338 
Transactions of the Society. 
Abbe's method : — 
1-5 
/DV 1 D <o 
,X \M/ ' w + ^ M ' NX 
/250V 1 , _ 250 -0005 
\io) -25o + 1 ‘ 5x -io- x ^r 
10/ 250 
1-5 x 625 
250 
+ 1-5 X 25 x -005 
7-5 
+ ' 187 = 3 • 94 mm. 
By my simplified formula with the same data — 
IL (fL . _L_ \ _ U> /250 ' 127> j 
m'm + n.a./ “ 10 V 10 + -1 / 
= - 15 x 26*27 = 3*94 mm. 
We have found, however, that owing to the paralysis of the 
accommodation, the penetrating power falls short of the above 
theoretical values. We must, therefore, construct a table that will be 
of practical use. To this end I propose to multiply the first fraction 
in the bracket by 
M 
10U 
for all magnifications up to 50 diameters. 
It must also be understood that the above formulae are constructed 
on the understanding that the cone of illumination is equal to the full 
aperture of the objective. 
Now we know that the highest illuminating cone for the most 
critical work we can use is a 3/4 cone; this will slightly increase the 
penetration, and we should have therefore to multiply the second term 
in the bracket by 4/3. As. however, a 1/2 cone is more generally used 
than a 3/4 cone, it will be better perhaps to make the formula suit 
general rather than critical use. 
Putting in these two corrections and simplifying, we have for 
general work up to 50 diameters for emmetropic vision, the formula 
JL ( w 4. AM 
M V100 + N.A./ 
(Hi.) 
For powers of 100 and 150 diameters, I prepose to drop the 
accommodation depth and use only the second term multiplied by 2, 
thus, 
4 ft s 
M N.A. 
(iv.) 
