FOCOMETRY AND APERTOMETRY. 339 



method the length can be read off directly and simply with a 

 powerful hand-magnifier, such as a X 16. Whichever method is, 

 however, adopted, it is of the utmost importance that the apex of 

 the cone of light entering the objective should be sharply defined, 

 for reasons fully set out by Abbe in his paper on Apertometry 

 published in the Journal Roy. Mic. Sac, 1880. This may be 

 done in the back-focus method by fitting the auxiliary objective 

 with a small stop, just within its back-focus, as is done by Zeiss 

 in the objective he supplies for use with the apertometer. In the 

 eye-ring method it can be done in a more simple, but not less 

 elfective way, by dropping a small stop of a diameter of about 

 3 mm. into the eyepiece, so as to be at the principal focus of the 

 eye-lens. In whichever position the stop is placed its projected 

 image functions as the stop shown in Fig. 3. By both methods 

 the determination is very much facilitated by completely filling 

 the objective with light. This can easily be done, even when 

 using Abbe's chromatic condenser, by using as a source of light 

 either (1) the sky, or (2) a strongly illuminated sheet of ground 

 glass at the principal focus of the bull's-eye. 



Calibration of the Condenser Scale. — In whatever way the 

 length of the condenser scale projected is found, a determination 

 of the N.A.-equivalent of 1 mm. of that scale should have been 

 previously made. This may be done by one of the three following 

 methods : — 



I. Use an objective of known N.A. to project the condensei- 

 scale in the way, and with the precautions already de- 

 scribed. The length S divided into the known N.A. gives 

 the N.A.-equivalent to be found. 



II. Hest a cover-glass on the top lens of the condenser. Lower 

 an immersion lens, with oil between as usual, on to the 

 cover-glass. Adjust for the critical image of the gauze 

 with the fine adjustment. Under these conditions a thin 

 layer of air is left between the cover-glass and the con- 

 denser, the N.A. of which is thus cut down to I'O. The 

 N.A.-equivalent to be found must therefore equal the 

 reciprocal of the length S. 



III. Find the focal length /of the condenser in the way described 



