206 



Transactions of the Society. 



X 



yB 



The divergence of the deli- 

 neating pencils at an optical 

 image is always reduced, in com- 

 parison to the divergence of the 

 incident rays at the object, in 

 proportion to the linear ampli- 

 fication of that image. Although, 

 therefore, the angle between the 

 lines of perspective (r, I) in the 

 case of microscopic vision is very 

 small only, there is no other 

 element which can account for a 

 different perspective of the images 

 obtained through opposite por- 

 tions of the aperture.! 



t It may, at first sight, appear sur- 

 prising, that the very slight angle of 

 perj-pective, which is allowed for the 

 microscopic image, should be competent 

 to exhibit an appreciable difference of 

 projection. But it must be noted that 

 the solid image depicted by an optical 

 system is by no means similar to the 

 solid object. The amplification of the 

 depth varies always with the square of 

 the lateral amplification; therefore an 

 extra amplification of the depth is ob- 

 tained, which increases exactly in the 

 eame degree as the divergence of the 

 delineating pencils decreases. Owing to 

 this general feature of optical action, the 

 small divergence of the emergent rays, 

 r, I must produce, in the projection of 

 the distorted image, parallactic displace- 

 ments of the same amount as would result 

 from the original divergence of the inci- 

 dent rays K, L, in an image of uniform 

 amplification. 



Let S and 5* denote the axial dis- 

 tances of consecutive planes in the object 

 and image (S = a ... 6, S* = a* ... 6* in 

 Fig. 37), n and n* the refractive indices 

 of the media at object and image, N 

 and M the linear amplification of the 

 two images at a* and 6*, we have quite 

 in general and in perfect strictness, for 

 every kind of optical system, and every 

 position of object and image, 



S* 



and this gives 



NM; 



