and if we join the point Δ″ thus found and c, the line Δ′c will be the united image of ac and bc, the binocular centre ranging from Δ″ to c, in order to see it as one line. In like manner, we may find the position and length of the image Δ‴c, Δ′c, and Δc, corresponding to the position of the eyes at e‴e and e. Hence all the united images of ac, bc, viz., cΔ‴, cΔ″, &c., will lie below the plane of abc, and extend beyond a vertical line ng continued; and they will grow larger and larger, and approximate in direction to cg as the eyes descend from e‴ to m. When the eyes are near to m, and a little above the plane of abc, the line, when not carefully observed, will have the appearance of coinciding with cg, but stretching a great way beyond g. This extreme case represents the celebrated experiment with the compasses, described by Dr. Smith, and referred to by Professor Wheatstone. He took a pair of compasses, which may be represented by acb, ab being their points, ac, bc their legs, and c their joint; and having placed his eyes about e, above their plane, he made the following experiment:—“Having opened the points of a pair of compasses somewhat wider than the interval of your eyes, with your arm extended, hold the head or joint in the ball of your hand, with the points outwards, and equidistant from your eyes, and somewhat higher than the joint. Then fixing your eyes upon any remote object lying in the plane that bisects the interval of the points, you will first perceive two pair of compasses, (each by being doubled with their inner legs crossing each other, not unlike the old shape of the letter W). But by compressing the legs with your hand the two inner points will come nearer to each other; and when they unite (having stopped the compression) the two inner legs will also entirely coincide and bisect the angle under the outward ones, and will appear more vivid, thicker, and larger, than they do, so as to reach from your hand to the remotest object in view even in the horizon itself, if the points be exactly coincident.”[38] 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.[39] 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 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 ab.
CHAPTER VII.
DESCRIPTION OF DIFFERENT STEREOSCOPES.
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.
Fig. 28.