350 Transactions of the Society. 



case needs to be considered. For the " eye-point ' of the Micro- 

 scope coincides, practically, with the posterior principal focus of the 

 total system. With a hand-magnifier, however, the eye may 

 change its place to some extent, and the crossing-point of the 

 principal rays will therefore be subjected to deviations from the 

 posterior focus of the system. In regard to this more general 

 case the exact formula for determining the power of a system in 

 the manner indicated above is 



tanw* 1 /, d\ 1 Id 



7(-0=} 



h f\ • U f ' f 



in which I denotes once more the distance of distinct vision of the 

 observing eye, and d the deviation of the said crossing point, or 

 the place of the eye, from the posterior focus, (d must be intro- 

 duced with positive sign if the focus is behind the eye, and with 

 negative sign if it is in front.) 



According to this general formula the exact ratio of the visual 

 angle to the linear magnitude of the object is expressed by a 



principal term ( /- ), which is independent of all particular cir- 



cumstances, and an additional term ( -^ • y ) which varies with the 



position and the accommodation of the observer's eye. As in all 



d 

 practical cases y will be a small fraction, the additional term indi- 



cates merely a small correction, and this correction alone depends on 

 the distance of vision and the place of the eye. The simple 

 reciprocal of the focal length will therefore afford in all cases 

 a proper measure of the amplifying power of a lens-system, because 

 it expresses that component of the amplifying power which is 

 inherent in the system itself, and independent of the variable 

 circumstances under which it may be used. 



The other generally adopted expression of the power by N = -^ 



may be put on a somewhat more rational basis than is generally done, 

 by defining the length I (10 in.) not as " distance of distinct vision," 

 but rather as " distance of projection of the image." As far as 

 "distinct vision" is assumed for determining the amplification, the 

 value of N has no real signification at all in regard to an observer 

 who obtains distinct vision at 50 in. instead of 10 in., and in fact 

 many microscopists declare the ordinary figures of amplification to be 

 useless for them, because they cannot observe the image at the 

 supposed distance. It appears as if — and many have this opinion — ■ 

 the performance of the Microscope in regard to magnification 

 depended essentiallij on the accommodation of the observer's eye. 



