14 



XOTE OX THE THEORY OF ELECTRIC ABSORPTION 



[American Journal of Mathematics, J, 53-58, 1878] 



In experimenting with Leyden jars, telegraph cables and condensers 

 of other forms in which there is a solid dielectric, we observe that after 

 complete discharge a portion of the charge reappears and forms what 

 is known as the residual charge. This has generally been explained 

 by supposing that a portion of the charge was conducted below the 

 surface of the dielectric, and that this was afterwards conducted back 

 again to its former position. But from the ordinary mathematical 

 theory of the subject, no such consequence can be deduced, and we 

 must conclude that this explanation is false. Maxwell, in his ' Trea- 

 tise on Electricity and Magnetism,' vol. 2, chap X, has shown that a 

 substance composed of layers of different substances can have this 

 property. But the theory of the whole subject does not yet seem to 

 have been given. 



Indeed, the general theory would involve us in very complicated 

 mathematics, and our equations would have to apply to non-homo- 

 geneous, crystalline bodies in which Ohm's law was departed from and 

 the specific inductive capacity was not constant; we should, moreover, 

 have to take account of thermo-electric currents, electrolysis, and 

 electro-magnetic induction. Hence in this paper I do not propose to 

 do more than to slightly extend the subject beyond its present state 

 and to give the general method of still further extending it. 



Let us at first, then, take the case of an isotropic body in general, in 

 which thermo-electric currents and electrolysis do not exist, and on 

 and in which the changes of currents are so slow that we can omit 

 electro-magnetic induction. The equations then become 1 



, 



in which y is the specific inductive capacity of the substance, If the 



'Maxwell's Treatise, Art. 325. 



