OF DENISON UNIVERSITY. 
133 
ing to the position of the optical plane, in the plane l-I, i-i or a prismatic surface. 
Hence isotropous sections are more rare and less regular than in isometric minerals. 
Sections parallel to the vertical axis in the zone i-I, i-i extinguish perpendicularly. 
In monoclinic minerals only the ortho- diagonal {b) coincides with one of the 
axes of elasticity, the other axes of elasticity form angles with a^ and of . The op- 
tical plane is either parallel or at right angles to the plane of symmetry i-i. 
If optic plane = i-I the acute bisectrix = C) ^ 
or “ “ = a i 
then c and a are inclined toward C and a. 
If optic plane is at right angles to i-i. 
the acute bisectrix = b=a 
“ “ =b=C ' 
or the obtuse “ = b=a 
“ ‘‘ “ = b=c 
then h and c or b and a are inclined toward c^ and a^. 
As a result of the inclination of the axes of elasticity to the crystallographic 
axes certain of the longitudinal sections are not extinguished when the crystallo- 
graphic axes coincide with the principal plane of the Nicol’s prism. Sections in 
the zone O. i-i, all are extinguished perpendicularly, for in this case the orthodi- 
agonal coincides with an axis of elasticity. 
In Triclinic minerals none of the three axes of elasticity coincides 'with the 
crystallographic axes. All sections parallel to the three pinacoid surfaces, there- 
fore, are obliquely extinguished. The angle of extinction in the planes O and 
i-i is known for most triclinic minerals and forms a ready means of determining 
these minerals. In thin sections the shape of the section will generally make it 
clear whether it is or is not parallel to a pinacoid. Accurate measurements of the 
angle of extinction must be made in cleavage plates parallel to i-i and O. 
Twinning Phenomena. 
Twins in the regular system cannot be recognized by the polarizer. Twins in 
the tetragonal and hexagonal systems cannot be recognized unless the axes of the 
twins are inclined toward each other. If one individual, in such a case, appears 
dark between crossed Nicols the other may appear colored. 
In some cases a crystal individual is made up of alternate lamellae of the same 
mineral in different position relative to the axis. Such aggregates are called poly- 
synthetic twins. In plagioclase feldspar, calcite and disthene this frequently oc- 
curs. In such minerals the adjacent lamellae will not be extinguished simultane- 
ously under polarized light. 
In the rhombic system the twinning plane is usually one surface of a brachy- 
dome, a pyramid or a prism. Pleochroism in colored minerals assists in deter- 
mining the relation of twinned crystals. 
In the monoclinic system the plane is often i-P. 
In the tr-iclinic system the polysynthetic form appears very frequently. In 
plagioclase the twinning plane is generally i-i (albite type). Sections at right 
angles to this plane in the zone O. i— i always exhibit the banded colors in polarized 
light. Twins of this type are impossible in the monoclinic system, because the 
