330 F F. Wright — Measurement of the Oj)tic Axial Angle 



different. On an average, a movement of 6 divisions or •03 ram 

 corresponded to one degree, so that with this method of special 

 refinement, the probable error for E remains at least ± 10', 

 and in wide hyperbolic bars, differences of 1° and over should 

 be expected. 



If only a single screw micrometer ocular be used, the section 

 should be cut very nearly normal to the acute bisectrix, other- 

 wise the values become much less certain. With a double 

 screw micrometer ocular, however, this error can be eliminated 

 directly and equally good values obtained on sections only 

 approximately normal to the acute bisectrix, as will be shown 

 later (page 336). 



In place of solving the above equations D=K sin E and 

 sin E = /3 sin V by logarithms, it is possible to use a graphical 

 method which is sufficiently accurate for the purpose and which 

 Fedorow appears to have been the first to use.* An accurate 

 drawing (Plate II) is made once for all which serves for all 

 possible angles and all refractive mineral indices to be encoun- 



. D 



tered. To solve the equation' D=K sin E, or sin E = ,— , draw 



the circle with radius K (Plate II, preferably in colored ink); 



the intersection of the ordinate D with this circle makes then 



the angle E in degrees, as is evident from the right angled tri- 



i m i i • • i^ r> • T-r s i n E sin V 

 angle, lo solve the equation sin E = p sin V , or = , 



J 



find the intersection of radius E° with the circle for the given 



refractive index and pass horizontally from this point to inter- 

 section with outer circle of drawing, which point indicates "V 

 in degrees. 



Examples. 



(1) K = 54-0 D = 21-l 

 Intersection of ordinate D with K-circle is at radius 23°. 



(2) E = 42° j8 = l-65 



Pass along radius 42° to intersection with circle labelled 

 yS = l - 65, and then horizontally to outer circle and read V = 24°.f 



* Fedorow, Zeitschr. f. Kryst. xxvi, 225-261, 1896. F. F. Wright, this 

 Journal, xx, 287, 1905. 



f The drawing of Plate II can also be used to solve the birefringence for- 

 y — a' 

 inula of Biot, = sin a a sin a 2 , which is very approximately correct and 



has been used frequently in optical work and in which / — a' denotes the 

 measure of birefringence for any given section of a mineral, y — a, that of 

 the maximum birefringence of the mineral, a^ and a 2 the angles included 

 between the normal to the section and the two optic axes respectively. 

 This formula can be solved graphically at once by noting the length of the 

 ordinate of the point of intersection of the radius a 2 with that circle whose 

 radius is equal to the ordinate of the point of intersection of the radius a x 

 with the outer circle. This graphical solution gives directly the relative 

 birefringence of the section in per cent of the absolute birefringence (y — a) 

 as represented by the radius of the outer circle. 



