vision (by parallax, as it is called,) depend on the geometrical relation existing between this unknown distance and certain directions which are seen and determined at once by the eye. We take the direction of a body from two stations; those angles, with the distance between the stations, furnish all the requisite data for the solution of the problem. We cannot, in such a case, be said to see the distance of the body, although all the data are obtained by sight. For the directions are not observed together, but in succession; or, if at the same moment by two different observers, we can hardly call that the result of direct sensation which requires two persons. Moreover, in either case, the calculation which gives us the distance may follow at a long interval.

These angles which, in important cases, are measured by nicely graduated instruments, accurately pointed by the help of lenses, are ordinarily judged of, or guessed at, by the eye. And these calculations which, for the delicate objects of science, are laboriously and leisurely performed with tables of logarithms, may be instantaneously and unconsciously gone over in the mind. In such cases, we think we see approximately the distance of a body. But the nature of the process is the same; it is the same mind which geometrizes, though the data and calculations, and consequently the results, do not aspire to an equal degree of accuracy. As this process takes so little time, as the observer may not move his body, or even his eye, he easily persuades himself that he enjoys the power of seeing distances. Its failure in many exigencies best reveals the character and extent of this power.

1. In the first place the two eyes, directed from their two positions in the head, upon the same body, as two telescopes upon two remote mountains point to the signal that shines upon a third, furnish the data for calculating the distance of the body. A single eye, if the head move, can do the same work; it may do it much better if we move the head further than the interval between the eyes, and, best of all, if we move the whole body and enlarge our base of operations. Whenever the distance of the object is very large, compared with the interval between the eyes or the base line, we have what is called an ill-conditioned triangle, and our unconscious geodesy fails us; we commit great errors in estimating the distance, or are wholly at a loss about it.

2. Another method, and which can be practised by a single eye, rests upon the adaptation of the focus of the eye to different distances. By the effort made to change this focus, we are informed of the diver

gency of the rays which have entered the pupil, and consequently the distance of their radiating centre. It would not be difficult to trace an analogy between this operation and that which enables us to measure an air line across seas and mountains. But in this miniature exhibition of the process, the base line is no larger than the diameter of the pupil, and we arrive very soon upon ill-conditioned triangles. As the distance increases, this second method fails us much sooner than the first method. Whenever the distance of a body is large, compared with the focal length of the eye, the rays from it are sensibly parallel and remain so for all larger distances. The rays, therefore, from all bodies outside of this limit have sensibly the same focus, and consequently their exact distances cannot be appreciated through the change in the focus of the eye as it passes from one to the other.

Assuming now that a body is within such limits of distance from the eye that its distance may be approximately calculated from such data as the eye itself will furnish, by one or other of the two methods described, it may still be true, if the body is small compared with its distance, that the observer will not be able to say which parts of the body are nearest, and which are most remote; and now we come to the case of the windmill. If the arm on the left is the nearest, then the plane of rotation is as is represented in figure 1. If the arm on the right is the nearest, the position of this same plane is as it appears in figure 2. So far as this position is to be settled by an accurate comparison of the relative distances of the several parts of the mill, it is obvious that our judgment must be at fault, whenever the wheel is at any considerble distance, for want of precise data on which to ground its calculations. The only thing which the eye can see accurately is the direction of the different parts. If the distances are eliminated, the position in figure 2 represents the directions as faithfully as that in figure 1. Whenever we know beforehand the real shape of a body, we have some assistance in ascertaining its real position. Suppose we know that W M is a straight line turning upon its middle point; if the position is as in figure 1, WC must subtend a larger angle than M C. The contrary will be true in the position of figure 2. Let us now call up the image of the whole mill; let us suppose that we know it to be a circle presented obliquely to the eye; our geometrical sense will tell us, that if the left side is turned away, the centre of the wheel will be projected on the ellipse of projection of the whole wheel nearest to the left edge. If the right side is most remote, the projected centre will be towards the right edge. An eye,

nicely disciplined in perspective, has here the means of determining the position of the plane from the relative fore-shortening of its parts. Suppose the observer to use both eyes, that comparison of the images which gives the position of the body will be still easier. For the images of the wheel on the two eyes will be different; and the image which is on the left eye, when the wheel has the position in figure 1, will be on the right eye, when the wheel is in the position of figure 2. Finally, we may invoke the aid of the lights and shadows to confirm us in our decision. If the sun, or principal source of light, is on the right, then the side at which we look will be illuminated when the real position of the mill is as in figure 1; but it will lie in shade when the position of figure 2 is the true one.

If this view of the subject bc correct, we certainly cannot be said to see directly the position of a body by a simple effort of sight. By means of this organ we gather up a variety of data, which are submitted to a rapid mental analysis. When the body is near, the differential qualities on which our judgment is based are substantial and obvious, so that he who runs may read. As the distance increases, the calculation grows nicer; only a careful, scrutinizing eye will notice the delicate touches in outline, proportion, or shading, on which the problem hangs. At still greater distances it is impossible for any eye, or any mind, however geometrical, to divine the true position. Before this limit is reached, our decision is held by so weak a tenure, that a slight circumstance, the absence of strong sunlight, an obliquity in the eye, or a scarcely perceptible motion of the head, is sufficient to alter it. The mind halts between the two opinions; at one moment thinking the body is in one of the possible positions, and the next moment believing as confidently that it is in the other.

This instability in the judgment which reason pronounces on the testimony of the eye, in doubtful cases, is not of rare occurrence. Many have been struck with the difficulty of determining in which of two positions a flag or a vane is situated; and, therefore, in which of two widely different directions the wind is blowing. Of two observers at the same spot, one may affirm that it is in one position, while the other is equally sure that it is in the other position. The deception in regard to the direction of rotation, though a necessary consequence of the displacement in position, has not been so frequently observed, and has never, so far as I know, been explained. Suppose a wheel, whose plane of rotation is in a vertical plane nearly coincident with the axis of vision. What distinguishes a rotation in one direction

from a rotation in the opposite direction, except that, if, in one case, the edge nearest the eye is descending, in the other case it will be ascending? But the displacement which has been under discussion consists in an illusion as to the relative distances of the parts; those which are nearest being placed as if they were the most remote. If, therefore, in the true position, the nearest parts are ascending, in the fictitious position, the remote parts will be ascending, and hence the motion will appear as one in the opposite direction to the real one.

Prof. SNELL remarked that he had often noticed similar optical illusions. He thought that an uncertainty between two such positions. of the object, as would give the same projected figure, usually occur. red, where there was no decided light or shade falling upon it, to aid the observer. But on the other hand, if the observer was in any way deceived with regard to the direction in which the light came, instead of being in doubt, he would make a wrong judgment as to the position of the object or the nature of its surface. He then instanced the illusion in an inverting microscope, where the direction of the light being known, a raised surface is liable to appear depressed, and vice

versa.

Prof. HENRY stated that he had noticed the same illusion just before leaving home. Dr. Foreman and himself, endeavoring to ascertain the direction of the wind, referred for this purpose to the motion of a windmill near by; they disagreed as to the direction of its rotation. The phenomenon struck him as singular, but his mind at the time was much occupied with other subjects, and he did not attempt to make out the cause.

There is another illusion belonging to a similar class; I refer, said Prof. H., to the apparent motion of a body at rest, and the converse; this is an illusion of very frequent occurrence, but which I have not seen as minutely analyzed as might be desirable. I was led, a few years ago, to reflect upon the cause of it from this circumstance. Standing with two of my little girls, upon the edge of the canal basin, and looking down upon a boat gradually approaching the place on which we stood, I observed that suddenly the motion of the boat was apparently transferred to the wharf, and at the same instant each of the children exclaimed, Oh! I am moving. The question immediately occurred to my mind, why should these observers be subjected to this illusion at the same moment? What are the conditions necessary to produce this effect? The following hypothesis suggested itself as

the most plausible answer, namely: By long experience, the mind has acquired the habit of inferring without reflection, that when two bodies are relatively in motion, the real motion belongs to the smaller, and that the larger is at rest. It is not necessary to the effect, that one of the bodies should really be the larger, but that at the time it should occupy the larger portion of the field of view. Thus in the case of the boat; while it was at a distance, and occupied but a small part of the field of view, it was the smaller object, and with reference to the wharf appeared, as it was, in motion; but, when it came almost directly beneath the observers, so as to occupy the principal part of the field of view, and consequently the greater share of attention, it became the fixed body, and the wharf the moving one. То bring this hypothesis to the test, an experiment was instituted on the spot; a new position was taken in advance of the boat, and as it approached this, the same phenomenon was again exhibited; the wharf and the observer began to move; the eye was then gradually turned, so that the boat would occupy the smaller portion of the field of view, and the wharf became the larger object. The result was as I had anticipated. At a given position the motion of the latter instantly ceased.

It was observed, however, that there was a tendency in the mind to persist in its affirmation, if it may be so called, as to the motion. When the wharf once appeared to get into motion, the illusion did not vanish immediately when the boat became apparently the smaller body, but it required that the wharf should be considerably larger, before the effect was produced. In the same way, when the mind had concluded that the boat was the moving body, it required an interruption of the attention, together with a much greater apparent size of the boat, to transfer the motion to the wharf.

The illusion is most perfect, when the moving body occupies the whole space around the observer. Visiting, said Prof. H., a few months ago, the Observatory of my friend Mr. Hallowell, of Alexandria, the whole external covering of which, namely, the cylindrical sides and hemispherical dome was made to revolve, while I was within. The illusion in this case was so perfect, that without thought, I exclaimed "stop! I shall fall, and the instruments will be all deranged."

The same apparent transfer of motion may be produced in another way, depending however, on the same mental tendency. If we are in a car which is in a state of rest in a depot, after we have travelled