818 



Transactions of the Societij. 



so that if we had an objective of l-8th in. and an eye-piece of 2 in. 

 the focal length of the Microscope 



/ = 



X 2 

 10 



2 



40 



A Microscope of a focal length of l-40th in. would magnify 

 400 times, so that if this method of arriving at the focal length of 

 the Microscope were correct, we should only have to multiply the 

 power of the (l-8th in.) objective (80) by that of the (2 in.) eye-piece 

 (5) to have the total magnifying power (400), the brass tube being 

 assumed to be constant at 10 in. 



The fallacy of this method lies in the fact that the true formula 

 is not 



10 ' 



/ = 



but 



^ A 



Fig. 154. 



A heingi the distance hetween the ])osterior principal focal plane 

 of the objective, and the anterior -principal focal plane of the eye- 

 p)iece, or, as Professor Abbe terms it, the 

 rational or optical tube-length, in contradis- 

 tinction to the mechanical or physical length.* 

 The accompanying fig. 154, where F^ is 

 the posterior focal plane of the objective and 

 F^ the anterior focal plane of the eye-piece, 

 will illustrate this more clearly. 



As A is the divisor of the fraction which 

 represents the focal length, the latter is of 

 course larger or smaller accordiug as A is 

 smaller or larger, that is, it varies inversely 

 as A ; and as the magnifying power is in- 

 versely to the focal length, the magnifying 

 power varies directly as A, which is therefore 

 seen to be a fundamental factor of microscopic 

 amplification. 



We can now see how it is that two ob- 

 jectives of the same focal length may yet give 

 difi'erent magnifying powers with the same 

 tube and eye-piece. By the different methods 

 of construction adopted by their makers, the 

 focal plane of the one objective may be further 

 off" the back lens than is the case with the 

 other. The distance A between the focal 

 planes of the objective and eye-piece will be correspondingly 



* The principal focal planes are the planes passing through the point on the 

 axis jn which parallel raya coming from the opposite side of the lens are brought 

 to a focus. " Anterior " and " posterior " are used in reference to the direction 

 in which the raya come to the observer. 



