178 PROCEEDINGS OF THE ACADEMY OP [March, 



his theory has stood unrefuted up to the present time; but recently 

 there has been a feeling aroused that, without further modification, 

 it fails to fully account for all features of observed microscopical 

 images. 



The old dioptric theory has accordingly been re-expounded and 

 amplified, and it is unnecessary to explain it in detail, as this has been 

 most admirably and completely done in Wright's "Principles of 

 Microscopy," published in 1906, which, while characterized by inac- 

 curacies in connection with such matters as the measurement of focus 

 and aperture, and indicating a lack of acquaintance with the diffrac- 

 tion theory, covers the ground from the dioptric point of view so tho- 

 roughly that I find but one point open to criticism, which is the employ- 

 ment of bright points and lines, equivalent to self-luminous objects, 

 in explaining the formation of the diffraction patterns termed " anti- 

 points. " This is not a condition which is met in practical microscopy 

 except with dark ground illumination, but every skilled microscopist 

 knows that this form of illumination, although advantageous for 

 many purposes, particularly for increasing the visibility of isolated 

 points and lines, is never equal to direct light in developing true images 

 of structure, the elements of which are not separated by distances 

 exceeding their own diameters. The decreased resolution has recently 

 been explained by Nelson, and, in addition to this, false appearances 

 intermediate between true structural elements may be produced by 

 the coincidence of diffracted rays, which would not be visible with 

 direct light. 



In the rare case of opaque particles in a transparent medium, such 

 as is furnished by a rock section containing minute crystals of mag- 

 netite or pyrite, the phenomena observed at the margins of these crys- 

 tals may be explained as just the reverse of those arising from a bright 

 point image; but in the vast majority of all structures examined with 

 the microscope there will be little difference in the illumination on 

 opposite sides of a marginal line, possibly only a difference in color, and 

 whether the margin be considered as imaged by slightly refracted rays 

 or by slightly deflected diffracted rays, whether an image of the margin 

 is produced at all or only an interference of " antipoints," it is unques- 

 tionable that in certain classes of objects at least, as my experiments 

 have not covered the whole ground sufficiently to generalize, there is 

 something visible corresponding to a limiting margin, which may be 

 recognized and measured by a practiced eye, whether isolated when 

 illuminated by a wide cone or flanked on both sides by diffraction 

 bands with a narrow one. This fact had been impressed on me by 



