Fig. 43.
Let L, R, [Fig. 43], be the left and right eye, and A the middle point between them. Let MN be the plane on which an object or solid whose height is CB is to be drawn. Through B draw LB, meeting MN in c; then if the object is a solid, with its apex at B, Cc will be the distance of its apex from the centre C of its base, as seen by the left eye. When seen by the right eye R, Cc′ will be its distance, c′ lying on the left side of C. Hence if the figure is a cone, the dissimilar pictures of it will be two circles, in one of which its apex is placed at the distance Cc from its centre, and in the other at the distance Cc′ on the other side of the centre. When these two plane figures are placed in the stereoscope, they will, when combined, represent a raised cone when the points c, c′ are nearer one another than the centres of the circles representing the cone’s base, and a hollow cone when the figures are interchanged.
If we call E the distance between the two eyes, and h the height of the solid, we shall have
| AB : h = | E | : Cc, |
| 2 |
| and Cc = | hE | or, | 5h | , |
| 2AB | 4AB |
which will give us the results in the following table, E being 2½, and AC 8 inches:—
| Height of object. | AB = AC - h | Cc |
|---|---|---|
| BC = h | Inches. | |
| 1 | 7 | 0.179 |
| 2 | 6 | 0.4166 |
| 3 | 5 | 0.75 |
| 4 | 4 | 1.25 |
| 5 | 3 | 2.083 |
| 6 | 2 | 3.75 |
| 7 | 1 | 8.75 |
| 8 | 0 | Infinite. |
If we now converge the optic axes to a point b, and wish to ascertain the value of Cc, which will give different depths, d, of the hollow solids corresponding to different values of Cb, we shall have
| Ab : | E | - d : Cc′, |
| 2 |
| and Cc′ = | dE | , |
| 2AB |