534 On the Electro-statical Capacity of a Leyden Phial, fyc. 



Assigning the constants A and C so that the potential may have 

 the value V at the surface of the wire, and may vanish at the 

 hollow conducting surface round it, if r and r' denote the radii 

 of these cylinders respectively, we have 



log * 



i r 



and dv _t>_ V 1 



dx~ ~ , I s x' 



T 



Taking x=r, we find by this the electric force in the air infi- 

 nitely near the inner electrified conductor; and dividing the value 

 found, by 4ur (according to the general theorem), we have 



1 V 



47T , ? J 



rlos- 



for the electrical density on the surface of the conductor. Mul- 

 tiplying this by 2irrl, the area of a length / of the surface, we 

 find 



1 VI 



2, r' 

 lo S~ 



for the whole quantity of electricity on that length. Hence, if 

 k be the specific inductive capacity of gutta-percha, the electri- 

 city resting on a length I of the wire in the actual circumstances 

 will amount to 



1 JL V 



log- 

 .r 



Or if S denote the surface of the wire, we have, for the quantity 

 of electricity which it holds, 



V * S • 



• r " 



47rrlog— 

 r 



and therefore its capacity is the same as that of a Leyden phial 



with an equal area of coated glass of thickness equal to j- rlog-, 



if I denote the specific inductive capacity of the glass. In the 

 case experimented on by Mr. Faraday, the diameter of the wire 

 was T ^th of an inch, and the exterior diameter of the gutta- 



