On Angular Aperture of Immersion Objectives. 107 
include the case of a slide of dry-mounted objects, it is safe to state 
that with whatever kind of objective used, when the slide and 
covering glass are by balsam between fused into one (nearly) 
homogeneous transparent piece, this first refraction limits the angle 
of transmitted pencil to less than 82°. The barrier evidently is at 
the first refracting surface of the slide. The little (or large) 
hemispherical lens cemented to the outer surface of the slide * gives 
the case I first gave substantially. It is evident that as the light, 
say a ray for simplicity, is carried from the axis round to the 
extremest obliquity, the path of the ray will be a straight line to 
the centre of curvature of the plano-convex lens. This figure 
illustrates plainly that the hemispherical lens gives access for the 
largest angular pencil to the balsam-mounted object, say 179°. 
Here the lens is not fully a hemisphere, but nearly of the requisite 
thickness. The diagram previously given t shows the full pencil 
admitted. 
In giving my first note and illustration I assumed as evident 
enough from what had already appeared that with a balsam- 
mounted object-slide an immersion objective would have more angle 
for rays radiant from the object in the balsam than a dry objective 
could have. But it is denied. And yet it is safe to say that with 
air between the immersion-front and slide-cover, the latter being 
of glass commonly used, the “ well-settled laws of refraction ” limit 
the pencil, emergent, at the outside surface of the “cover” to 82°, — 
within the glass, before emergence ; but with water between the 
cover and front surface of the immersion objective it would be 
larger according to the difference between refraction of covering- 
glass in water and covering-glass in air. Whether the immersion 
objective would be competent to transmit the whole angular pencil 
or not is another question. That it could be made to do so did 
not seem to me to admit of doubt. Mr. Wenham’s T V” 170° air 
angle, 100° water angle, probably would not transmit or “collect” 
to exceed 82°. “ Mr. Tolies is ” not “ unable to perceive this.” 
All of my own save one, so far as tried, do take up more than 82° 
when immersed in balsam. That exceptional one has the same 
angle in air and in water as given by him as pertaining to his T? in- 
When I “ seized ” upon his own experiment as proof that my 
experiment was valid, it was only because his result agreed exactly 
with my result — objective 170° in air, 100° in water. All that his 
or my experiment proved was that more than 82 3 could get out of 
the balsam through the cover into water, unless I include that my 
plan showed that in air all but 82° of pencil was turned back, 
which his did not ! Now again, “ 100° is surely more than 82 3 ”! 
Perhaps Mr. Wenham “is unable to perceive this, and so let it 
remain.” 
* See ‘M. M. J.,’ No. xxxix., p. 117, Fig. 3. 
f ‘M. M. J.’ for Nov. 1871. 
