688 SUMMARY OF CURRENT RESEARCHES RELATING TO 



whatever may he the composition and focal length of the system, and in 

 whatever position A and B and their images may he supposed. 



The quotient on the left-hand side of this equation expresses the 

 axial amplification of a solid object extending from A to B, and shows 

 this axial amplification (or the amplification of the depth) to be pro- 

 portionate to the product of the lateral amplifications of the extreme 

 layers of the object (or to the square of the geometrical mean of those 

 amplifications). 



If A and B are situated on the same side of the principal focus of 

 the system (both in front and both behind), and their distance $ is 

 taken shorter and shorter, the value of M must approach more and 

 more to N, and the formula will give 



and 



if the medium at the back of the system is air (n* = 1), as is the case 

 with the Microscope. 



Though the above general proposition has not yet been recorded, 

 the fact that the axial amplification increases for short distances with 

 the square of the lateral amplification has been noticed by various 

 writers. The influence of this marked feature of optical delineation 

 on the performance of optical instruments has not, however, been 

 previously pointed out. 



(2) The depth of accommodation (a) in microscopical vision depends 

 on the range of accommodation of the observer's eye in direct vision. 

 If S denotes the longest and s the shortest distance of distinct vision 

 for a given eye, the range of accommodation is strictly defined by the 

 expression 



1 1 

 s-S = ^- 



If, now, the equivalent focal length of an optical system is = /, 

 and the object is in a medium of refractive index w, the absolute 

 depth of the object which is embraced by the accommodation is 



If N is the linear amplification of a virtual image projected by the 

 system at a distance L from its posterior principal focus (which in 

 the case of the Microscope is the " eye-point " above the eye-piece), we 

 have 



and therefore 



« ='" (nX 



