already alluded to in my last paper, (III, 1, 33,) devotes much time and many experiments to the subversion of this view, under the impression that it is still the universally accepted view.

See an admirable review of the whole subject by Claparède, Bib. Univ. Archives des Sci. Nouv. Per., vol. iii, p. 138 and seq.

Ibid. p. 155.

I give Wheatstone's result on the authority of De la Rive, (vol. ii, p. 184, trans.) and of Daguin (vol. iii, p. 518, trans.). It is somewhat remarkable that nearly all writers on physics give Wheatstone's result as a little less than 1000000 instead of 24 of a second. Prof. Rood in his recent admirable researches on this subject has unfortunately fallen into the same mistake. 10 of a second does indeed occur in Wheatstone's paper, but it is the time occupied by the electric current in passing from one interruption of the wire to

The

5

5

1

24000

ments of Fedderson in 1858, and of Prof. O. N. Rood in 1869, give nearly the same results; the former 00004 of a second, and the latter from 000022 to 000050* depending upon the degree of the charge and the length of the spark. The duration of a flash of lightning, according to Rood,t is about of a second. Now it is obviously impossible that in or even in of a second the eye can change its convergence so as to adapt it consecutively to single visions of different objects at different distances. The perception of stereoscopic relief under these circumstances is therefore inexplicable on any other theory than that which I propose. The true theory of binocular perspective seems, therefore, to be this: the eye, even when fixed steadily on one point, perceives the relative distance of objects by means of double images, as already explained; but this perception is made much clearer by the ranging of the eyes back and forth, uniting successively the images of near and distant objects.

If the pictures on a stereoscopic card be reversed, i. e. the right picture placed on the left side and the left picture on the right side, the binocular perspective is also reversed, the objects in the foregrounds being seen at a distance, and objects in the backgrounds near at hand; in other words, the foregrounds of the pictures become the background of the scene, and the backgrounds of the pictures the foreground of the scene. The reason is obvious. By changing the pictures, identical points in the backgrounds become nearer together than those of the foregrounds. Thus greater optic convergence is necessary now to combine objects in the backgrounds of the pictures than in the foregrounds, and therefore by the principles of binocular perspective the former will appear nearer than the latter. These facts are illustrated in figs. 1 and 2, in which SS is the septum of the stereoscope, r S the right and US the left picture, R and L the right and left eye, N the nose, aa identical points in the foregrounds, bb identical points in the backgrounds of the right and left pictures respectively, and A and B the places behind, where aa and bb are seen. Fig. 1 represents the result where the pictures are properly mounted, and fig. 2 when reversed. By comparing the two figures the reverse perspective and its cause becomes evident.

This inverse perspective was long ago pointed out and explained by Wheatstone, and stereoscopic pictures are often made expressly to exhibit it. I am not aware, however, that any one has drawn attention to the beautiful, and in some respects nother—the time between the occurrence of the sparks and not the duration of the sparks; it is measured by the arc of displacement of the image of middle spark, hot by the arc of elongation of the images of the sparks. I am indebted to my rother Prof. John Le Conte for having directed my attention to this mistake. *This Jour., II, vol. xlviii, p. 153. This Jour., III, vol. i, p. 15.

The italic a and b are underlined in the figures.

peculiar, results both of natural and inverse perspective, produced by the combination of stereoscopic pictures with the naked eye by squinting. I find that I am able to combine stereoscopic pictures in this way, quite as easily or even more easily than with the stereoscope. The results by this mode of combination differ from ordinary stereoscopic results in several respects. 1st. In combining on this side the plane of the pictures by squinting the right-eye image of the left picture, combines with the left-eye image of the right picture; while in combining beyond the plane of the pictures as in ordinary stereoscopic experiments, it is the right-eye image of the right picture, and the left-eye image of the left picture which combine to form the binocular result. This is evident on comparing fig. 1 with fig. 3. 2d. Besides the binocular result there are of course homonymous monocular pictures on the right and left; while in the stereoscope these monocular pictures (which, however, in this case would be heteronymous) are cut off by the septum. 3d. The binocular result, instead of being magnified as in the stereoscope, is seen in exquisite miniature and has all the charm of miniature pictures. 4th. The depth of perspective is proportionally less than in combination beyond the card. 5th. The perspective is always the reverse of that given by the stereoscope, and therefore, in order to produce the same perspective the mounting must be reversed.

If ordinary stereoscopic photographs be reversed and the pictures be then combined with the naked eye by squinting, the stereoscopic effect is as perfect as can be imagined. Miniature houses, gardens, lawns, statuettes, fountains, &c., such as Gulliver might have seen in the land of Lilliput, are presented in perfect perspective. I have often amused myself by changing the mounting of stereoscopic pictures in order to enjoy the exquisite effect. Of course in order that there should be perfect definition of the objects, there must be complete dissociation of the focal and axial adjustments, as already explained in my first paper.* If stereoscopic pictures are combined by squinting without reversing the mounting, then of course the perspective is reversed. These facts are represented by figs. 3 and 4. Fig. 3 represents the combination of fore and background when the mounting is suitable for the stereoscope. By comparing this with fig. 1, the reversal of the perspective is obvious. Fig. 4, represents the combination of fore and background when the mounting is changed. It will be observed that the perspective is true.

In combining with the naked eye stereoscopic pictures mounted in the usual way, it is not always easy, sometimes it

*This Jour., II, vol. xlvii, p. 68.

is not possible, to bring out the inverse perspective distinctly. The reason is that it violates other kinds of perspective, and sometimes sets at defiance the known properties of bodies. It is most distinct when other kinds of perspective are least distinct. In natural vision there are many kinds of perspective, or many modes of judging of the relative distance of objects; viz. aerial perspective or increasing dimness with increasing distance; mathematical perspective or decreasing size with increasing distance; change of focal adjustment necessary for distinct vision of near and distant objects; change of axial adjustment necessary for single vision of near and distant objects. The first three of these are monocular, the last is binocular. The painter can give only the first two. The stereoscope gives also the last, and its surprising effects are due to this cause. In natural vision alone all kinds concur. Now in reversing the binocular perspective we do not affect the other kinds. There is therefore, a discordance between this and the other kinds, and when they exist it must overpower them. This it cannot do when the mathematical perspective is strongly marked. Thus the curious effects of inverse perspective is best seen when the other forms of perspective, particularly the mathematical, are least marked. It is impossible to see it in cases of long buildings or long rows of buildings taken in perspective. In such cases the mathematical overpowers the binocular perspective. But in buildings and grounds seen directly in front it is very evident. I now combine with the naked eye stereoscopic photographs, taken directly in front, of a building, the profile outline of which is given in fig. 5; as soon as by rectification of the focal adjustment the image becomes clear, the inverse perspective comes out distinctly as represented in fig. 6. The roofs a a and the lawn b slope away downward as if we were looking at them from beneath. They are transparent, however, for the grass on the lawn stands upright. The column c is seen beyond the house as if through a transparency or as if the wall of the building was wanting in that part. I now try a scene in Lombardy taken on glass. Viewed in the stereoscope a village is seen in the distance and a row of poplars far in front with their straight trunks projected against the houses of the village; combined by squinting the village is seen in front and the trees through the houses far in the distance. Next I try stereoscopic pictures of the full moon. In the stereoscope it is egg-shaped with the end of the egg toward the observer; combined with. the naked eye, it is a shallow concave very perfect and beautiful. In a picture of Paris viewed in the same way, the mathematical perspective is entirely overpowered by the binocular perspective, and the city is seen sloping away downwards as if seen from beneath through a transparent ground, but with the smaller