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 *), 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. 



