NOTE ox THE THEORY OF ELECTRIC ABSORPTION 141 



8- -k dV 

 k Wi' 



and 



1 dm _. j^ /*. 

 cm - 4:rw 8 dn IS 



JL 



this equation (3) gives the value of - =m at all points of the body 



and at all times so that the phenomenon of electric absorption shall not 

 take place. As this equation makes m a function of x, y, z, S and t, 

 the relation in general is entirely too complicated to ever apply to 

 physical phenomena, without some limitation. Firstly then, as c is only 

 an arbitrary function of t, we shall assume that it is constant ; 



.. . 



cm 47:w 2 dn 6' 



The most important case is where m is a constant. Then 



dm _ ~ 

 ~dn ~ 

 and 



c = 4:xm, S=S a s-, p = p.e-. 



In this case, therefore, we see that both the electrification and the 

 currents die away at the rate c. The case where Ohm's law is true and 

 the specific inductive capacity is constant is included in this case, seeing 

 that when Jc and % are both constants their ratio, m, is constant. But 

 it also includes the cases where k and # are both the same functions of 

 V, S, or x, y, z, seeing that their ratio, m, would be constant in this 

 case also. 



When m is not constant, the chances are very small against its satis- 

 fying equation (4). 



Hence, we may in general conclude, that electric absorption will almost 

 certainly take place unless the ratio of conductivity to the specific inductive 

 capacity is constant throughout the body. 



This ratio, m, may become a variable in several manners, as follows : 



1st manner. The body may not be homogeneous. This includes the 

 case, which Maxwell has given, where the dielectric was composed of 

 layers of different substances. 



2d manner. The body may not obey Ohm's law; in this case k would 

 be variable. 



3d manner. The specific inductive capacity, , may vary with the 

 electric force. 



