820 SUMMARY OF CURRENT RESEARCHES RELATING TO 



the century, is still more inaccurate. It is of little importance, in order 

 to distinguish the details of an object, that its aerial image should be 

 much magnified, since it is so much the further from the eye, and so its 

 apparent diameter is diminished. It is the image on the retina which 

 should be magnified, and the effect of a lens will be measured by com- 

 paring the retinal images of the same object seen successively through 

 the instrument and by the naked eye. By following up this principle, 

 which had been previously grasped by Verdet and Guebhard, M. Monoyer 

 has obtained a general formula applicable to all optical instruments. 



Thus, taking the case of a simple lens represented by its principal 

 planes reduced to a single plane HK (fig. 110) at a distance d^ from 

 the nodal points of the eye united at the point 0, let P Q = ?/ be an 

 object situated perpendicularly to the optical axis of the eye at a 

 distance from the lens less than its principal focal length F H = /. Join 

 P and its image P' to 0, and prolong these lines as far as the retina ; 

 let a and a' be the angles which these rays make with the optic axis, and 

 let I and V be the distances of object and image from 0. Then if r 

 denote the amplifying power, G the magnification, and L' the inverse 

 of? 



r=^=|:.U^.^=GZL'; 

 a t y y '' 



i. e. the amplifying power of an optical instrument is equal to the 

 product of the magnification by the ratio of the distances of the eye 

 from the object and its image. In the case of the simple lens M. 

 Monoyer distinguishes several kinds of amplifying power. 



(a) Eelative amplifying power, corresponding to I = 1, i.e. com- 

 parison of the retinal images when the object is situated at an invariable 

 distance of 1 metre from the eye. 



We have then 



But 



r^ = GL'. (4) 



G = q'¥ (5) 



where ¥ = - and q' is the distance of the image from the second 

 principal focus ¥' and = V -}- f — d^. 

 . • . by substitution 



r, = (l'Jrf-d,)F. L' = F-f L'(l - d,¥). (6) 



This expression is identical with that which gives the dioptric power 

 ^jFL, of a binary system composed of two diopters of powers F and L'. 



In the case of the compound Microscope the dioptric power and focal 

 length are of opposite sign. Denoting these by $ and respectively, 

 we have 



Tr = _ ($_L'- d^^Jj'}. (7) 



Formula (6) serves to show the influence of accommodation ; for take 

 the case of the lens close to the eye and d^ < /; then the term 1 — d^F 

 is positive, and the amplifying power augments with L'. The accommo- 



