350 F. J. CHESHIRE ON A METHOD OF USING ABBE's APERTOMETER. 



microscope, the flame at L will be seen until light from it passes 

 along the line OB, that is, until the point L' coincides with L. 

 Fiom the figure it is obvious that this will be the case when the 

 apertometer has been turned through the angle a', which is equal 

 to the true aperture angle a plus the small angle /8. The angle 

 read off on the stage, therefore, will always be in excess of the true 

 angle by the angle p. 



Now sin (i — 



d sin a 



(1) 



Where d equals the length 00'. 



Since the real numerical aperture (N.A.) equals /x sin a, and 

 the found (N.A.^) equals fx sin (a +^). 



N.A.^ _ sin (a + y8) _ sin a cos ^ + cos a sin /? 



IN.A. sin a 



^ , . /^cos a 



= cos p + sin « 



sin a 



sin a 



(2) 



