RELATION OF APERTURE AND POWER IN THE MICROSCOPE. IQI 
of workmanship being, of course, disregarded, the ocular may 
always be considered as being unimportant except as a means of 
enlarging the objectiveimage; and all further discussion may, 
therefore, be confined to the circumstances on which the sharpness 
of that image which is projected by the odjective depends. 
(3) In objectives two different kinds of faults and aberrations 
must be distinguished. There are, firstly, accidental defects, arising 
from coarse errors of figure and want of centering of the lenses, 
or from the use of an unsuitable formula, or from temporary 
derangement of the corrections, as when the cover-glass is too 
thick or too thin, or the image is projected to a distance other 
than that for which the system was corrected. Defects of this 
kind can always be avoided by careful construction and proper 
management, and are, therefore, beside the question before us. 
Secondly, we have essentza/ defects in the performance of objectives ; 
the accumulated influence of certain slight imperfections in the 
technical work of the lenses, and certain residuary aberrations 
which cannot be eliminated by the most skilful construction under 
the actual conditions of optical work at the present time. These 
alone can claim a general signification, and admit of an approximate 
estimation according to the existing standard of optical art. 
In such an estimation we do not need any detailed analysis of 
the various sources of defective performance. For our present 
purpose it is quite sufficient to enunciate certain optical proposi- 
tions, by means of which the problem may be reduced to one 
question, to be answered on the grounds of practical observation. 
It may be easily shown, on well-established principles, that with 
one and the same objective the total effect of all essential abrerra- 
tions, if measured by the “ear diameter of the dissipation-circles 
in the image, always varies zz direct proportion to the linear amplt- 
fication of that image, provided the distance to which the image is 
projected is a considerable multiple (not less than about the ten- 
fold) of the clear opening of the objective. This holds good (with 
the restriction just named) for every position of the image, and 
whether this is changed from a real image to a virtual image, and 
vice versi—that is to say, that if the linear amplification is increased 
in the proportion of 1: 2 by projecting the image to a greater 
distance from the objective, the dissipation-circles which appear 
instead of sharp points are always increased in the same propor- 
tion, if the accidental aberrations attendant upon the change of 
the conjugate foci are eliminated. This latter condition means 
that if an objective has its est correction for a certain distance (A) 
from the back of the objective, and the image is now projected to 
another distance, z A, on the same side (or on the opposite side, 
the image being virtual in the latter case), the correction will pro- 
bably be largely deranged by the alteration, and a large amount of 
