CHAPTER IV. 
EXTINCTION ANGLES. 
For a mineral plate in the thin section the term extinction angle signifies 
the angle between a known crystallographic direction (e. g., cleavage line, or 
or trace of a crystal face on that plate) and one of its optic ellipsoidal axes C' 
or rt' or directions along which it extinguishes when these axes are parallel 
with the principal planes of the crossed nicols. In order to ascertain this 
angle satisfactorily one must be able not only to measure plane angles 
accurately, but also to locate correctly the position of the optic ellipsoidal 
axes of the particular crystal plate. The first condition is easily accom- 
plished and demands no special comment, while the second requirement is 
extremely difficult to meet satisfactorily without great expenditure of time. 
Many methods have been suggested by which the position of the optic 
ellipsoidal axes of a given crystal section can be located more or less exactly, 
and all are based on the fact that when the optic ellipsoidal axes are parallel 
with the principal planes of the crossed nicols the plane polarized light 
normally incident from the lower nicol passes through the crystal plate 
without changing its plane of vibration. In case the optic ellipsoidal axes 
of the plate do not coincide with the planes of the nicols, interference 
generally takes place and some light passes through the upper nicol. The 
different methods proposed have for their common object the rendering 
apparent the extremely small percentage of light which thus emerges from 
the analyzer when the angle of rotation of the crystal plate from its position 
of total darkness is very small. 
Before considering in detail the different methods for accomplishing this 
result and their relative merits and defects, it will be well to treat the 
subject mathematically and to derive the formulas for the intensity of light 
with special reference to the subject of extinction angles. This treatment 
is given in some detail in the following paragraphs, since the deductions 
recorded later are all drawn from these fundamental equations. 
MATHEMATICAL FORMUL/E FOR THE INTENSITY OF LIGHT. 
The phenomena of light are considered to be produced by periodic changes 
or disturbances in the ether, transverse to the direction of propagation. 
Different hypotheses have been proposed which assign different properties 
to this medium, but no one of the hypotheses yet suggested is satisfactory 
in all its details. For the purposes of this paper, however, these disturb- 
ances may be considered to be vibrations of ether particles about positions 
of rest and in a plane normal to the line of wave propagation. Adopting 
this view chiefly as a matter of easy expression, we may assert that in plane 
polarized light the disturbances or vibrations are confined to a plane, each 
particle vibrating then with simple periodic motion, to and fro, pendulum- 
"5 
