ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 



451 



In the formula, therefore, for the magnifying power of the Micro- 

 scope as a whole 



250 A 



N = 



/<?> 



(/ and being the focal lengths of the objective and ocular re- 

 spectively), N is in the one case 17 • 8 and in the other 31 • 3, assuming 

 (p to be 25 mm. 



Those who are interested in optical formulse may like to have 

 before them the method by which (1) the focal length of the objective 

 and (2) the distances of its posterior focal plane are determined, accord- 

 ing to the improved methods of Prof. Abbe, of which we hope to give 

 a more detailed account later. 



(1) To determine the focal length/ of the combination, we require 

 to know only the focal lengths /i and /j of the two lenses, and the 

 position of their anterior and posterior focal planes, whence we derive 

 / according to the formula 



/=- 



A/. 



(8 being the distance of the posterior focal plane of the first lens f from 

 the anterior focal plane of the second lens). 



Thus suppose in fig. 59 that we have given/ = — 24*8 mm. and 



/ = 48 • 4 mm., we require only to determine S to solve the equa- 

 tion. 



We can determine 8 from the distances (supposed to be given) of the 

 focal planes from the respective lenses, the distance of the posterior 

 focal plane of the first lens Fj* = 24 • 5 mm. and that of the anterior 

 focal plane of the second lens Fg = 46 • 3 mm. For the diagram shows 

 that if from the total distance between Fi* and the front of the second 

 lens (which is made up of the variable distance between the lenses d 

 and the quantity 24-5), we deduct the distance 46 '3 mm. of the 

 focal plane Fg from the second lens we shall have the distance 8. 



t The first lens being a plano-concave the posterior focal plane (i. e. which 

 relates to the posterior medium, or to the image) is in front of the lens, and not, 

 as with convex lenses, at the back. 



2 H 2 



