124 THE AMERICAN MONTHLY [Jun 
in the seventh edition of ‘‘Carpenter,” published in 1891, 
which is peculiarly authoritative and weighty as having 
been submitted to Professor Abbe himself, and as having 
obtained his cordial endorsement, together with the ex- 
pression of his greatest satisfaction of seeing his “views 
represented in the book so extensively and intensively,” 
have not been in any way modified in the eighth edition 
published ten years later. This taken in conjunction 
with the significant fact that the best substage condenser 
constructed by the firm of Zeiss for use with the highest 
powers still only affords a maximum aplanatic cone of 
N.A. ‘65, clearly indicates that, whatever admissions or 
changes of front his self-constituted supporters and de- 
fendersmay have thought fit to make, Professor Abbe 
himself continues to unwaveringly maintain that strictly 
similar images are alone to be expected with the central 
narrow incident pencil, this being the necessary condi- 
tion for the admission of the whole of the diffracted light. 
What more wise and logical conclusion could be pos- 
sibly reached on the hypothesis that microscopical vision 
is sui generis, and that “the images of minute objects are 
not delineated microscopically by means of the ordinary 
laws of refraction; they are not dioptrical results, but de- 
pend entirely on the laws of diffraction” ? Undoubtedly 
_ onany such assumptions as these, it is reasonable to 
maintain that the nearest possible approach to truth in 
the rendering of minute structure will be only attained 
with a narrow central illuminating pencil, for we can all 
easily satisfy ourselves by experiment that the strongest 
and most marked diffraction images and effects are thus 
obtainable. As we increase the diameter of the illumin- 
ating pencil we can experimentally observe that the pic- 
ture rapidly becomes worse and worse from a diffractive 
point of view until when we reach a five-sixths or six- 
sevenths cone, no certain diffraction effects are discern- 
ible. In the case of a delicate object possessing fine 
