On " Optical Tube-length.'" By Frank Crisis. 817 



tube and eye-piece will not give magnifying powers in proportion 

 to their focal lengths ; thus a 1-2 in. will not necessarily give 

 double the ;gower of a 1 in. 



Conversely, two eye-pieces will not amplify in proportion to 

 their focal lengths, though used with the same tube and objective. 



Indeed, the true magnifying powers may differ from the powers 

 which would be obtained on the ordinary assumptions by more 

 than 100 per cent., and Prof. Abbe records the existence of objec- 

 tives (of somewhat exceptional construction it is true) which 

 exhibit this paradoxical behaviour : that one of longer focal length 

 amplifies much more than one of shorter focal length ; that one 

 gives the same amplification with a long and a short tube, and that 

 one gives a higher amplification with a short tube than with a long 

 one. 



What then is the explanation of these paradoxes ? 



The explanation is not to be found in any question of the length 

 of the objective or eye-piece, or the character of their respective 

 settings, but depends upon the fact that hitherto microscopists have 

 regarded the outside only of the tube and have left out of consider- 

 ation the optical action which goes on within it. 



To properly understand the matter it will be necessary to con- 

 sider the principles on which the action of the Microscope in regard 

 to magnifying power is founded. 



The magnifying power of a lens depends of course upon its 

 focal length and varies inversely with it ; the ordinary mode of 

 obtaining the power being to divide the distance of distinct vision I 

 (assumed as 10 in.) by the focal length, or expressing it by a formula 



N =^. Thus if the focal length / of an objective is l-8th in. 



10 -f- 1 = 80. The same applies to the action of the Microscope 

 as a whole, that is with eye-piece and objective combined ; when we 

 have determined its focal length we similarly obtain its magnifying 

 power.* 



"We have therefore to ascertain the proper mode of determining 

 the focal length / of the entire Microscope, having given the focal 

 length /^ of the objective and the focal length /^ of the eye- 

 piece. 



The usual assumption hitherto has been that / is determmed 

 by multiplying /^ and /^ together and dividing by the length of 

 the tube 10 in., or 



* The quotient obtained by dividing 10 in. by the focal length gives the 

 linear amplification of an image — real or virtual — which is projected by an 

 objective to a distance of 10 in. from its posterior focus, and not from the objective, 

 as has been so commonly assumed. 



