448 Sir David Brewster on the Law of Visible Position 



side DB under the much smaller angle BLD; the apparent 

 magnitude being in the one case A' C, and in the other D B'. 

 In like manner, the right eye R sees D B under the large 

 angle BRD, and with an apparent magnitude D V ; while it 

 sees A C under the smaller angle ARC, and with an apparent 

 magnitude Co.'. Hence it follows, that, with both eyes, we 

 shall see the solid in perfect symmetry, with its summit C D 

 concentric with AB; and hence the reason is obvious why 

 the two dissimilar pictures in the retina give a resultant pic- 

 ture corresponding with the solid itself. 



Quitting our solid frustum of a cone, let us now suppose 

 that its two dissimilar projections A BCD, 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 A B, a b at the base, can be united only 

 by converging the optical axes to M, and the summit circles 

 CD, cD only by converging the axes to N. Hence mnop 

 will represent the solid frustum of a cone, whose axis is M N. 

 Now, all the rays which flow from any point of the two pro- 

 jections A B, 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 m n op. 



In order to see the base m n t the optic axes must be con- 

 verged 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 M N is so very small, that the whole out- 

 line mnop will be seen with great distinctness; though it is 

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



The height MN of the cone, fig. ] 8, is = cot± A -coti A', 

 A, A' being the angles of the optic axes LMB, L N R, and 

 O L or O It radius. But as these angles are not known, we 

 may find MN thus: — Let D = distance OP; d = Ss, the di- 

 stance of the two points united at M; d = S's', the distance 

 of the two points united at N ; C = L R = 1\ inches. Then 



MP-™; NP= M,; „„dMN = ^-j^, 

 C + d C + d' C + d C + d 



When the two figures are united by converging the axes be- 

 yond P, the base mn of the line will be nearest the eye; and 

 consequently the cone will appear hollow. In this case, 



M if - C _^ J* * - C -d' C-d C-d" 



and the cone will be much larger than in the other case. If 

 we make 



