1909.] NATURAL SCIENCES OF PHILADELPHIA. 177 



MICROSCOPICAL IMAGE FORMATION. 

 BY F. J. KEELEY. 



This subject is of importance to every user of a microscope, as a 

 correct understanding of the optical laws which govern the formation 

 of the image would assist in determining to what extent the true 

 structure and size of the object under examination is correctly repre- 

 sented by the appearances presented to the eye. We are confronted 

 with two radically different theories of microscopical vision, which may 

 be termed the diffraction and dioptric theories, although the former 

 requires the presence of both diffracted and dioptric beams, while the 

 latter deals principally with the effect of diffraction, but only such as 

 arises in the instrument itself and not from the object under exami- 

 nation. As the exponents of each seem to take partisan views and fail 

 to give adequate consideration to the opposing theory, it appeared to 

 be worth while to make a careful study of both in as far as possible 

 an unprejudiced manner, supplemented by experiments, with the 

 view of endeavoring to learn whether they are wholly irreconcilable. 



From 1771, when Benjamin Martin applied a low power achromatic 

 objective to a microscope and explained that its superiority was largely 

 due to the increased aperture available, until Tolles, a century later, 

 realized the possibility and practicability of producing objectives with 

 apertures in excess of the equivalent of 180° in air, the principal efforts 

 of the opticians and their collaborators, the microscopists, was in the 

 direction of increased aperture and improved chromatic corrections, and 

 no serious doubts appear to have been raised regarding the dioptric 

 theory, in the form in which it had been worked out for the telescope; 

 but when the practical limit of aperture with available materials had been 

 reached by all the leading opticians, more attention was paid to theoret- 

 ical questions, and it began to be apparent that there were certain phe- 

 nomena connected with image formation in the microscope which could 

 not be satisfactorily explained by accepted theories. Abbe investigated 

 this problem with characteristic acumen and evolved the theory which 

 has since borne his name, and although immediately attacked and 

 later somewhat modified by himself, although in a radical direction, 

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