IN PERFECTLY TRANSPARENT MEDIA. 207 



observer, who looks in the direction opposite to that of the propagation 

 of the light,* we have 



(35) 



By the preceding equation, this reduces to 



- (36) 



Without any appreciable error, we may substitute U 4 for V E 2 V L 2 , 

 which will givet 



< 37 > 



19. Since these equations involve unknown functions of the period 

 they will not serve for an exact determination of the relation between 

 and the period. For a rough approximation, however, we may 

 assume that the manner in which the general displacement in any 

 small part of the medium . distributes itself among the molecules and 

 intermolecular spaces is independent of the period, being determined 

 entirely by the values of r\, and their differential coefficients with 

 respect to the coordinates. J For a fixed direction of the wave-normal, 

 <f> and <' will then be constant. Now equations (15) and (36) give 



To express this result in terms of the quantities directly observed, we 

 may use the equations 



A -r-r K> -\-f *C f-r- K 



P = k> v *=v VL= < U= V 



where k denotes the velocity of light in vacuo, \ the wave-length 

 in vacuo of the light employed, TI R , n L the absolute indices of refrac- 

 tion of the two rays, and n the index for the optic axis as derived 

 from the ellipsoid (24) by Fresnel's law. We thus obtain 



2 /OQX 



X 4 



* When the rotation of the plane of polarization appears clockwise to the observer, 

 it has the character of a left-handed screw. But the circularly polarized ray to which 

 V R relates, the rotation of which also appears clockwise to the observer, has the 

 character of a right-handed screw. 



t The degree of accuracy of this substitution may be shown as follows. By (33) 



V R (V K 2-U 2 ) = V I .(U 2 -V L 2), 

 whence 



Compare 12 of the former paper, on page 189 of this volume. 



