DISTANCE GIVEN BY BINOCULAR VISION. 



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 A B to diminish, the binocular centre will advance towards 

 G, and the length and inclination of the united images D C, D' C, &c., will diminish 

 also, and vice versa. If the distance R L (Fig. 2) 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 A B be invariable. 



While the eyes at E' are running along the lines A C, B C, let us suppose 

 them to rest upon the points a, b equidistant from C. Join a b, and from the point 

 #, where a b intersects G C, draw the line g E", and find the point d" from the 



formula q d" 9 -^ *", . Hence the two points a, b will be united at d", and when 



a b + K L 



the angle E" G C is such that the line joining D and C is perpendicular to G C, the 

 line joining d" C will also be perpendicular to G C, the loci of the points D" d" d' d 

 will be in that perpendicular, and the image D C, 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 A C B C ; but the points A, C, and all 

 the .other points of these lines, may be united by fixing the binocular centre 

 beyond A B. Let the eyes, for example, be at E" ; then if we unite A B when 

 the eyes converge to a point, A" (not seen in the figure), beyond G, we shall have 



G A" = T -pg-, and if we join the point A" thus found and C, the line A' C will 



\\ JL A 13 



be the united image of A C and B C, the binocular centre ranging from A" to C, in 

 order to see it as one line. In like manner, we may find the position and length of 

 the image A"' C, A' C, and A C corresponding to the position of the eyes at E"' E 

 and E. Hence all the united images of A C, B C : viz. C A'", C A", &c., will lie be- 

 lo\v the plane of A B C, and extend beyond a vertical line N B continued ; and they 

 will grow larger and larger, and approximate in direction to C G as the eyes de- 

 scend from E'" to M. When the eyes are near to M, and a little above the plane 

 of A B C, the line, when not carefully observed, will have the appearance of coin- 

 ciding with C G, but stretching a great way beyond G. This extreme case repre- 

 sents 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 A C B, A B being their points, A C B C 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 



