396 OBJECTIVES, EYE-PIECES, THE APERTOMETER 



= 00 = n ; sine 60 = '866 (by the tables) ; n = 1-52 ; H' = 1-615 ; 

 it sine u = n' sine u' = 1*01") x '8(50 = 1-4, which is the X.A. 

 required. 



n' sine u' 1-615 X "86(5 



(vi) Again, sine n = = = '92. 



?, 1'52 



// = 67 (by the tables), 2n = 134, the angle required. 



It is manifest that if the refractive index of the apertometer 

 equals that of the oil of cedar, the mean angle measured is the semi- 

 angle of aperture of the objective, and its sine multiplied by that 

 retractive index is the numerical aperture. 



This will l)e found the more accurate and universally applicable 

 method of measuring the apertures of objectives, as the extinction 

 of the light shows precisely when the limit of aperture is reached. 



Powell and Lealand's stands lend themselves admirably for use 

 with the apertometer. The body being removable, the lens can be 

 placed in the upper part of the nose-piece, and any measurement 

 can be accurately made. We would advise every microscopist to 

 master the use of this admirable instrument, and to demonstrate for 

 himself the aperture capacity of his lenses, that he may know with 

 precision their true resolving powers. It will facilitate this that 

 Mr. Nelson has shown ( Journ. R.M.S.' 1896, p. 592) that the use of 

 the internal lens is not required ; the point of rotation of the stage 

 when the edge of the flame is eclipsed by the limiting aperture of 

 the objective can be readily observed by means of a low-power eye- 

 piece. 



When the apparatus is accurately set up in the manner described 

 above, the exact point is indicated by the dark segments coming 

 across the field of the eye-piece. One dark segment will be found to 

 advance slowly from one side, and then when the precise point of 

 rotation of the stage is reached the other dark segment will come in 

 from the other side and meet it. For this purpose the glass disc 

 with its refractive index only engraved upon it is alone required. 

 Messrs. Zeiss supply this at a much lower cost (25s.) than the 

 engraved disc and the supplementary lens. 



Boucher's circular slide rule is a convenient adjunct to the 

 apertometer, for the N.A. can be read off by inspection without the 

 necessity of looking out sines or making calculations. 



