362 SIR DAVID BREWSTER ON THE LAW OF VISIBLE POSITION 



solidity. When we view the cone with both eyes, we have the same indistinct- 

 ness of outline when the optic axes are converged to a single point : but in addi- 

 tion to this, we have the greater indistinctness arising from every point of the 

 figure being seen double, except the single point to which the axes are converged. 

 But this imperfection, too, is scarcely visible, from the rapid view which the eyes 

 take of the whole solid, converging their axes upon every point of it, and thus 

 seeing each point in succession single and distinct. Hence, we must draw a 

 marked distinction between the vision, of the solid (as an optical fact) when the 

 eyes are fixed upon one point of it, and the resultant perception of its figure ari- 

 sing from the union of all the separate sensations received by the two eyes. 



Let ABCD, fig. 16, be the solid frustum of a cone, having its axis MN pro- 

 duced, bisecting at the distance LR between the two eyes L,R. Draw AL, AR, 

 BL, BR ; and also CL, CR, and DL,DR. Then, if we look at this solid with the 

 left eye L only, the projection of it will be as shewn in fig. 17 at ABCD, and in 

 fig. 16 at A'B'CD ; AC being much greater than DB, and the summit-plane CD 

 appearing on the right-hand side of the centre of the base AB. The reason of 

 this is obvious from fig. 16, where the left eye L sees the side AC under the angle 

 ALC, Avhile it sees the other side DB under the much smaller angle BLD ; the 

 apparent magnitude being in the one case A'C, and in the other DB'. In like 

 manner, the right eye R sees DB under the large angle BUD, and with an appa- 

 rent magnitude D V ; Avhile it sees AC under the smaller angle ARC, and with an 

 apparent magnitude C a'. Hence it follows, that, with both eyes,, we shall see the 

 solid in perfect symmetry, with its summit CD concentric with AB ; and hence 

 the reason is obvious why the two dissimilar pictures in the retina give a resultant 

 picture corresponding with the solid itself. 



Quitting our solid frustum of a cone, let us now suppose that its two dissimi- 

 lar projections ABCD, abed, fig. 17, are united by the two eyes L,R, converging 

 their axes to a point nearer the observer. By drawing lines from A,B,C,D, a, b, c, d, 

 to L and R, the centres of visible direction, it will be seen that the circles AB, a b at 

 the base, can be united only by converging the optical axes to M, and the summit 

 circles CD, c D only by converging the axes to N. Hence, mnop will represent 

 the solid frustum of a cone, whose axis is MN. Now. all the rays which flow from 

 any point of the two projections AB, a b, cross each other at the figure mnop; 

 and, consequently, this figure is seen by both eyes in identically the same manner 

 as if the rays which really emanate from the plane figures had emanated from 

 their points of intersection, that is, from the outlines of the solid figure mnop. 



In order to see the base m n, the optic axes must be converged to M, or any 

 other point of the base ; and in order to see the summit op distinctly, the axes 

 must be converged to N. But the distance MN is so very small, that the whole 

 outline mnop will be seen with great distinctness ; though it is certain that 

 every point of it, but one, is seen double. 



