ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 
C83 
the two divisions adjusted by the movement from right to left, and Y x , Y 2 
the displacements of the scale s, then, since 
f = 
ft ~ ft 
where 
Yi 
ft = 
Y 2 -y 2 
Y, 
we have 
V± _ 
y, 
The Dioptric Conditions for the Measurement of Optic Axial 
Angles by means of the Polarization Microscope.* — Dr. S. Czapski 
lays down the following conditions in the determination of the optic 
axial angles of crystals : — 
(1) The condenser system must have an aperture at least as large as 
that of the objective. 
(2) The crystal plate must be parallel. 
(3) The relation between the axial angles of rays in a pair of con- 
jugate points 0 and 0* of the objective must be known. 
(4) At 0 must be the crystal plate, and at 0* the eye. 
(5) It is best to use an aplanatic eye-piece, and to make the path of 
the rays of the auxiliary Microscope “ telecentrisch.” 
((>) For measurement with different wave-lengths the objective must 
be apochromatic, i. e. spherically chromatic, and corrected for the whole 
visible spectrum. 
Geometrical Representation of the Formula for Lenses. t — M. 
D’Ogagne states that by a well-known construction the magnitudes 
occurring in the formula 
I + i = 1 
V f f 
may be represented by the distances in which a straight line rotating 
about a fixed point cuts two rectangular axes, and the distance of the 
centre of rotation from the centre of the co-ordinates. He remarks that 
this construction is more convenient if the axes are taken as intersecting 
at an angle of 120° instead of 90°. 
Rings and Brushes.— Mr. E. M. Nelson read the following note at 
the April meeting ; — It is a curious fact that nowhere in microscopical 
text-books is any account given of the method of viewing the rings and 
brushes which certain minerals show under polarized light. 
There are perhaps some microscopists who, thinking that such objects 
c m only be seen with a petrological Microscope, and having no desire 
to prosecute deep research in that direction, and being unwilling to 
purchase a petrological Microscope, are content to shelve the subject. 
Now as these beautiful objects are within the reach of all those who have 
an ordinary microscopical outfit, I thought it worth while to bring before 
the Society an explanation of a simple way of seeing them. 
If you set up your instrument as if for viewing ordinary polariscope 
objects, not a ring or a brush will you see. 
The whole point lies in the fact that it is a wide-angled telescope 
you require and not a Microscope at all. Once this is recognized the 
* Zeitschr. f. Wiss. Mikr., ix. (1892) p. 130. 
f Central-Z tg. f. Optik u. Mechanik, xiii. (1892) p. 146. 
