Aperture of Object-glasses. 
231 
microscopic definition have, as a rule, since 1869 at least, been 
rather shown in the advance of various makers to the highest 
standard then attained, than in any actual progress beyond what 
had then been done. This qualified advance should, however, be 
most satisfactory to microscopists, since it promises a competition 
likely to bring down the present extravagant prices of good objec- 
tives. 
But beyond this general movement, which is so creditable to all 
concerned, I must believe that Mr. Tolies* has been so fortunate 
as to make a real advance, and I shall continue to hold this belief 
until some one can produce an objective which, in my hands, or 
those of some other observer, shall succeed in doing better work on 
the plate than that herewith submitted. 
In conclusion, I mention that the price paid Mr. Charles Stodder 
for the objective above described was one hundred and seventy-five 
dollars U. S. currency. 
IV. — Aperture of Object-glasses. By F. H. Wenham. 
In declining to continue a discussion directly with Mr. Tolies on the 
question of angle of immersed objectives, I meant no discourtesy, 
fully appreciating the temperate manner in which he has endeavoured 
to maintain his point. My withdrawal was in consequence of his 
diagrams,! in which rays were drawn through lenses in a direction 
so adverse to my belief in optical theory, and against plain rudi- 
mentary principles that I never could abandon, further argument 
therefore became useless. 
But as I agree with the remark in the last Journal, that the 
question of aperture has not been “ quite satisfactorily determined,” 
I offer some further information. The vexed question has been 
extended over such a long period, and scattered over so many pages, 
that the main point at issue from the first announcement of the 
fabulous increase of aperture of immersion lenses has perhaps faded 
from memory. I therefore condense the principle in a brief demon- 
stration. Let a, b, represent the maximum working diameter, or 
actual surface of the front lens, that is, sufficient for the passage of 
a pencil of rays of 170° from the focal point c. By the law of re- 
fraction these rays will take the direction d, e, in the body of the 
front lens, completely filling the nearly hemispherical back surface 
to its edge. Now let the front lens be immersed in water. This 
of course lessens the refraction at a, b. The focus is extended to f 
* These words — “that Mr. Tolies” — are omitted from the MS., but we 
presume they were intended to have been used by the author. 
t Page 117, ‘ M. M. J.,’ March, 1872. 
