658 
SUMMARY OF CURRENT RESEARCHES RELATING TO 
is in direct opposition to that of Prof. Ahbe,’ and to maintain it he 
denies the truth of the diffraction theory as applied to microscopical 
images. He says of it : * The diffraction theory rests on no mathemati- 
cal proof — in the main it accepts the physical law of diffraction ; but on 
experiment it utterly breaks down, all criticism is stopped, and every- 
thing connected with it has to be treated in a diplomatic kind of way.’* 
I state Mr. Nelson’s position without any purpose of discussing it, and 
only to point out that it is this to which Mr. Smith refers in his paper 
•when he says : ‘ This capacity of standing more light was pointed out 
from the first by Mr. E. M. Nelson, but has not received the attention 
it deserves, and the neglect of this point has stultified the efforts of many 
microscopists, both here (in England) and on the Continent, to get more 
out of the new glasses than the old objectives.’ 
Mr. Smith’s investigation of diatom-structure is thus closely con- 
nected with Mr. Nelson’s views and experiments upon the diffraction 
theory. Both will challenge the attention of practical microscopists as 
well as physicists. I have not gone far enough in my own investiga- 
tions to warrant me in expressing a judgment on the questions involved; 
but I would urge every microscopist to make his ordinary work the 
occasion for accumulating evidence which may help to settle the very 
important debate. My suggestions are only such as are based upon the 
well-known history of diatom-study and my own experience. They are 
offered by way of clearing the field by pointing out the limits of the 
discussion and the known facts which ought to be kept firmly in mind 
in all such investigations. 
It is no reproach to the Microscope as an instrument of investigation 
that there are limits to its powers and capabilities. Such limitations 
are common to all methods of investigation. If, trusting to my natural 
eyesight, I am trying to make out the meaning of appearances on a 
distant hillside, I find at once that all perception by the sense of sight 
is an interpretation of visual phenomena which are not in themselves 
decisive. They may lack clearness by reason cf the mist in the air. 
They may be obscured by something intervening, like foliage, or may 
be partly hidden by inequalities of surface. A thousand things may 
prevent clear and easy interpretation of what I see. I may have to 
change my point of view before I can reach a conclusion, or even have 
to go to the object itself. If I cannot do this 1 may be left in abiding 
doubt as to what I have seen. 
Microscopical examination is precisely analogous to this. If I am 
examining a mounted object I am tied to one point of view. I cannot 
approach nearer, and cannot do more than note the visual appearances 
and make theories to account for them in accordance with facts already 
learned. We try to vary the conditions as much as we can ; we change 
our objectives ; we try central light and oblique light ; we examine one 
specimen dry and another in a dense medium ; one by transmitted and 
another by reflected light ; but when we approach the limit of minute- 
ness of object or detail which our instruments will define, we are in the 
same situation as when using our natural eyes across a chasm, neither 
better nor worse : we have to account for what we see by a reasonable 
* Quekett Club Journal, July 1890, pp. 124-5. 
