336 F. J. CHESHIRE ON SIMPLE METHODS OF 



converging to the common focal point. The system B i» shown 

 transmitting a cone of light of greater N.A. than the system A 

 can take up. The effective and equivalent semi-apertures are 

 R and r respectively, and for these the N.A's must obviously 



be equal, thus : — 



r ^ R 



R F 



or — = — = a constant. 



'• / 

 In other words, any ray passing through the system will pass 

 through the outer or posterior focal planes at distances from 

 the axis having a constant ratio. It follows from this, that, 

 if by means of a stop in the common focal plane the image- 

 forming rays are restricted to those which upon incidence are 

 practically parallel to the axis, a number of equidistant parallel 

 lines, such as a scale, in one posterior focal plane will be 

 projected as equidistant parallel lines— i.e., orthoscopically— 

 in the other. Now let us suppose that F is known, and 

 that a scale is placed in the focal plane R. Then to deter- 

 mine the N.A. of the lens A, it would only be necessary 

 to examine in its focal plane r the image of the scale at 

 R, and to read off the length projected, say 2R, as a 

 diameter of the disc of light seen. Since the N.A. of the lens 



A = - = 5, it could thus be obtained by dividing the length 



/ F 

 2R by twice the focal length F. 



Now, given a sub-stage condenser spherically corrected for its 

 principal focus, it is obvious that this method could be carried 

 out practically by placing a scale of length accurately in the 

 lower focal plane, which should be that of the stop-ring,* 

 and projecting it into the upper focal plane of an objective. 

 Unfortunately, however, those condensers (achromatic) in which 

 this correction is best made have a virtual lower focus, at which 

 it is therefore impossible, physically, to place a scale. It is 

 a remarkable and fortunate fact, however, that by adjustment 

 of the axial distance between the condenser and the objective, 

 Abbe's two-lens chromatic condenser can in general be made 



* This is important, because otherwise the magnification would vary with 

 the axial distance between the objective and condenser. 



