542 
SUMMARY OF CURRENT RESEARCHES RELATING TO 
From fig. 79 we have 
from C N. 
IM 
m 3 
A- + f Qr q p ^ oeg nQ j. geng ibly 
A. +i? 
Replacing p by its value drawn from the equation - — i = 
& V + / V V 
f 
IM X+i/ , *>' 2 _ t , 1 
+ a p ' + a/+p'/ + a / x/' 
“V+/ p ' 2 
Fig. 79. 
This shows that the binocular image 1 1' appears so much greater 
with respect to the monocular image I x 1/ as A and f will be smaller and 
jp' greater. To see the phenomenon under the most favourable conditions 
therefore, it would be necessary to take a lens of short focus, separate 
the object as far as possible from the lens, and place the eye close to the 
lens. 
II' 
For the normal eye, since p' is without limit - - — can become equal 
-*-i m 
to -j- oc ; but actually the binocular image never appears more than 
double the monocular, for when the virtual image is very far from the 
eye, the sentiment of the reality of things is opposed to the idea that the 
subjective image which represents it is very far from it. 
Numerical Aperture. — Dr. M. D. Ewell writes as follows on this 
subject : * — 
“ It is not proposed in this paper to enter upon any theoretical dis- 
cussion, but to give the results of actual measurements of the aperture 
of such objectives of different makers as I have been able to procure for 
that purpose. The measurements were made with an Abbe apertometer, 
which will be found figured and described on p. 24 of Zeiss’s English 
Catalogue, 1891, as ‘No. 2.’ | 
I intended to repeat the measurements on another apertometer of 
* Proc. Amer. Micr. Soc., xiv. (1892) pp. 44-7 (2 figs.), 
t See also Journ. Roy. Mier. Soc., Jan. 1878, p. 19; 1880, p. 20. 
