1886.] A General Theorem in Electrostatic Induction. 425 

 dC 



when - — and Q are finite and C is extremely large. Hence, in con- 



sidering what is happening when two bodies are rnbbed together, we 



need only take account of the value of — -y^p ^ or eacn - 



To simplify discussion of (8) we will take the second body as 



" neutral "; i.e., = 0. We shall see that boxwood appears 



\ dV/o 



nearly to fulfil this condition. Also for brevity and convenience, we 



will put ^' 7r =0L. 

 y dV 



Two cases arise for consideration. 

 Case I. 



-J^( a ) positive, i.e., work is done against electric forces by in- 

 creasing the specific inductive capacity. 



(a) . "Positive" liquids. If a Jiquid dielectric be warmed, the 

 index of refraction, and therefore the specific inductive capacity, is 

 decreased. Hence, by friction there is a change of specific inductive 

 capacity — £K to be expected. Using AE in the same sense as 

 in (8)- 



AE=+a £K. 



It is shown by the experimental results quoted below, that AE 

 positive indicates that by friction this class of liquids tends to become 

 positively electrified. And since in this particular case the sign of 

 AE is the same as that of the electrification, it ought to hold in 

 general. It will be seen that this is true. 



(b) . " Positive " solids. Here friction, by raising the temperature 

 of the surface, tends to change the specific inductive capacity by an 

 amount + £K, 



.'. AE= — « cK. 



Such bodies tend to become negatively electrified by friction. 



3 II. 



(a) negative. Here work is done by electrical forces when 



Case II. 

 dw 

 ~dV 



the specific inductive capacity is increased. 



(c). "Negative" liquids. Friction tends to decrease the specific 

 inductive capacity by an amount —SK, 



.'. AE=-* . 6K. 



Hence " negative " liquids tend to become negatively electrified by 

 friction. 



