122 



Prof. 8. P. Thompson on the 



being frittered away into heat within the conducting medium 

 by reason of the resistance encountered. 



17. Case iii. (Medium possessing both Dielectric Inductive 

 Capacity and- Conductivity , the values of K and C being of 

 comparable order of magnitude, but having different values in 

 different directions). 



We have (from § 11) the equations 



. n d¥ L _ d 2 F d 2 F 





= W> 



. p dR _ dm 



F and G being the components of vector-potential in the x and 

 y directions respectively, the problem is to determine at what 

 rate these will be diminished by absorption in passing through 

 a given thickness z of the medium when the conductivities 

 per unit volume in those directions are respectively Ci and C 2 . 

 The proportion borne by the transmitted electromagnetic dis- 

 placements of the luminous wave to the original displacements, 

 after traversing a thickness z of the crystal, will (neglecting 

 tbe small proportion lost by surface reflexion) be expressed by 

 an exponential of the form 



where p is the coefficient of absorption. This coefficient Max- 

 well has calculated (art. 798) for the case of isotropic conduct- 

 ing media, from the general fundamental equation, on the 

 assumption that the disturbance may be expressed as a circular 

 function of the form cos (nt—qz). Following the lines thus 

 laid down, we will write:— 



F = e-^cos=-fVV-s), 

 M 



G=6-^cqs^(V 2 /-*), 



where p l and p 2 are coefficients of absorption in the x and y 

 directions respectively, and where V 1 and Y 2 are the two velo- 

 cities of propagation (see § 13), and where X x and \ 2 are the 

 corresponding lengths of waves. Now, putting 



2tt 



(9) 



0i= 



08 = 



2tt 



(10) 



