The stereoscope

by David Brewster

This takes place when

Cos. A =	gc	.
	go

When o coincides with c, the images cd, cd′, &c., will have the same positions and magnitudes as the chords of the altitudes a of the eyes above the plane gc. In this case the raised or united images will just reach the perpendicular when the eye is in the plane gcm, for since

GC = GO, Cos. A = 1 and A = 0.

When the eye at any position, e″ for example, sees the points a and b united at d″, it sees also the whole lines ac, bc forming the image d″c. The binocular centre must, therefore, run rapidly along the line d″c; that is, the inclination of the optic axes must gradually diminish till the binocular centre reaches c, when all strain is removed. The vision of the image d″c, however, is carried on so rapidly that the binocular centre returns to d″ without the eye being sensible of the removal and resumption of the strain which is required in maintaining a view of the united image d″c. If we now suppose ab to diminish, the binocular centre will advance towards g, and the length and inclination of the united images dc, d′c, &c., will diminish also, and vice versa. If the distance rl ([Fig. 26]) between the eyes diminishes, the binocular centre will retire towards e, and the length and inclination of the images will increase. Hence persons with eyes more or less distant will see the united images in different places and of different sizes, though the quantities a and AB be invariable.

While the eyes at e″ are running along the lines ac, bc, let us suppose them to rest upon the points ab equidistant from c. Join ab, and from the point g, where ab intersects gc, draw the line ge″, and find the point d″ from the formula

gd″ =	gE″ × ab	.
	ab + RL

Hence the two points a, b will be united at d″, and when the angle e″gc is such that the line joining d and c is perpendicular to gc, the line joining d″c will also be perpendicular to gc, the loci of the points d″d″, &c., will be in that perpendicular, and the image dc, seen by successive movements of the binocular centre from d″ to c, will be a straight line.

In the preceding observations we have supposed that the binocular centre d″, &c., is between the eye and the lines ac, bc; but the points a, c, and all the other points of these lines, may be united by fixing the binocular centre beyond ab. Let the eyes, for example, be at e″; then if we unite a, b when the eyes converge to a point, Δ″, (not seen in the Figure) beyond g, we shall have

GΔ″ =	GE × AB	;
	RL - AB