288 Wright — Optical Character of Birefr acting Minerals. 



Bertr and- Mallard method for measuring the optic axial angle 

 (2E) under the microscope. Mallard has shown that the distance 

 of the trace of an optic axis from the center of the interference 

 figure is proportional to the sine of the angle which the optic 

 axis makes with the axis of the microscope ; that, if the distance 

 D be measured by means of a micrometer ocular, the angle E 

 can be figured from the formula 



sm & = = 



in which K is the constant of the microscope to be determined 

 once for all on a substance whose 2E is known. By drawing a 

 circle of radius K in fig. la (once for all), the angle E corre- 

 sponding to any number of divisions of the micrometer ocular is 

 then the angle in the figure included between its base and the 

 radius passing through the intersection of the arc K with the 

 horizontal line at the distance D from the base line. To convert 

 2E into 2V use fig. la, which was derived from the formula 



. ^ sin E 



sm V = 



n m 



n m being the medium refractive index of the substance. The 

 angle 2V is then the angle on the degree circle included between 

 the base line and the horizontal line which passes through the 

 intersection of the radius E and the given refractive index arc. 



Michel Levy method. Michel Levy has developed a formula 

 from which approximate values of the axial angle 2E can be cal- 

 culated, provided the index of refraction of the objective lens 

 in which the interference figure is observed be known. As this, 

 however, is not generally the case, a modification of the formula 

 by introducing Mallard's constant in place of the refractive index 

 is better suited to actual practice. 



Fig. 2. 













X 











/F 



~~i£~ 



\fl, 













, 



ia. ^^ 







/ 







1 









' / 









t° 



e 





'/ 





** 





| 





HY 















In fig. 2* let the plane of the paper represent the section per- 

 pendicular to the bisector of the acute optic axial angle and the 

 figure itself the achromatic lines observed in convergent polar- 



* Compare Preston, Theory of Light, 3d ed., pp. 400-401. 



