STUDY OF ORES AND METALS. 431 



shown above, small and therefore the cosme of the angle (A2 — A^) 

 not greatly different from unity indicates that </' is only slightly 

 smaller than whose tangent is (equations (22) and (44)) 



^''"' " r,' [(«2 + ly + n2^K2'][(wi - I)' + wi'/ci^ • 



The right-hand side of this expression is identical with that ob- 

 tained for the intensity ratio. Therefore, in general, the square of 

 the tangent of the angle of rotation 6 is approximately equal to the 

 intensity ratio. As this increases so also does the angular rotation 

 of the plane of polarization. 



The above equations and the methods based on these equations 

 do not sufihce for the determination of the optical constants n^, n^, 

 Kj, /Co of an opaque crystal examined only under vertical incidence. 

 They do indicate, however, that for the detection of anisotropism 

 the phase difference between the two components Rs and Rp is ordi- 

 narily not sufficiently large to be readily measured and that therefore 

 the phase difference is of little value as a diagnostic feature. The 

 other variable factor is the amplitude ratio. This gives rise to a 

 difference in intensity of the components of the reflected wave. For 

 certain cases in which the reflected waves are plane-polarized one 

 of the components is more intense than the second and the excess in 

 intensity in the one direction produces a certain amount of polarized 

 light after reflection of the non-polarized, incident waves ; this can 

 be detected by methods similar to those which have long been in use 

 for the detection and measurement of polarized light in the sky. 

 Since for most substances the phase difference between the reflected 

 components is not great, methods suitable for the detection of small 

 angular rotations of the plane of polarization of incident plane- 

 polarized light may also be used to detect anisotropism in opaque 

 bodies. A brief description of the several methods which may serve 

 for this purpose will now be given. 



Methods Based on Intensity Contrast. 

 These methods are wndely used in the measurement of sky polar- 

 ization and have proved to be of great usefulness in that connection. 

 One of these methods has been applied by J. Koenigsberger to the 

 detection of anisotropism in plates of opaque crystals. 



