M. A. AINSLIE ON A VARIATION OF CHESHIRE'S APERTOMETER. 28i> 



(H for each radial line passed over ; the second figure is found by 

 estimating the position between two adjacent radial lines of the 

 point where the spiral cuts the margin of the back lens. In 

 tig. 8, for example, the N.A is about - 73. 



The procedure is the same with the form suited to immersion 

 lenses ; the upper surface of a plate of glass is focused, and the 

 diagram is balsamed to the lower surface. It might be pre- 

 ferable to have 12 radial lines instead of 16, and read like 

 a clock ; this is a matter for experiment. 



Of course the value of the radius vector of the curve for 

 a diagram in optical contact with glass will not be quite the 

 same as before ; instead of r = C tan <, where sin < = N, we 



8 



Fig. 8. 



shall have r = C tan <' where /x sin <' = N\ but the principle 



is the same. 



The equation to the curve presents some interesting features; 



aO 



where C is the distance of the diagram 



it is r = Cr_ 



V 1 a 2 2 



from the lower focal plane of the objective and a is a constant 

 depending on ll and on the number of radial lines in the circle ; 



for 16 radial lines, and /x = 1 (dry form), a = ^ . The radius 



representing N.A. = I/O is obviously an asymptote to the curve ; 

 in the case of the glass form, N.A. = /x will be the asymptote. 



It is of interest to note that the same curve will serve for any 

 refractive index of the medium beneath which it is mounted : if 



