94 



SUMMARY OF CURRENT RESEARCHES RELATING TO 



just over unity. If the lamp is set near the instrument, so that D is 

 small, the error may become 10 p.c. The lamp should be at least a foot 

 away when the error sinks to 1 or 2 p.c. 



Simple Method of Focometry and Apertometry.* — F. J. Cheshire 

 first shows how Abbe's method j" of determining the focal length of an 

 optical system can be conveniently applied to a Microscope objective. 

 The magnifying power of the objective is first determined with the 

 draw-tube pushed in. This may be done by placing a sheet of ground 

 glass on the top of the draw-tube, from which the eye-piece has been 

 removed, and then focussing and measuring the image of a stage- 

 micrometer upon it. The magnification M having been determined 

 by this or any other method, the draw-tube is then pulled out to its full 

 extent, and the magnification M again found. Let 8 equal the amount 

 of draw-tube extension, then the focal length / of the objective 



S 

 system = m /^Tm" 



The author also gives allied ways of determining the focal and 



yyl X K 



Fig. 14. 



Fig. 15. 



principal points of objectives, eye-pieces, &c, and optical tube-lengths. 

 His methods of apertometry depend upon the following theory : — In 

 tne case of an aplanatic Microscope objective (fig. 14), let a equal the 

 semi-angle of the maximum cone of light which it can take up from an 

 object in a medium of refractive index p, and let p equal the radius of 

 the disc of light in the upper focal plane. By a well-known equation, 



if/ equal the back or upper focal length, the N.A. = //. sin a =-?. Now 



consider the two lens-systems A and B (fig. 15) with a common focal 

 plane and parallel incident light. Further, suppose that each system is 

 spherically corrected for light converging to the common focal points. 

 The system B is 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 



r R R F 

 obviously be equal. Thus -7. = y or — = -j =a constant. The 



author describes how, by use of an Abbe's two-lens chromatic con- 

 denser and a disc of fine wire-gauze, he takes the necessary measure- 

 ments. He also gives a comparative table of N.A.'s of a series of 

 lenses obtained by Abbe's apertometer and by the above method. The 

 two sets of results closely agree. 



* Journ. Quekett Micr. Club, Nov. 1902, pp. 331-42 (6 figs.). 

 f This Journal, 1892, p. 427. 



