182 F. E. Wright — Transmission of Light through 



In these last two equations, (b) and (c), the azimuth 8, may 

 assume any value, since the structure of isotropic substances 

 does not prescribe definite planes of polarization for transmitted 

 waves, as do anisotropic substances ; but if 8 X be once given, 

 8, is then = 8, ± 90° 

 and the last equation, (c), may be written 



tcl s> = tffd > fr c ' 



J ' cos (i-r) ~ cos (i-ry (46c') 



From this formula, the angle 8' can be calculated, provided 

 e„ i and r be given. The difference (e, — 8\) is. then the 

 amount of rotation which the plane of polarization of incident, 

 monochromatic light suffers on transmission through the 

 isotropic plate. 



In case the light wave passes through several plates, 

 cemented together as in a thin section mount where w, is the 

 refractive index of the object glass, n a that of the Canada 

 balsam, and n 3 that of the cover slip, an incident wave i 



becomes r, in the object glass, where sin r i = ; similarly, 



r 2 and ?' s are the angles of refraction in n 2 and n 3 and can be 

 calculated by the general sine formula above. From formula 

 (465) and (46c) it is evident that the total rotation of the plane 

 of polarization of a transmitted wave under these conditions is 



cot S' = cot e cos(e— rj cos(r 1 —r i ) cos(?' 2 — r 3 ) cos(i— r 3 ) 



Summary. — In the foregoing pages the formulas have been 

 developed which are especially useful in a consideration of the 

 phenomena observed on mounted crystal plates in convergent 

 polarized light. In this discussion, the effects of the plates on 

 reflected light waves have not been treated in detail, nor has a 

 study been made of the relative amplitudes of the reflected 

 and refracted waves ; attention has been directed rather to the 

 effects of transparent, inactive plates on the planes of polariza- 

 tion of transmitted light. In the calculation of these effects, 

 four steps are necessary ; (1) if. the angle of incidence * of the 

 entering light wave be given, the angles of refraction r 1} r^ of 

 the two transmitted waves are found by means of formula 

 (16) in the case of biaxial plates, or by (41) for uniaxial plates, 

 or by (46a) for the single transmitted wave in isotropic plates. 

 (2) The azimuths of the planes of polarization of the two 

 refracted waves are then found by use of equations (17) for 

 biaxial plates, or (42) for uniaxial plates. In the case of iso- 

 tropic plates the plane of polarization of transmitted waves 

 may have any azimuth, so far as such azimuths are dependent 

 on the structure of the material. (3) Having given the angle of 



