10 
sorby: optical characters of minerals. 
The characteristic peculiarity of crystals like aragonite, 
which have two optic axes, is that, when the section is so cut 
that the images are directly superimposed without lateral 
displacement, they give two bifocal images, and four apparent 
indices. When cut in particular directum s one of these 
images may become unifocal, but then there is a more or less 
considerable lateral displacement of the two images. When 
the section is cut perpendicular to the line bisecting the acute 
angle between the optic axes, so as to give two very bifocal 
images, the images of the circular hole are crosses at two 
different foci, and not, as in the case of calcite, two circles. 
Biaxial crystals have three true indices of refraction (/x, //, fx"), 
and, if the section be accurately cut in the plane of any 
two of the axes of elasticity, so that there is no lateral 
displacement of the images, the four apparent indices observed 
from the lines of the grating are as follows : — 
Polarised in 
one plane. 
Polarised in 
the opposite 
plane. 
From lines perpendicular to the plane ) 
of polarisation J 
From lines parallel to the plane of ) 
polarisation / 
a? 
Calling these observed indices a, b, c, and d respectively, 
we thus have = Ja^cov Jbd. It follows from this that 
we can determine the value of all three indices by very 
simple observations, made by employing a single section cut 
in the plane of any two of the three axes of elasticity. 
Absence of lateral displacement in the images at once shows 
us that the specimen in its natural state, or as artificially cut, 
is sufficiently parallel to one of these planes to be suitable for 
the determination of the indices ; but even if it is not such as to 
