33S 
NOTES AND MEMORANDA. 
Aiyo'i)T)¥ diameter, controverted, more or less, tlie views 
propounded by the two Professors : — 
“ Mr. Dallinger’s paper is interesting. To get sight of a flagellum 
inch diameter in the microscope implies very clever manipu- 
lation. Its measurement was, however, indirectly achieved by finding 
the ratio of the f magnified flagellum to the actually measured dia- 
meter of the body. 
There is no question of resolving a structure here, and I entirely 
fail to see that the subject has anything to do with the theories of 
Helmholtz and Abbe. It is a question of physiological not microsco- 
pical limits of sight. 
Look at a fixed star, or at a white-hot platinum wire 80 feet from 
the observer in a lecture theatre : you see it, that is, an impression on 
the retina is made, but you cannot distinguish its outlines, features, or 
structure. 
So, an isolated line or particle may be seen under clever manipu- 
lation, in which management of light is everything. 
But if Mr. Dallinger had placed half-a-dozen of the flagella close 
together with interspaces equal to their own thickness, and then found 
that he could distinguish them s'eparately, such a fact would militate 
against Helmholtz’s statements. 
Helmholtz demonstrates (and embodies his demonstration in a 
formula) that there is a calculable interspace between finely drawn 
lines, which, when these lines are looked at through a microscope, still 
allows them to be separately visible to the eye, and that if the lines are 
closer together than this computed interspace, diffraction occurs and 
wipes out the actual state of things, replacing it with a diffraction 
spectrum. But Helmholtz does not apply his formula to measure 
distinctness of definition, which is an English misreading of the facts and 
statements. 
If we look at a fine network of white-hot platinum wires, should 
we see each single wire distinctly because we readily see one such 
when isolated ? 
The question of resolution of structure is a very different one from 
that of seeing a single fine line. Volkman has long ago shown what 
acuteness of vision means, and he has outdone the particular case of 
Mr. Dallinger in seeing a fine line against the light, but of course not 
in the microscope. 
Abbe has not, in any optical essay that I have seen, said a word 
about the possible or impossible limit of vision in the physiological 
sense, though many other writers have. 
The whole drift of Professor Abbe’s theory of the microscopic 
ima"e seems to me to be misunderstood by those who suppose that it 
applies to some given standard of acute vision. But it is not with 
visual sense, or with the capacity of the eye, that he deals. It is with 
the optical capacity pertaining to the microscope of presenting to the 
eye distinct and distinguishable details. And the factors which he 
had to consider are — 1. The peculiarities attendant upon the optical 
outspread of the microscopic image by presenting it under large 
angular divergence. 2. The peculiarities which render geometric 
