Conductors conveying Steady or Transient Currents, 233 



Xdy .A' cos 6 dd 



a + " Xdy.X'dy'. cos 6 = r i f+i" 

 -." &2 "JoJ-frr 



Ka 



'^^(SjKC) 2 (1) 



Ka ~Ka 



Unless one of the conductors is very long there is another 

 term, which, however, it is unnecessary to write. 



The electrokinetic repulsion between the same conductors 

 is similarly 



jv = C Cfi Gdi/Cdy* cos _ 2fd ^ ^ ,^\ 



Steady Currents. 



Hence with steady currents the ratio of the static attraction 

 to the magnetic repulsion is 



F_S* 1 E* 



F _ "^K ' (6 > 



which on every possible system of units is a pure number. 



To get a notion of its value, suppose the wires to be round 

 and of radius p ; then 



8 1 =K/uo g p 



so, remembering that 



£= (the velocity of light)- (^?)*, 



we see that the above numerical ratio is 



-p, f number of ohms in the wire R'J 2 



f={~ 120 kg? "}••• (3 ° 



Suppose, for instance, the wires were 50 diameters apart, or 

 4 log a/p=18*4, the two forces would be equal, and just balance 

 each other, if R was 552 ohms. 



With any resistance greater than this the electrostatic force 

 would have the advantage, and two opposite currents in the 

 given wires would attract. 



Alternating Currents. 



If the current used is an alternating one, impedance must 

 be inserted in (1) and (3) instead of resistance : no other 

 change is necessary. Hence an impedance-meter suggests 

 itself. Send a current alternating with given frequency 

 through the pair of conductors joined by the impedance to be 



