ON THE THEOBT OF THE MICROSCOPE. 229 



rSECTioN III. — The physical conditiom under which images of minute 

 structure ar« formed. 



XIII. That the performance of the microscope does not 

 always depend solely on the geometrical perfection of the image, 

 but also, in addition to this, in certain classes of objects, upon 

 amount of angular aperture, is a fact long recognised, and one 

 which has greatly influenced the construction of the microscope 

 in recent times. The exact significance of this fact has neverthe- 

 less remained just as problematical as the exact nature of that 

 especial quality which has, in connection with it, been attributed 

 to the microscope ("resolving" or discriminating power — penetra- 

 tion). It remained, namely, a question, What value might be 

 assigned to the quality thus related with angular aperture in the 

 ordinary scientific application of the 'instrument, and does its 

 significance extend any further than to certain particular cases 

 in which shade effects were supposed to be produced by oblique 

 illumination. ? 



In the endeavour to establish a theoretical basis for the con- 

 struction of the microscope, it was a matter of the first importance 

 to define the exact function of angular aperture in the ordinary 

 normal performance of the microscope, lest I should, in following 

 a mere tradition, fall into a misdirection of my labours towards 

 aims of very problematical worth. A definitive settlement of the 

 principal points in question has been reached, as I believe, in the 

 results now communicated, except in so far as new facts brought 

 to light by these researches suggest further problems of a different 

 kind. 



As, then, it is important before all thing to ascertain more 

 exactly than lias been hitherto set forth in micrographic litera- 

 ture the actual facts respecting the operation and effect of angular 

 aperture, I endeavoured to determine first by experiment in what 

 cases a distinct advantage resulted from larger angular aperture, 

 and in what cases no such advantage could be perceived, all other 

 differences which might possibly influence the operation being 

 most carefully eliminated. For this purpose a series of objectives, 



