30 THEORY OF THE MICROSCOPE. 



o o 



Third double-lens. Let r = 10 , d = ^, d' = ^ 

 then 



*' = JT : - ~, /*- 



Hence .#" = e + 1-23456 = .Y 6 + 170331 



r =i' + 7732 = JV* + -2469 



</>" = 24-6913 . 



Since the second and third double-lenses are sometimes used with- 

 out the first when lower magnifying powers are required, it will be to 

 the purpose if we, first of all, combine these two, and then follow 

 out somewhat further their united action as an objective. For 

 this purpose, we must make the further assumption that N 6 

 coincides with /'; the lens-surfaces, which face each other, are 

 therefore at a distance of -1487 apart, so that t' (the distance of 

 the principal points /' and E" on that side) in this case = 170331, 

 while ^ and u, as usual, are to be taken as equal to the reciprocals 



of the relative focal lengths, that is, ---- , and --- 7f - For the 







abscissie of the resulting principal and focal points, which we 



denote by (E) (E*) and (F) (F*), we therefore get 



(E) = E' + "470468 = .Y 3 + 1-905158 

 (E*) = r 1-32419 = .Y 3 + x,-:52143 



(F) = (E) - 6-82064 = .Y 3 - 4-91548 

 (^) = (E*) + 6-82064 = ^Y 8 + 5*74437 . 



The focal length (/) of the objective therefore = 6'82064, and 

 the distance of the focal point (F) from its anterior surface = 

 4*91548. If the image is to be at a distance of p* = 200 mm., 

 as is approximately the case in most of the modern instruments, 

 the distance p of the object from the first principal plane can 

 easily be determined from the relation 



1.11 

 P " P* "/' 



We find^; = 7'06146 mm.; therefore j? / = '24. As coefficient 

 of magnifying power we get 



m = -.--- = - 28-3. 

 f-P 



