98 THE MICROSCOPE. 



ture, however, which prevents all this confusion. This is known as 

 the numerical aperture. i8o c in air is taken as the unit, and when 

 an immersion objective has an angular aperture greater than 82' as 

 measured in balsam, it is expressed as a certain amount more than 

 this unit. By the numerical system the amount of light which 

 passes through the back lens of the objective is considered, as com- 

 pared with the focal length (magnifying power), and no attention is 

 paid to the direction of the light as it enters the front. That is to 

 say, with an objective of .given power a certain definite acting sur- 

 face must be given to the back lens, to give it an angular aperture 

 whose numerical expression shall be i - og — corresponding, as before 

 stated, to i8o r ' in air or 82 ° in balsam; and with an increase in the 

 acting diameter of the back lens above what is required for the 

 numerical value of i - oo. (The magnifying power remaining the 

 same) the numerical value is increased accordingly. 



Professor Abbe has shown that the numerical aperture may be 

 obtained by multiplying the sine of half the angular aperture by the 

 mean refractive index of the fluid in front of the front lens— be it 

 air or some immersion fluid. This necessitates the correct measure- 

 ment of the angular aperture; and as means for this purpose are not 

 embodied in every microscope stand, it is sometimes, to say the 

 least, inconvenient. 



For some time past I have made use of a method which, in its 

 practical application, I think is somewhat new. It is by accurately 

 measuring the acting diameter of the back lens when the full aper- 

 ture is in use, and also when only the numerical equivalent of 180 

 air is used. Then, by dividing the former by the latter, the numer- 

 ical aperture is obtained. The practical operation is as follows: 



A low power objective — a three or four inch is convenient for 

 the purpose — is to be screwed to the .microscope and the latter 

 placed in a horizontal position. The objective to be measured is 

 now to be screwed into the substage with its front from the stage, 

 the mirror having been removed. If the microscope be properly 

 focused, a bright circle of light will be seen, which is the acting 

 diameter of the back lens for 180 air=N. A. i-oo. The camera 

 should now be slipped upon the eye-piece and the diameter of this 

 circle marked upon a piece of paper. A hemispherical lens is now 

 to be placed in front of the objective being measured, which should 

 have immersion contact with it. This will enlarge the bright circle 



