The Belation of Aperture and Poiver. By Frof. E. Ahbe. 791 



the focal length) could therefore be obtained just as well by- 

 means of a strong ocular at the upper end of the tube, as at the 

 lower end by means of a strong objective. The only reason why 

 a difference of division is of importance, is the accumulation of 

 the effects of faults and aberrations of the lenses in the idtimate 

 intake of the Microscope. In order to prevent an obnoxious 

 accumulation, and for no other reason, we are confined to certain 

 hmits in the distribution of the total power as between objective 

 and ocular. 



(2) The ocular is practically unimportant under the actual con- 

 ditions of the Microscope, so far as the sharpness of the image at 

 the central portion of the field is concerned — the quality of the field 

 outside the axis being disregarded. The length of the tube being 

 always a considerable multiple of the clear diameter of the ob- 

 jective, the pencils of light are contracted to very small angles at 

 their entrance into the ocular. The numerical computation of the 

 spherical and chromatic aberrations originating in similar pencils, 

 in the case of ordinary Huyghenian or Eamsden oculars, shows 

 at once that in the neighbourhood of the axis their amount is 

 utterly inconsiderable in comparison with the residuary aberrations 

 of the most perfect objective. Consequently the axial aberrations 

 which are inherent in the ohjecfive-imsige, can neither be increased 

 nor diminished by any kind of ocular ; they are enlarged only for 

 the eye in the same ratio as the image itself is enlarged. Other 

 properties of the image (outside the axis) — flatness of the field, 

 uniform amplification, &c. — which are influenced by the ocular, 

 are doubtless of practical importance in the use of the instrument, 

 but they do not touch the essential points, whether a given 

 degree of sharpness and distinctness is reached with a given power. 

 For it makes no difference, in regard to this question, whether the 

 available field of maximum excellence is somewhat greater or 

 somewhat less. The interference of gross defects of workmanship 

 being, of course, disregarded, the ocular may always be considered 

 as being unimportant except as a means of enlarging the objective- 

 image ; and all further discussion may therefore be confined to the 

 circumstances on which the sharpness of that image which is pro- 

 jected by the objective depends, 



(3) In objectives two different kinds of faults and aberrations 

 must be distinguished. There are, firstly, accidental defects, arising 

 from coarse errors of figure and want of centering of the lenses, 

 or from the use of an unsuitable formula, or from temporary 

 derangement of the corrections, as when the cover-glass is too 

 thick or too thin, or the image is projected to a distance other 

 than that for which the system was corrected. Defects of this 

 kind can always be avoided by careful construction and proper 

 management, and are therefore beside the question before us. 



