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in the horizon itself, if the points be exactly coincident." 1 Owing to his imperfect apprehension of the nature of this phenomenon, Dr. Smith has omitted to notice that the united legs of the compasses lie below the plane of ABC, and that they never can extend further than the binocular centre at which their points A and B are united.

There is another variation of these experiments which possesses some interest, in consequence of its extreme case having been made the basis of a new theory of visible direction, by the late Dr. Wells.2 Let us suppose the eyes of the observer to advance from E to N, and to descend along the opposite quadrant on the left hand of NG, but not drawn in Fig. 27, then the united image of AC, BC Will gradually descend towards CG, and become larger and larger. When the eyes are a very little above the plane of ABC, and so far to the left hand of AB that CA points nearly to the left eye and CB to the right eye, then we have the circumstances under which Dr. Wells made the following experiment :- "If we hold two thin rules in such a manner that their sharp edges (AC, BC in Fig. 27) shall be in the optic axes, one in each, or rather a little below them, the two edges will be seen united in the common axis, (Gc in Fig. 27;) and this apparent edge will seem of the same length with that of either of the real edges, when seen alone by the eye in the axis of which it is placed." This experiment, it will be seen, is the same with that of Dr. Smith, with this difference only, that the points of the compasses are directed towards the eyes. Like Dr. Smith Dr. Wells has omitted to notice that the united image

1 Smith's Opticks, vol. ii. p. 388, § 977.
2 Essay on Single Vision, &c., p. 44.

rises above GH, and he commits the opposite error of Dr. Smith, in making the length of the united image too short.

If in this form of the experiment we fix the binocular centre beyond c, then the united images of AC, and BC descend below GC, and vary in their length, and in their inclination to GC, according to the height of the eye above the plane of ABC, and its distance from A B.



ALTHOUGH the lenticular stereoscope has every advantage that such an instrument can possess, whether it is wanted for experiments on binocular vision-for assisting the artist by the reproduction of objects in relief, or for the purposes of amusement and instruction, yet there are other forms of it which have particular properties, and which may be constructed without the aid of the optician, and of materials within the reach of the humblest inquirers. The first of these is

1. The Tubular Reflecting Stereoscope.

In this form of the instrument, shewn in Fig. 28, the pictures are seen by reflexion from two specula or prisms placed at an angle of 90°, as in Mr. Wheatstone's instrument. In other respects the two instruments are essentially different. In Mr. Wheatstone's stereoscope he employs two mirrors, each four inches square-that is, he employs thirty-two square inches of reflecting surface, and is therefore under the necessity of employing glass mirrors, and making a clumsy, unmanageable, and unscientific instrument, with all the imperfections which we have pointed out in a preceding chapter. It is not easy to understand why mirrors of such

a size should have been adopted. The reason of their being made of common looking-glass is, that metallic or prismatic reflectors of such a size would have been extremely expensive.

It is obvious, however, from the slightest consideration, that reflectors of such a size are wholly unnecessary, and that one square inch of reflecting surface, in place of thirtytwo, is quite sufficient for uniting the binocular pictures. We can, therefore, at a price as low as that of the 4-inch glass reflectors, use mirrors of speculum metal, steel, or even silver, or rectangular glass prisms, in which the images are obtained by total reflexion. In this way the stereoscope becomes a real optical instrument, in which the reflexion is made from surfaces single and perfectly flat, as in the second reflexion of the Newtonian telescope and the microscope of Amici, in which pieces of looking-glass were never used. By thus diminishing the reflectors, we obtain a portable tubular instrument occupying nearly as little room as the lenticular stereoscope, as will be seen from Fig. 28, where ABCD is

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a tube whose diameter is equal to the largest size of one of the binocular pictures which we propose to use, the lefteye picture being placed at CD, and the right-eye one at AB. If they are transparent, they will be illuminated through paper or ground glass, and if opaque, through openings in the tube. The image of AB, reflected to the left eye L from the small mirror mn, and that of CD to the right eye R

from the mirror op, will be united exactly as in Mr. Wheatstone's instrument already described. The distance of the two ends, n, p, of the mirrors should be a little greater than the smallest distance between the two eyes. If we wish to magnify the picture, we may use two lenses, or substitute for the reflectors a totally reflecting glass prism, in which one or two of its surfaces are made convex.1

2. The Single Reflecting Stereoscope.

This very simple instrument, which, however, answers only for symmetrical figures, such as those shewn at A and B, which must be either two right-eye or two left-eye pictures, is shewn in Fig. 29. A single reflector, MN, which

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may be either a piece of glass, or a piece of mirror-glass, or a small metallic speculum, or a rectangular prism, is placed

We may use also the lens prism, which I proposed many years ago in the Edinburgh Philosophical Journal.

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