ON DR. CARPENTER’S ADDRESS. 31 
rect view of the biological work of Mr. Dallinger I would refer 
you to the letter he wrote to Mr. Miles, which was published in 
“‘The Northern Microscopist” for last October, in which he states, 
“No one has ever appreciated or found more pleasure and profit 
in the use of the large angles with which our lenses have been 
more and more perfectly provided for the last ten or twelve years 
than I have. As they have been produced I have obtained them 
each and all that had any real value.” . . . “ Much that had been 
done could never have been done without them.” ... “The 
homogeneous lenses have given me splendid results, some of which 
will shortly be published ; but no immersion lens of any kind could 
be used to work out to the end an organic life history,—that is, 
if it involved life and movement,—because, the object being in a 
limited area, and possibly in fluid, the fluid wder the cover does 
(when the movements of the object are followed) at length, without 
the spectator’s knowledge, mingle with the fluid adove employed 
for the lens, and thus destroy the whole object of search and study.” 
This, however, is no argument against the use of immersion lenses 
on preserved specimens. 
Dr. Carpenter tells us in the Address that he holds “the Podura 
scale as the best test of an objective for biological research ;” and 
again, “a good 2 inch should resolve the Podura scale with suffi- 
cient magnification from the eye-piece.” He has taught us in his 
“ Revelations” that it requires a ;‘jths to resolve the larger scales. 
Now, if we want a 2 inch to do the work of a higher power, we 
must extend its aperture; but this can only be done at the ex- 
pense of that quality of penetration which the Address advocates 
so strongly, and without which the Doctor considers that a lens 
must be an “inferior” one. With a low power the so-called 
“notes of exclamation” on the larger scales are seen as fine lines 
only, and Prof. Abbe’s theory of microscopical vision may be 
usefully summoned to our aid in order to ascertain the theoretical 
aperture that is capable of resolving them. From my own mea- 
surements of several of the larger scales on one of Topping’s slides 
I have come to the conclusion that a resolving power which may 
be expressed in the number of lines to ar inch as varying from 
20,000 tO 25,000 is necessary to separate the marks on these scales. 
Now, the aperture required to give this power of resolution ranges 
from 243° to 31°, an aperture which is possessed by no two-inch 
lens made in this country ; but in America these lenses are made 
with angular apertures ranging up to 25°, and they ought therefore 
to resolve some of the coarser scales. According to Prof. Abbe, 
the capacity of the eye for distinguishing lines in close parallel 
approximation varies in individual observers, those of keen sight 
being able to see a space having an angular extension of two 
minutes, whereas others may require double that quantity. This 
