230 ON THE THEORY OF THE MICROSCOPE. 



diifering widely in focal length and angular aperture, "were con- 

 structed with the greatest accuracy, according to my calculations, 

 and their accuracy specially tested, so as to afford a certainty of 

 correctness in comparing the observations made with them. The 

 test objects employed included prepared insect scales of various 

 kinds, diatom valves, striped muscle fibre, diamond-ruled lines on 

 glass, groups of lines on silvered glass, fine and coarse powdered 

 substances, and, besides these, the minute optical images of 

 natural objects (lattice bars — wire-net) obtained by means of air 

 bubbles, or, preferably, by objectives of short focus, fitted to the 

 stage cf the microscope. 



XIV. These experiments yielded the following results : — 



(i.) So long as the angle of aperture remains within such limits 

 that no noticeable diminution of sharpness of image results from 

 its diffraction-effect, no sensible improvement in the delineation 

 of the outlines (that is to say, of the confines between unequally 

 transparent parts) of the object takes place, {provided these parts 

 are not of less size than ^-^-^-^ inch. 



(ii.) On the other hand, the difference is wholly in favour of 

 the larger aperture for every object which yields details minuter 

 than the limits above given ; and this is quite irrespective of the 

 question whether such details are due to unevenness of surface or 

 to unequal transparency in an infinitely thin layer, or whether 

 the detail takes the form of striation, granulation, trelliswork, 

 or images of natural objects' reflected from bubbles or produced 

 by refraction of lenses. 



(iii.) The smaller the linear dimension of such details so much 

 the larger must be the angle of aperture of the objective, if they 

 are to be made out with any definite kind of illumination, e.^., 

 whether purely central or very oblique : and this is irrespective 

 of the more or less marked character of the delineation and of 

 the focal length and necessary amplifying power of the objective. 



(iv.) When the detail in the real object appears in the form of 

 striation, groups of lines, &c., a given angular aperture always 

 reaches much finer details with oblique than direct illuminations, 



