ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 
665 
found in all, but tlie evidence does not yet seem complete. There is 
here a good field for further investigation. 
This leads me to say that the size of the fibrils shown by Mr. Smith 
does not seem to me so minute that any good 1/10 or 1/15 objective 
should not define them. We must remember that the condition of an 
object may count for much in the resolution of its structure. A thickly 
silicified shell may not show what an imperfectly silicified one will 
demonstrate. The former will break into small angular bits with a 
mineral fracture ; the latter may separate into threads or membranes. 
The floating off of the fibrils in print No. 15 seems to show that the 
shell was in a peculiar condition ; a sort of dissection of an uncommon 
kind having taken place naturally or artificially. It would be an inter- 
esting experiment to subject various species of Pleurosigma to the action 
of hydrofluoric acid for varying periods, and then mount them for 
examination. To extend Prof. Bailey’s old experiments in this direction 
would be very useful, but the danger of injury to the objective is such 
that it would hardly be advisable to watch the action of the acid under 
the Microscope. 
If I seem to have reduced the new matter in Mr. Smith’s observa- 
tions to a minimum, I should not do justice to my sense of the real 
value of his work unless I add that enough remains to make it, in my 
judgment, a very important and interesting step in the investigation of 
diatom-structure. It is also full of promise that still further results 
may be attained by pursuing the investigation on the same line. I am 
confident, therefore, that the Society will join with me in expressing a 
sincere sense of obligation to him for communicating the results of his 
observations, and especially for the valuable aid in understanding them 
which is given by his beautiful series of lantern slides and prints.” 
On a new Method for the Measurement of the Focal Length of 
Lenses or Convergent Systems.* — Sig. G. Yanni gives the following 
method for measuring the focal length of lenses. If F denote the focal 
length, p and q the distance of the object and image from the two focal 
points, we have pq = F 2 . Small displacements of the object A 
produce corresponding small displacements of the image 8 8 1 in such a 
way that always (p + A) (q — 8) = F 2 and (p — A x ) (q -f- S x ) = F 2 . 
These three equations determine p, q , and F when the displacements 
are known. The plane object is movable on the optical bank and the 
position of the image corresponding to known displacements of the 
object is determined by means of a Microscope. 
Proof of a simple Relation between the Resolving Power of 
an Aplanatic Objective of the Microscope and the Diffraction of 
the finest Grating which the Objective can resolve. | — M. C. J. A Leroy 
starts with the general theorem of Abbe that an objective in order to 
resolve a grating must have its aperture sufficiently large to admit at 
least two spectra of the grating. Abbe deduces this relation as the 
expression of a special function of the angular aperture of the 
* See Central-Ztg. f. Optik u. Mechanik, xii. (1891) p. 152 ; and Atti dell’ Acc. 
d. Nuov. Line., 6, 90. 
f Seances de la Soc. Franc, de Phys., 88. See Central-Ztg. f. Optik u. 
Mechanik, xii. (1891) p. 152. 
