Electrostatic Capacity of a Conductor. 115 



Consider an elementary tube of force proceeding from 

 the elementary quantity of electricity dq on A: this tube 

 will evidently end on another conductor, B, and enclose 

 there a quantity of electricity = --dq. Let dS be the area 

 of a perpendicular section of this tube, at a distance = r, 

 measured along the tube, from any convenient point. Then 

 if F is the value of the force at ^S we have, by the theorem 

 of the flow of force, 



Iv 



dY \Tzdq 

 dr ~ K^S 

 -^V . K dr 

 ^itdq dS 

 or, integrating along the tube of force, from A to B, we have^ 

 since dq and K are constant along this tube, 

 y-2 



I 



:vi- 



47rdq 



K.(Vi-V2) fdr^ 



4Trdq 



K(Vi-v,)-y 



= rdr 

 dS 



or if the whole quantity of electricity on A which is at the 

 base of the tubes of force proceeding to B is q, we get, 

 since (Vi - Vg) is constant for these tubes of force, 



K(Vi-V,)= rdr^ 



:j ds 



where -— has to be inte^-rated alon^ a tube of force 



between limits of r given by the surfaces of A and B, and 

 then the reciprocal of this integral has to be integrated so 

 as to include all the tubes of force proceeding from A to 



B. Again, ^ is the capacity of that portion of the 



VI- Va 



