The Penetrating Power of the Microscope. By E. M. Nelson. 339 
For powers from 200 diameters and upwards I propose to use the 
second term only, viz. 
- 2 . ?* . . (v.) 
M ■ N.A. v ’ 
After 300 diameters on a balsam mount, the penetration becomes 
less than 1/10 of one division on the head of Zeiss’s fine-adjustment, a 
quantity which may be neglected. 
With regard to myopic sight, unless a large number of measure- 
ments of the accommodating powers for different degrees of myopia 
with the respective penetrating powers were made, it would be quite 
impossible to state what corrections should be made, and whether 
various degrees of myopia required different corrections. The follow- 
ing formula may be used as a very rough approximation up to 50 
diameters. 
£{£(*- ?) + £}• <*> 
With the data given in our example above, the corrected penetra- 
tion for normal sight will be 
1-5 /250 2 x -127\ 
10 \100 ■* -1 / 
= -15 (2-5 + 2*54)= -756 mm. 
This is 1/5 of the previous result ; if, however, a full cone had been 
used in this instance as in the former, this result would have been 1 /7. 
Another question arises, viz. : What is the photographic penetrating 
power ? 
If we assume that the permissible amount of fluff is double that 
of the visual image, it will be the same as that of formula (iv.). 
It only remains now to construct a table of penetration which will 
yield values in agreement with practical results. The following table, 
although based on formulae obtained theoretically, is really empirical, 
owing to the corrections that have been applied. 
Being unable to find a reason for the paralysing effect, it is 
impossible to construct a formula on theoretical grounds that will 
meet the case. 
With regard to optical formulae which are frequently applied to 
the Microscope, it is, I think, a great pity that the proof is assumed. 
As the proof is not given in the text-books, that for the two 
formulae used in this paper, and which, moreover, are always 
occurring in microscopical papers, is appended. I start from the 
well-known fundamental optical formula - + - =1, but would ask 
P P f 
those who wish to take an intelligent interest in the theoretical 
2 b 2 
