146 Transactions of the Society. 



quotient is the Working Ratio ; but in order to find the N.A. it is 



necessary to measure both the diameter of the eye-disc, corresponding 



to the entire back lens, in linear measure, and also to determine the 



magnifying power of the entire Microscope, either by projection, or 



by means of some convenient camera, the distance of the eye-disc to 



the paper, or screen, being 10 in. Then if B be the diameter of the 



back lens,* and e, that of the eye-disc for the full aperture, <£ being 



the focal length of the entire Microscope, and / that of the object 



glass, M being the magnifying power of the entire Microscope at a 



projection distance of 10 in., and m the initial magnifying power of 



the objective. The following relations between these quantities will 



subsist : 



10 10 e <f> m 



M = - ;OT = 7 ;and F = 7 = -; 



M" p 

 e = 2 N.A. <f> ; and B = 2 N.A./; so N.A. = =^. 



r j > 20 



The optical index = = 50 B. 



m 



All that is required, then, in order to find the N.A. is to multiply 

 the magnifying power of the complete Microscope by the diameter 

 of the eye-disc, corresponding to the full aperture, and divide the 

 product by 20. 



When the measurement of the eye-disc is made, it is important 

 that the back lens of the objective be either filled with light by the 

 substage condenser directly, or if, on account of insufficiency of 

 aperture in the condenser, that cannot be done, indirectly, by dispersed 

 light from a coarse diatom, or other suitable object, placed on the 

 stage. 



It therefore becomes a question of practical microscopy whether 

 to purchase an Apertometer or a Dynamometer. As an Apertometer 

 will only do the one thing, viz. measure the aperture of an object 

 glass, the preference will probably be given to the Dynamometer, 

 which, besides measuring the N.A., will measure either the Working 

 Ratio, or Working Aperture, and also is useful for many other 

 purposes. 



The Measurement of the Focus of a Lens. 



In the Journal for 1901, p. 126, a formula is given for finding 

 the true focal length of any objective, by the help of a reciprocal 

 table, without calculation, the magnifying power, at a projection dis- 

 tance of 100 in. from the micrometer to the screen, being known. 

 Another method of accomplishing the same object may be of interest. 



* In this article " Back lens " means of course the optical, and not the actual 

 back lens ; its diameter equals the Optical Index divided by 50. 



