The Microscope. 



211 



to a doublet has the first principal plane of the first lens as its 

 face and the second principal plane of the second lens as its back, 

 whilst its thickness is represented by the transit-distance between 

 the second principal plane of the first, and the first plane of the 

 second lens. Otherwise we employ the same formulae as before 

 for combining the focal lengths of the component lenses so as to 

 get the focal lengths and principal planes and position of the 

 •equivalent lens. 



IV. Having determined the Doublets, we use the same for- 

 mulae for combining them into the Objective. I have thus followed 

 Nageli and Schioeiidener''s problem by combining the second and 

 third doublet to get a low-power objective, and by combining this 

 with the front doublet, to get a high-power objective. The results 

 reached are same as by their method (saving a trifling arithme- 

 tical error in one of their calculations); but these results are 

 reached in a much simpler and more intelligible way than the 

 •one which they follow. By combining the lenses of the eye- 

 piece together, and finally the eyepiece and objective, every step 

 only a repetition of previous steps, we come to find the dimen- 

 sions and focal length of an imaginary lens equal to the micro- 

 scope or telescope. 



V. Example. — The 



example to be worked 

 is a microscope having 

 an Objective consisting 

 of three doublets and 

 the ordinary Huyghe- 

 nian eyepiece. The 

 Objective has its doub- 

 lets, C, B, A, com- 

 posed each of a plano- 

 concave flint-glass lens 

 backed by an equally- 

 convex crown-glass 

 lens; the flint-glass 

 — ' ^ having 1.6, and the 



—J'M,. crown-glass 1.5 as re- 



fractive index. The first doublet has flint-glass lens ^ millime- 



