418 



Mr. J. Buchanan. 



[May 27, 



cool, and meanwhile to undergo electrolysis by the action of the 

 electric forces of the field ; and when cold carried out of the field. 



The important part here played by the element time, renders it 

 quite impossible to maintain a priori that the above hypothetical 

 equation should hold under all circumstances : the proof would need 

 to be experimental. • 



The investigation given below is designed to express in definite 

 terms the effect of the somewhat general conditions therein specified. 



Let us denote the potential of the primary by V, its charge by q ; 

 the specific inductive capacity of the dielectric placed in the field of 

 force by K ; and the electrostatic capacity of the whole system by C. 

 Then the theorem is that the magnitude and sign of the " apparent 

 electrification" of the dielectric are given by an equation of the 

 form — 



where h denotes the rate of change of the apparent electrification 

 of the dielectric with regard to the specific inductive capacity K as 

 independent variable ; and ir denotes the rate of change of the work 

 done against electrical forces with regard to the same independent 

 variable. 



By translating the theorem into the language of magnetism, we 

 obtain a theorem relating to magnetic induction in matter placed in a 

 magnetic field of force. 



Proof. 



The dielectric being supposed in the field of force, let the specific 

 inductive capacity be changed. The influence of this change of 

 specific inductive capacity of the dielectric on the electrical state of 

 the primary can be expressed by taking as independent variables the 

 potential V of the primary, and the specific inductive capacity K of 

 the dielectric. Due to an arbitrary change of potential SV, and an 

 arbitrary change of specific inductive capacity £K, there will be an 

 augmentation $q of the charge of the primary — by connecting it to 

 proper sources of electricity — given by an equation of the form — 



Bq=C.BV + Y.^.8K + h.8K . .... (1.) 

 dK. 



The first term of the right hand member expresses the well-known 

 relation between the charge, the potential, and the capacity of an 

 electrical system ; the second term expresses the effect of the change 

 of capacity caused by the alteration of specific inductive capacity ; 

 and the third term expresses the effect of the electrification of the 

 dielectric due to the same cause. What I propose to show is, that 



