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II. — On the Abbe Count Castracane's Photographs of Noherfs 
im Band. By H. C. Sorby, F.K.S. 
I HAVE lately received from Count Castracane some photographs, 
taken by him, of Nobert's 19 th band, and a letter on the subject, 
which I translate as follows : 
" I read with much attention the interesting address given by 
you at the annual meeting of the Koyal Microscopical Society, and 
having well considered it, I wish to be allowed to make some obser- 
vations on the ultimate limits of the microscope, referring to some 
personal experiments, which, however they may on the whole tend 
to confirm what you have demonstrated, yet still seem to prove 
that the formula of Helmholtz is not yet the last word that may 
be said on the subject of the final powers of the microscope. 
" The illustrious American microscopist, Dr. Woodward, having 
had the politeness to send to me examples of his magnificent 
microscopical photographs, and amongst these those of Nobert's lines, 
I also wished to ascertain whether I could succeed in photographing 
the 19th band, containing a series of lines at a distance of tt^V^tt 
of an English inch. After many and various trials, I was at length 
most fortunate in reproducing those exceedingly fine striae, by using 
a magnifying power of 800 linear. The photographic negative was, 
however, much obscured by general shading, but as it was more in 
accordance with what could be seen by direct vision, I was satisfied 
with the result. In order to convince myself that the lines seen 
on the photograph are genuine, and not due to interference fringes, 
I resolved to measure their distance by means of the microscope, 
and by dividing this distance by the magnifying power, I found 
that I had not been deceived. That I did not find the thirty-seven 
lines observed by Dr. Woodward, depends on the difierence in the 
preparation of the original. I therefore have also obtained the reso- 
lution of a series of lines at a distance of tt^W^ of an inch, by 
using a photo-micrographic objective of -f^ of a Grerman inch in 
focal length, very accurately constructed for me by Gundlach. 
" In your address you asserted, on the authority of Helmholtz, that 
the limit of the power of resolution of a dry lens was equal to three- 
quarters that of an immersion lens, all the conditions being the 
same, and thus if I had used an equally perfect immersion lens 
I may perhaps conclude that I should have arrived at a resolution 
of T^-oVoir of an inch. At all events, it appears that I may con- 
clude that with a dry lens I have attained to the true and certain 
resolution of tt2Vt> o of an inch, which is somewhat beyond the limit 
indicated by Helmholtz's theory. 
" Although I do not feel able to demonstrate theoretically how 
this is possible, I am anxious to furnish the data necessary to enable 
