A DYNAMICAL THEORY OF THE ELECTROMAGNETIC FIELD. 575 



The instantaneous discharge is therefore p or the quantity which would 



be discharged by a condenser of air of the equivalent thickness a, and it is 

 unaffected by the want of perfect insulation. 



(88) Now let us suppose the connexion between the extreme surfaces 



broken, and the condenser left to itself, and let us consider the gradual dissi- 



pation of the internal charges. Let ' be the difference of potential of the 

 extreme surfaces at any time t ; then 



(56); 

 but 



Hence f l = A t e r - , f t = Af, r * ', &c. ; and by referring to the values of e\, e,, 

 &c., we find 



1 



_ I 



1 ~~ r a fa ak 



(57), 



>Tf \ff 



A, = \ r 



r ajc t ak 



&c. 

 so that we find for the difference of extreme potentials at any time, 



r? }e r * + &c (58). 



r ak ) 



(89) It appears from this result that if all the layers are made of the 

 same substance, * will be zero always. If they are of different substances, 

 the order in which they are placed is indifferent, and the effect will be the 

 same whether each substance consists of one layer, or is divided into any number 

 of thin layers and arranged in any order among thin layers of the other sub- 

 stances. Any substance, therefore, the parts of which are not mathematically 

 homogeneous, though they may be apparently so, may exhibit phenomena of 

 absorption. Also, since the order of magnitude of the coefficients is the same 

 as that of the indices, the value of ' can never change sign, but must start 

 from zero, become positive, and finally disappear. 



