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in.— the Measurement of the Angle of Aperture of Objectives, 
By F. H. Wenham, F.K.M.S. 
{Read hefore the Royal Microscopical Society, November 13, 1878.) 
In arranging in the form of a paper, some recent investigations on 
this yet undecided question, I have no desire to maintain a con- 
troversy that has at times appeared as one of personal feeling 
instead of scientific reasoning. The facts cannot be established by 
a majority of opinions, but by actual experiments. It is to these 
principally that I now refer. 
Professor Stokes, at the meeting of this Society held in July 
last, has brought forward a question, and shown in theory that by 
means of a front lens, with an emergent surface exceeding the 
hemisphere, a ray may be refracted within the substance of the glass 
in a direction at right angles to the axis or at an angle of 180°. 
He then remarks that if the reduction of the surface be to a hemi- 
sphere, “ the aperture in glass, though reduced from the extreme of 
180, still remains very large.” 
It is with front lenses having refracting surfaces less than a 
hemisphere that we have been dealing, and to such Professor 
Keith’s paper on the Tolies ^ refers. It may be stated that 
we are not seeking for foci within the front lens, or yet on its 
surface. An immersion lens is not useful for viewing diatoms 
in balsam only. Every lens that I have seen professing 180'^, 
whether it has an adjustment or not, is expected, and does, in fact, 
focus upon dry mounted objects. This necessitates a correct focus 
at a little distance beyond the last surface, from a position which 
must include a less air angle than 180°, and is consequently within 
the critical angle of nearly 82° in the crown glass. 
The -J- referred to belonging to Mr. Crisp has considerable 
focal distance in air, and I am confident that when the axial angle 
is correctly measured it will be proved far short of 1 80°, and the 
whole of Professor Keith’s calculations concerning it must fall to 
the ground. The practical obstacles which have hitherto prevented 
the construction of any objective reaching to an air aperture of 
180° still exist. 
As much importance, both theoretically and practically, appears 
to have been attached to the last few degrees of extreme angle of 
aperture verging upon 180°, I repeat that the value of aperture in 
theory, considered as a question of rays collected, is palpably as the 
chord of the arc including the angle, or, in other words, in propor- 
tion to the sine of the half angle ; for large angles so small is the 
comparative increase, that the difference between 170° and 180° is 
only as 99 ’6 to 100. But setting theory aside in this question 
as not always working harmoniously with practice, let it bo consi- 
dered, experimentally, what is the probable importance to definition 
