THE CENTEK1XG OF THE SYSTEMS OF LENSES. 



79 



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VIII. 



THE CENTEKING OF THE SYSTEMS OF LENSES. 



IN our previous consideration) of the path of the rays of light in 

 the Microscope, we have throughout assumed that the refracting 

 surfaces form an exactly concentric system, 

 i.e., that their centres of curvature all lie in /> 



one straight line. The optician will always 

 endeavour to realize this assumption ; but the 

 best workmanship results in an approximation 

 only, and in the high-power objectives there 

 are always unavoidable errors. The question 

 therefore arises, how defective centering in- 

 fluences the clearness of the image, and what 

 errors are of especial importance ? 



According to the usual view, exact centering 

 is one of the conditions of aplanatism. Hart- 

 ing 1 states that even a slight inaccuracy will 

 necessarily be very detrimental ; and Mohl 2 

 affirms that a distortion of the image on one 

 side is caused by it. This view seems at first 

 sight plausible and comprehensible; it is, 

 nevertheless, opposed to theory as well as to 

 observation, as we will show. 



Let us assume a perfectly concentric ob- 

 jective-system composed of three double-lenses, 

 which is as far as possible aplanatic for all 

 points of a field of view of given diameter, and 

 inquire what influence a slight lateral dis- 

 placement of the lenses would exert upon the 

 combined effect of the system. Let E v E 2 , and 

 JZ 3 (Fig. 37) be the pairs of principal planes 

 of the three double-lenses, F 2 and F 3 the 

 corresponding focal planes of the two posterior -p IG 37. 



lenses, and o v 2 , and 3 , the optic axes, the 

 first of which we suppose to coincide with the axis P Q of the 



1 Harting: " Das Mikroskop," p. 275, and 2nd ed. i. p. 304. 



2 Mohl: "Mikrographie," p. 176. 



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