FOCOMETRY AND APERTOMETRY. 



341 



adjusted in its lower focal plane. The length S of this scale 

 projected into the upper focal plane of each objective was then 

 determined. This length for each lens was then divided into the 

 corresponding N.A. to obtain the N.A.-equivalent of 1 mm. of 

 the scale S. The average value (0"038) of the N.A.-equivalent 

 thus found was then multiplied by the length S to obtain figures 

 for comparison with those obtained by the apertometer. The 

 results are given in the above order in the first five columns of 

 the following table : — 



Finally, in the last column the results obtained by dividing the 

 length S by twice the focal length of the condenser are given. It 

 will be remembered that this method does not necessitate the 

 calibration of the condenser scale, and is therefore the simplest. 



For the ready determination of N.A.s by the method I have 

 described, 1 would suggest the nse of a glass disc fitting the stop- 

 ring and ruled in ^ mm. or I mm. squares on its upper surface 

 and ground on its lower. Such a disc, in addition to its use as a 

 scale, would also serve the purpose of the wire gauze, and render 

 unnecessary the special precautions as to lighting. 



A condenser, having been calibrated, should be marked with 

 the result. For example, the one used in the above experiments 

 would be marked " 1 mm. = 0-038 N.A." 



In conclusion, allow me to say a word as to the limitations 

 of the methods I have described. For general applicability 

 and accuracy throughout the whole range of N.A., that simple 

 and beautiful instrument — Abbe's apertometer — must stand 

 unrivalled. It represents, in my humble opinion, the ne plus 

 ultra of apertometers, but it is, unfortunately, expensive, 



