622 SUMMAKY OF CURKENT RESEARCHES RELATING TO 



with different tube-lengths will be necessary to determine both. Two- 

 such observations give us two equations : 



II. M, = {A'F^f) 

 M, = (A'-^F-h/) 



and subtracting the second from the first we obtain 



Ml - M, = (Ai A2 -i-/) 



which, transposed and put into ordinary language, means that the 

 equivalent focus of the objective is equal to the increase of tube-length 

 between the two experiments divided by the resulting increase of 

 magnification of the primary image. 



The equivalent focus having thus been determined, it can be intro- 

 duced into one of the equations II. ; for instance, the first of them ; and 

 will then determine the distance A^ F = M^ x /; and the position of A. 

 having been measured off in the manner suggested above, it is a simple 

 matter to lay off the length A^ F, and thus to determine the point F 

 usually described as the position of the upper focal plane of the 

 objective. 



In the experiments shown at the demonstration, an 8 mm. Holos 

 objective was employed with a short tube-length. It was found' 

 that one space of -^^ mm. of the stage micrometer covered 18 • 6- 

 similar spaces in the eye-piece micrometer. When the tube had been 

 lengthened by 73 mm., it was found that one space of the stage- 

 micrometer now covered 28 spaces of the eye-piece micrometer. An 

 increase of tube-length of 73 mm. had therefore produced an in- 

 crease of magnification of 9 • 4 times ; and on dividing the first number 

 by the second, according to the above rule, the equivalent focus of the 

 objective is found to be 7'8 mm. Multiplying the latter figure by the 

 magnification found in the second measurement, it was found that the 

 upper focal plane lay 217 mm. below the eye-piece micrometer, and 

 making the measurement suggested above, this led to fixing the upper 

 focal plane itself at a position 14 mm. below the shoulder of the standard 

 screw. It should be mentioned that when Professor Abbe introduced 

 his system of nomenclature when bringing out the apocbromatic 

 objectives, the angular magnification assigned to the compensating eye 

 pieces was based on the assumption that the upper focal plane of the 

 objectives should He 32 mm. below the shoulder of the standard screw. 

 It follows, therefore, that if the position of the upper focal plane differs 

 from this, as indeed it does in the case of the above 8 mm. Holos 

 objective, the magnification obtained according to Abbe's rule by 

 multiplying the initial power of the objective into the angular magnifi- 

 cation of the eye-piece will give a wrong result, and to compensate for 

 this, opticians occasionally purposely mis-state the equivalent focus of 

 objectives in order that the magnification determined by Abbe's method 

 may come out approximately correct. Thus, in the case of our example, 

 it would appear at first sight as if the objective, being of 7*8 mm. focus 

 instead of 8 mm., would magnify about 2| per cent, too much. As a 

 matter of fact, this is heavily over-compensated ])y the circumstance 

 that its upper focal plane lies 18 mm. higher than Abbe's assumed 



