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Y. — On the Limits of the Optical Capacity of the Microscope. 
By Professor Helmholtz ; with a Preface by Dr. H. Fripp. 
The last number of the * Proceedings of the Bristol Naturalists' 
Society ' contained a translation of Professor Abbe's article on the 
" Theory of the Microscope," originally published in Schultze's 
* Archives.' In that article Professor Abbe stated the general con- 
clusions at which he had arrived after a prolonged investigation of 
the optical laws affecting the transmission of light through the 
lenses of the microscope. These laws relate to — 1. The divergence 
of the rays of light forming a geometrical image ; 2. The bright- 
ness of that image ; 3. The dispersion of coloured rays, and its 
consequences ; and 4. The diffraction of light occasioned by minute 
particles in the objects placed under (or before) the microscope. 
In explanation of these several phenomena, a theory of the micro- 
scope was stated in general terms, the mathematical demonstration 
of this theory, and its various applications, being reserved for a 
future communication. 
Simultaneously with Professor Abbe's researches, a most inter- 
esting investigation of the same subject was completed by Professor 
Helmholtz, and appeared in Poggendorff's 'Annals' (1874). The 
theoretical grounds taken by these two authors are identical, and 
their results, so far as the researches were directed to the same 
points, also agree. But in each essay the mode of treatment is 
thoroughly independent, and the experimental proof of the conclu- 
sions respectively obtained is conducted by each writer in a separate 
and original method. The mathematical demonstrations omitted 
in Professor Abbe's article are fortunately supplied by Professor 
Helmholtz, and the two essays are confirmatory and supplementary 
to each other in several other respects, whilst in both we recognize 
that clearness of thought and precise knowledge of the subject 
treated, which justifies entire confidence in the conclusions. It 
seems therefore to me that Professor Helmholtz's essay should 
naturally follow in this number of our ' Proceedings.' For, takto 
together, these two essays form the most complete and authori- 
tative exposition of the optical principles involved in the action of 
microscope objectives, and the most trustworthy interpretation of 
that action, and consequently of the capacity of performance of such 
objectives, that have as yet been made public. 
In introducing the first of these essays to the notice of our 
readers, I expressed my strong conviction of its high value as a 
contribution of really scientific character to the theory of the micro- 
scope. The essay of Professor Helmholtz deals somewhat more 
fully with that aspect of optical science which is known as physio- 
logical optics, and of which no physicist of our times has a more 
VOL. XVI. c 
