312 Sir D. Brewster on the KnouoJedge of 



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 inclina- 

 tion of the optic axis 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 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 e(juidistant 



from C. Join a b, and from the point g, where a b intersects 



G C, draw the line g E", and find the point d" from the 



„ . ,,, gYJ'y.ab . , .,, , 



lormula o- a"=^-; — ^tt-. Hence the two ponits ab will be 



united at d", and when 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 

 AC, 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" = -j5-j Tjx'' 



and if we join the point A" thus found and C, the line A' C 

 will 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 below the plane of A B C, and 

 extend beyond a vertical line N B continued ; and they will 



