118 



Prof. S. P. Thompson on the 



ving only functions of the free electricity, or its volume-den- 

 sity, such as V 2 ^j since these will be independent of t. 



11. In order further to simplify the equations, we will nar- 

 row down the case to that of a plane wave of unpolarized light 

 propagated along the axis of z, and therefore lying in planes 

 parallel to the plane (pay), in which planes also the electric and 

 magnetic disturbances are executed. We will further suppose the 

 crystal under consideration to be, as tourmaline is, a uniaxal 

 crystal, and to have its optic axis coincident with the axis of x, 

 so that the x and y components of the disturbances will be 

 respectively parallel and at right angles to the optic axis. 

 We shall also make the assumption that in tourmaline the 

 vectors, or linear vector operators, which should stand for 

 K, fi, and C, may be represented with sufficient accuracy by 

 assigning to these quantities the values 



K D K 2 , K 3 , 



/^lj ^2) t^Zj 



Ql, C 2 , 3 , 



for their respective values as measured in the directions of 

 x, y, and z. 



We may then write, neglecting functions of J, which in the 

 case of periodic disturbances can at most be a linear function 

 of the time, 



clF . ^ d?F 

 df 



4z7rfJjlGl ~di +fJ,lKl 



+ V 2 F = 0, 



2 ^+^ 2 K 2 ^ + V 2 a=0, 



dt- 



: 3 ^+v 2 h=o. 



dt 



cm 



dt 



(2) 



Since, however, we are going to deal only with disturbances 

 in the plane (xy) propagated along the axis of z, we may sim- 

 plify the above to the following form : — 



(3) 



Or, in words, the rate of change in the transverse com- 

 ponents of electromotive force as the wave advances along the 

 axis of z is expressed as the sum of two time-functions of the 





dz 2 V > 



. n dG , ^ d 2 G 

 47r/ , 2 C 2 - +/ , 2 K 2 ^- 



dz 2 u? r 



. n dK , ^ dm 



= 0. 



