132 
BULLETIN OF THE LABORATORIES 
(/. e. that passing at right angle to the optical axis and vibrating in the principal 
section. If the axis c coincides with the optical axis a and e the mineral is neg- 
atively double refractive, while if c= c and wc^e, the mineral is positively double 
refractive. A thin section of a crystal of either the tetragonal or hexagonal sys- 
tem, if ^ basal, (£ e. parallel to O) acts as though isotropous and remains dark in 
all positions between crossed Nicols. On the other hand, sections taken vertical 
to O, or parallel to one of the prismatic faces, are dark fwice in a revolution and 
these points occur when the sides of the section are parallel to the principal section 
of the NicoPs prisms. In such a cas^e the extinction is said to be perpendicular 
or parallel to the crystallographic axis. Sections inclined to the vertical axis or 
such as are parallel to a pyramidal face are extinguisned parallel to the vertical 
axis, but not necessarily to all the sides. Whether the mineral proven to be uni- 
axial is hexagonal or tetragonal can only be discovered by ascertaining the num- 
ber of sides of a section transverse to the vertical axis. 
In biaxial minerals there are two directions without double refraction. Three 
axes are assumed, each of which is at right angles to the others and has a differ- 
ent amount of elasticity of the ether. These elasticity axes are lettered a, h and 
C, in order of elasticity. Two of the optical axes do not correspond with the 
crystallographic axes, but the two sets of axes form with each other larger or 
sm iller angles. The line which bisects the acute angle = acule bisectrix, that 
which bisects the obtuse angle = obtuse bisectrix. The optical axes and both the 
acute and obtuse bisectrix lie in the same plane, called the optical plane, perpen- 
dicular to which is the optic normal. The axis of intermediate elasticity (6) co- 
incides with the optic normal, while the axes of least and greatest elasticity may 
coincide with either bisectrix. If a coincides with the acute bisectrix, then c co- 
incides with the obtuse bisectrix and the mineral is negative. If, on the other 
hand, c coincides with the acute bisectrix and a with the obtuse, it is positively 
double refractive. a, /3, y are the indices of refraction corresponding to the three 
axes of elasticity. 
In the case of minerals of the Orthohombic system the three axes of elasticity 
a>&>-C correspond with the crystallographic axes a, b, and c, but not necessarily 
in such a way that a always corresponds to a, etc. a and c are always bisectrices 
and the optical plane is always parallel to one of the three pinacoids. 
The following are possible i 
If Opt. plane = O, a=a, b-=c I / y. 
a=c, b=a ) “ 
If Opt. plane =i-i,c^=a, a=c 1 i y, 
C^=c, a=a / 
If Opt. plane = i-L c'=a, b=c 1 .. y- 
c'=c,b=a}‘‘=^ 
Sections parallel to one of the three pinacoid surfaces (usually rectangular) extin- 
guish perpendicularly, i. e. become dark between crossed Nicols when one side of the 
rectangle or one of the pinacoid cleavage lines is parallel to the main section of the 
Nicol. Distinguished from isometric minerals by the fact that basal sections (par- 
allel O) are not isotropous Only such sections are isotropous as are exactly verti- 
cal to the one or the other of the optical axes, which would be the case, accord- 
