On Angle of Aperture. By H. J. Slack. 237 
angled ^ths in existence by our great makers, of remarkable merit, 
and their resolying powers would probably be found very consider- 
able if new modes of illumination were applied to them. Dr. 
Pigott possesses a |th of Andrew Boss's, angle about 68°, which with 
E eye-piece and 16 inches of tube can show his famous Podura beads, 
which are certainly fine tests, whatever disputes may continue as 
to the structure that causes their appearance. 
In Professor Abbe's paper there is a reference to Dr. Pigott's 
" Aplanatic Searcher," which is condemned, not on the ground taken 
by certain objectors here, but for a reason that its inventor will be 
the first to endorse, namely, that the corrections it can make ought 
to be effected by the optician through an improvement in the 
combinations he employs. 
Some years ago Dr. Carpenter showed that excess of angular 
aperture led to great distortion of objects seen with the binocular 
microscope, converting spherical bodies into ovals, &c. He stated 
that he " had caused Messrs. Powell and Lealand to construct for 
him an objective of half-an-inch focus, with an angular aperture of 
40°, and found it to answer most admirably."* If we take this angle 
of 40^, as best suiting magnifications of from 90^ to 120° or a little 
higher, what angle will best suit higher powers so as to avoid dis- 
tortion ? This is a question for which it is difficult to find the data 
for a mathematical calculation, but we may perhaps arrive at it 
approximately by well-conducted experiments. 
It is often supposed that an object- that requires very oblique 
illumination must also require a large-angled glass to view it ; but 
the better the spherical correction and the less false light — that is, 
light not concerned in forming an optical image — that is admitted, 
the smaller seems to be the angle of aperture necessary for seeing 
an obliquely illuminated set of surface markings well. 
Professor Abbe observes that " chromatic aberration for large 
angles of aperture not only depends upon the focal difierences 
which afiect the image-making light cone, by reason of the unequal 
passage of the different coloured rays through crown and flint glass, 
but also upon incurable inequalities in recomposing the coloured 
rays of differently refracted pencils, so that an objective achromati- 
€ally corrected for direct illumination must be more or less over- 
corrected for oblique rays." 
He makes similar observations on spherical corrections, and 
points out that increasing angles of aperture beyond narrow limits 
augments the outstanding deficit of correction and damages defini- 
tion. It is probable that many favourite objectives have had their 
definition damaged in this way, and it is curious that large angles 
do not work well with the silica films described by the writer, and 
that with suitable illumination small angles will resolve them. 
* Note to 'The Microscope,' 5th edit., p. 72. 
