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of the chair upon a table, the height of the eye either when sitting or standing, so that the cane bottom with its luminous pattern may have a vertical position, as shewn in Fig. 25, where MN is the real bottom of the chair with its

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openings, which generally vary from half an inch to threefourths. Supposing the distance to be half an inch, and the eyes, L, R, of the observer 12 inches distant from MN, let Lad, Lbe be lines drawn through the centres of two of the open spaces a, b, and Rbd, Rce lines drawn through the centres of b and c, and meeting Lad, Lbe at d and e, d being the binocular centre to which the optic axes converge when we look at it through a and b, and c the binocular centre when we look at it through b and c. Now, the right eye, R, sees the opening b at d, and the left eye sees the opening a at d, so that the image at d of the opening consists of the similar images of a and b united, and so on with all the

rest; so that the observer at L, R no longer sees the real pattern MN, but an image of it suspended at mn, three inches behind MN. If the observer now approaches MN, the image mn will approach to him, and if he recedes, mn will recede also, being 11⁄2 inches behind MN when the observer is six inches before it, and twelve inches behind MN when the observer is forty-eight inches before it, the image m n moving from mn with a velocity one-fourth of that with which the observer recedes.

If we next

The observer resuming the position in the figure where his eyes, L, R, are twelve inches distant from MN, let us consider the important results of this experiment. If he now grasps the cane bottom at MN, his thumbs pressing upon MN, and his fingers trying to grasp mn, he will then feel what he does not see, and see what he does not feel! The real pattern is absolutely invisible at MN, where he feels it, and it stands fixed at mn. The fingers may be passed through and through between the real and the false image, and beyond it, now seen on this side of it, now in the middle of it, and now on the other side of it. place the palms of each hand upon MN, the real bottom of the chair, feeling it all over, the result will be the same. No knowledge derived from touch-no measurement of real distance-no actual demonstration from previous or subsequent vision, that there is a real solid body at MN, and nothing at all at mn, will remove or shake the infallible conviction of the sense of sight that the cane bottom is at mn, and that dL or dR is its real distance from the obIf the binocular centre be now drawn back to MN, the image seen at mn will disappear, and the real object be seen and felt at MN. If the binocular centre be brought

server.

further back to f, that is, if the optic axes are converged to a point nearer the observer than the object, as illustrated by Fig. 18, the cane bottom MN will again disappear, and will be seen at uv, as previously explained.

This method of uniting small similar figures is more easily attained than that of doing it by converging the axes to a point between the eye and the object. It puts a very little strain upon the eyes, as we cannot thus unite figures the distance of whose centre is equal to or exceeds 21 inches, as appears from Fig. 22.

In making these experiments, the observer cannot fail to be struck with the remarkable fact, that though the openings MN, mn, uv, have all the same apparent or angular magnitude, that is, subtend the same angle at the eye, viz., dLc, dRe, yet those at mn appear larger, and those at uv smaller, than those at MN. If we cause the image mn to recede and approach to us, the figures in mn will invariably increase as they recede, and those in uv diminish as they approach the eye, and their visual magnitudes, as we may call them, will depend on the respective distances at which the observer, whether right or wrong in his estimate, conceives them to be placed,—a result which is finely illustrated by the different size of the moon when seen in the horizon and in the meridian. The fact now stated is a general one, which the preceding experiments demonstrate; and though our estimate of magnitude thus formed is erroneous, yet it is one which neither reason nor experience is able to correct.

It is a curious circumstance, that, previous to the publication of these experiments, no examples have been recorded of false estimates of the distance of near objects in conse

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quence of the accidental binocular union of similar images. In a room where the paper-hangings have a small pattern, a short-sighted person might very readily turn his eyes on the wall when their axes converged to some point between him and the wall, which would unite one pair of the similar images, and in this case he would see the wall nearer him than the real wall, and moving with the motion of his head. In like manner a long-sighted person, with his optical axes converged to a point beyond the wall, might see an image of the wall more distant, and moving with the motion of his head; or a person who has taken too much wine, which often fixes the optical axes in opposition to the will, might, according to the nature of his sight, witness either of the illusions above mentioned.

Illusions of both these kinds, however, have recently occurred. A friend to whom I had occasion to shew the experiments, and who is short-sighted, mentioned to me that he had on two occasions been greatly perplexed by the vision of these suspended images. Having taken too much wine, he saw the wall of a papered room suspended near him in the air; and on another occasion, when kneeling, and resting his arms on a cane-bottomed chair, he had fixed his eyes on the carpet, which had accidentally united the two images of the open octagons, and thrown the image of the chair bottom beyond the plane on which he rested his

arms.

After hearing my paper on this subject read at the Royal Society of Edinburgh, Professor Christison communicated to me the following interesting case, in which one of the phenomena above described was seen by himself :-" Some years ago," he observes, "when I resided in a house where several

rooms are papered with rather formally recurring patterns, and one in particular with stars only, I used occasionally to be much plagued with the wall suddenly standing out upon me, and waving, as you describe, with the movements of the head. I was sensible that the cause was an error as to the point of union of the visual axes of the two eyes; but I remember it sometimes cost me a considerable effort to rectify the error; and I found that the best way was to increase still more the deviation in the first instance. As this accident occurred most frequently while I was recovering from a severe attack of fever, I thought my near-sighted eyes were threatened with some new mischief; and this opinion was justified in finding that, after removal to my present house, where, however, the papers have no very formal pattern, no such occurrence has ever taken place. The reason is now easily understood from your researches."

"1

Other cases of an analogous kind have been communicated to me; and very recently M. Soret of Geneva, in looking through a trellis-work in metal stretched upon a frame, saw the phenomenon represented in Fig. 25, and has given the same explanation of it which I had published long before.2

Before quitting the subject of the binocular union of similar pictures, I must give some account of a series of curious phenomena which I observed by uniting the images of lines meeting at an angular point when the eye is placed at different heights above the plane of the paper, and at different distances from the angular point.

1 See Edin. Transactions, 1846, vol. xv. p 663, and Phil. Mag., May 1847, vol. xxx. p. 305.

2 Bibl. Universelle, October 1855, p. 136.

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