OF ARTS AND SCIENCES. 269 



For a single wire surrounded by a homogeneous non-conductor to 



an indefinite distance, the electric capacity is J -. , where I is the 



" log _ 

 a 

 length of the wire and a its radius. 



For a wire surrounded by a homogeneous dielectric to a limited 



distance, the capacity is | , where K is the specific inductive 



log -I 



capacity of the dielectric, and a^ and a.^ the outer and inner radii of 

 the dielectric. 



As the energy required to charge a condenser is 



and as no work is done in moving the one conducting surface within 

 the other, the same expression for the work done in charging a cable 

 will hold when the wire is not concentric with the outside as when it 

 is, as was supposed in the above. 



Hence the work required to charge a unit length of cable, even 

 when the wires are not in the centre, will be equal to 



log -J 



On account of this static capacity of a cable, there is a retardation 

 in the transmission of signals from the greater amount of energy 

 which must be supplied from the electrical source before the potential 

 along the wire will be raised sufficiently to cause the required current; 

 just as, in the case of heat, the specific heat of a bar determines how 

 much heat must be given to one end of the bar before heat will flow 

 along the bar at any given rate. 



With a single wire cable let Vhe. the potential at any point of the 

 wire. Let Q be the total quantity of electricity which has passed 

 through a section of the cable at that point since the beginning of the 

 current. Then the quantity which at the time t exists between 

 sections at x and x-\- bxis 



and this is equal to q Vdx. 



Hence o K = — . 



ax 



--- dx 

 dx 



