39 
required to produce such miracles of art cannot be too much 
praised; and up to a certain point it must be confessed, that 
the performance of these objectives corresponds fully to their 
promise. It seems to me, however, that in the extreme cases 
to which I refer, there is not unfrequently some defect of con- 
struction which prevents them from being quite as effective as 
their great aperture might lead us to expect. 
‘« The effect of angular aperture is merely an increase of 
illuminating power* analogous to that of linear aperture in a 
A Cc B 
E 0 ¥F 
telescope. Let O be a point of an object seen by an ob- 
jective whose anterior surface is AB. This point, in the case 
of a test object, may be considered as self-luminous and 
equally so in every direction. Therefore, the light which it 
sends to the objective is measured by the portion of the 
hemisphere ECF, which is included by the cone AOB. If 
all that light came to the eye, the illumination would be mea- 
sured by 47 sin? 0 being = AOC; but this is never the 
case. The object is almost invariably covered with a piece 
of thin glass, both whose surfaces reflect a portion of the 
light if it be mounted dry, one only if it be in balsam.t A 
* It does not depend on greater convergence of the rays; when the disked 
stop, hereafter described, was placed in a quarter 105° aperture, the ring of 
the objective left free showed a test object just as the same illuminating 
power of an ordinary one would do. 
+ For objects in balsam no light can escape at a greater incidence than 
46°; therefore, notwithstanding the absence of the first reflexion, they will 
' be less illuminated than in the other way. It is in fact equivalent to re- 
ducing the aperture of the objective below 100°, as far as illumination is 
concerned, though a much larger one may be required to take in the pencil ; 
and it should not be used when it is desired to see details of the utmost 
minuteness. 
