1886.] A General Theorem in Electro static Induction. 417 



specific inductive capacity is changed, what will be the electrical con- 

 dition of the dielectric ? The subject has occupied me both fn its 

 theoretical and experimental aspects for a considerable time, and I 

 believe that the answer to the question throws light upon some 

 fundamental electrical phenomena. 



This investigation has led me to a general theorem in electrostatic 

 induction which may be stated as follows : — 



When a dielectric is brought into a field of electric force and the 

 specific inductive capacity is there altered, in general the dielectric 

 becomes electrified. 



To give definiteness to our notions, let us imagine a field of electric 

 force to be due to an electrified conductor, which we will call the 

 " primary ;" inclosing this primary is a conducting shell which is 

 connected to earth. 



For simplicity we will assume, for the present, that the charge on 

 the primary remains unchanged in magnitude daring this series of 

 operations : — 



(1.) The dielectric is brought into the field of force ; 

 (2.) The specific inductive capacity is increased ; 

 (3.) The dielectric is carried out of the field. 



The state of the field is exactly the same as it was before the 

 operations were performed. We can therefore fix our attention on 

 the dielectric. 



Let us compare the work done by electrical forces with the work 

 done against them in the operations (1), (2), (3). We have in (1) 

 work done by electrical forces in assisting to bring the dielectric into 

 the field; work is also done by (say) the forces in (2). In operation 

 (3) work is done a-gainst electrical forces. The question to be answered 

 is this, does the following equation hold in every case ? 



Work done by electrical forces in bringing the dielectric into the 

 field 



+ work done by the forces during the change of specific inductive 

 capacity 



=s work done against the electrical forces in carrying the dielectric 

 out of the field. 



If this equation be true under all circumstances, there is no excess 

 of work done by or against electrical forces. We would have then no 

 reason to expect to find an electric distribution on or in the dielectric, 

 whose energy would be the equivalent of the excess of work done. 

 Now that the above equation should always hold seems to me at 

 variance with sound conceptions regarding the effect of an arbitrary 

 change in the physical state of a body. 



Take, for instance, a case such as that of a piece of hot glass left to 

 VOL. XL. 2 p 



