BuRTOX. — On the Minimum Visible in the Microscope. 249 



supposing both combinations to be perfectly corrected, would form an 

 image of the object precisely similar to it in the rear of B. 



The effect of any interference or of diifraction in the convergent 

 cone fi'om A will be undone in the divergent cone whose base is the 

 front lens surface of B. 



Therefore, whatever be the actual distribution of light and shade 

 in the common focal plane of A and B, the resultant after passing B 

 will be identical with the originant, i. e. the object of A. In other 

 words, B merely restores the rays to the identical mutual relation 

 which they possessed before entering A. 



The existence of any aberration in either or in both of the ob- 

 jectives or combinations of lenses used, A or B, disturbs the relation 

 of symmetry between the convergent and divergent luminous cones, 

 and consec[uently renders the restoration of theii' components to their 

 primary condition more or less incomplete. The final image thus be- 

 comes indistinct to a corresponding extent, so much so indeed that 

 the method of Dr. Pigott approves itself as an extremely sensitive 

 detector of aberrations outstanding in the opposed systems. 



But it is evident that no information as to the separability of ma- 

 terial lines as distinguished from focal images can be obtained by the 

 method just described. In the case of material objects, the light 

 which renders them visible has undergone very different treatment 

 from that adverted to above. Every system of material points, the 

 intervals of which are comparable in dimensions to the length of a 

 wave of light, acts as a more or less regular difitraction grating when 

 a pencil of rays is transmitted through it, and the pencil is redistri- 

 buted in the process of transmission into a direct pencil, and a varying 

 number of diffracted pencils dependent upon the number of regular 

 diffracting systems, of which we may conceive the assemblage of ma- 

 terial points to be composed, and divergent from the axis of the un- 

 diffracted pencil at angles which are determined by the degree of 

 closeness of the several imaginary component gratings. The angles 

 of divergence of diffracted pencils increase with the fineness of the 

 details producing diffraction until they approach equality (for direct 

 light) to a wave length of that light when the divergence becomes 

 equal to 90°, or, in other words, diifraction ceases. 



If the angular aperture of the observing objective be sufficiently 

 wide, it will receive one or more of these diffracted pencils besides the 

 direct pencil. 



Professor Abbe's researches have resulted in showing that the 

 representation of minute detail of any kiad is dependent on the ad- 

 mission of rays from these spectra to the final image in the focus of 

 the eye lens of the microscope, and that if these diffracted pencils 

 be entirely excluded from the final image no detail at all will be 

 shown, but merely the outline of the object viewed, e. g., the edge 

 and midrib of a diatom ; its markings, so called, being invisible. Fur- 

 thermore, Professor Abbe has proved that the fine details of an object 

 will be shown more nearly as they exist, the greater the number of 



