FOCOMETRY AND APERTOMETRY. 



336 



positions of the focal and principal planes of an eyepiece can be 

 similarly determined with respect to the flange of the eye-lens, 

 which rests upon the top of the draw-tube. If, then, the 

 mechanical tube-length L is known, the distance d of the upper 

 focal plane of the objective below, say, the flange, and the 

 distance d} of the lower focal plane of the eyepiece below the 

 flange of the eye-lens, it is obvious that the optical tube-length, 

 i.e., the distance between the upper principal focus of the objec- 

 tive and the lower principal focus of the eyepiece, must be equal 

 to L -f cZ — d^. 



Apertometry. 



The methods of apertometry which I am about to describe are 

 based upon the use of a condenser scale, in the way, I believe, 

 first suggested by myself, and very briefly described by Mr. 

 Angus in the last number of this Jourmd {ante, p. 211). I have 



■F/G 2. 



F/G.3.- 



during the last few months been working at the method with a 

 view of determining its limitations, and the precautions to be 

 observed to ensure the most accurate results. To understand 

 and appreciate these, it will be necessary for us to consider for 

 a moment the theory of the method. 



In the case of an aplanatic microscope objective (Fig. 2), let 

 a equal the semi-angle of the maximum cone of light which it 

 can take up from an object in a medium of refractive index /x, 

 and let p equal the radius of the disc pf light in the upper focal 

 plane. B}'^ a well-known equation, if / equal the back or upper 

 focal length, the numerical aperture is obtained from 



N.A. = /x sina = ^ 



Now let us consider two such lens systems A and B (Fig. 3), with 

 a common focal plane and parallel incident light. Further, let 

 us suppose that each system is spherically corrected for light 



