340 F. J. CHESHIRE ON SIMPLE METHODS OF 



in the first part of this paper. Then, since at any time 



S 

 the working N.A. of the condenser is equal to— -, it follows 



that the N.A.-equivalent of the scale is equal to the 

 reciprocal of twice the focal length. 



The first method is probably the best, especially if several 

 objectives of known N.A. are available, so that a mean value of 

 the N.A.-equivalent can be obtained. 



Now the eye-ring method requires the minimum amount of 

 auxiliary apparatus and on the whole probably gives the most 

 reliable results ; it is therefore to be preferred. In practice, then, 

 the N.A. of an objective should be determined as follows : — 



(1) Use as a light source the sky, or an illuminated sheet of 



gi-ound glass, at the principal focus of the bull's-eye, i.e., 

 in place of the ordinary flame. 



(2) Screw on the objective to be tested, insert the wire-gauze 



disc in the stop-ring, and the stop in the low-power eye- 

 piece. 



(3) Rack up the condenser until it practically touches the 



objective ; then, whilst viewing the eye-ring with a hand- 

 magnifier, rack back the condenser to the furthest point 

 at which the gauze is orthoscopically projected, i.e., to the 

 point at which the image is about to show waist-shaped 

 distortion. 



(4) Replace the gauze by the condenser scale and read off the 



length S projected. 



(5) Mutiply the length S by the N.A.-equivalent of the scale 



to obtain the N.A. of the objective. 



To determine whether this condenser-scale method is equally 

 reliable throughout the range of the N.A's of dry objectives, five 

 objectives were taken, ranging in N.A. from 026 to 0-90. The 

 N.A. of each was first determined by Abbe's apertometer in the 

 usual way. An Abbe's chromatic condenser, of a focal length of 

 13 '4 mm., as determined by the method described in the early 

 part of this paper, was then taken, and a | mm. scale carefully 



