EXTINCTION ANGLES 
265 
allel with the same cross-hair. The graduated stage circle is 
again read. The difference between the two readings is the 
angle sought. 
If it is known that the cross-hairs in the eyepiece are exactly 
at right angles, a slightly quicker method consists in measuring 
the complement of the angle and deducting it from 90 degrees. 
Or, if the angle be obtuse, measure the amount that is greater 
than 90 degrees. This method does not necessitate as careful 
centering of the stage, and can, therefore, be used with high 
powers with sufficient accuracy for analytical work. It is essen¬ 
tial in all measurements of crystal angles that the instrument 
be most carefully focused upon an edge, and that care be taken to 
avoid error due to the projection of an image of another edge 
through the crystal. In the case of very transparent crystals 
it is sometimes difficult to tell which is the proper line (edge) 
to employ, unless the crystal is thin. 
For the measurement of solid angles where several planes 
meet, the crystals must be of sufficient size to permit their being 
turned first in one position, then in another. Cementing to the 
point of a needle (method of Kley 1), imbedding the head of the 
needle in a cork and cementing the cork to a glass slip will per¬ 
mit of the crystals being sufficiently easily orientated to yield 
fairly accurate measurements. 
Or, we may employ the glass hemisphere (see Fig. 74), or the 
orientating apparatus of Klein (Fig. 75). 
Microscopes having fixed stages require the employment of a 
goniometer eyepiece, consisting essentially of a cross-hair system 
rotating in conjunction with a graduated circle. With this device 
the centered crystal remains in a fixed position and the ocular 
cross-hairs are rotated in such a manner that one of them is first 
made parallel to one boundary edge, and then to the other edge 
of the angle sought. 
Extinction Angles.2 — The extinction angle of a crystal may 
be defined as “ the angle between an axis or direction of elasticity 
and some known crystallographic direction.” The crystallo- 
1 Kley, Rec. trav. chim. Pays-Bas, 19 (1900), 13. 
2 See Wright, Measurement of Extinction Angles ; Am. J. Sci. (4), 26 (1908), 349. 
