Currents in Concentric Cables. 73 



§ 10. Applying these results to a cable having the fol- 

 lowing constants, represented by half the circle of fig. 4: 



Length 4000 kilometres = 4.10 8 units. 



Resistance of each conductor, 5 ohms per kilometre, i. e. 

 2.10 13 units for the whole cable. 



Capacity measured between the conductors, — =-„ — 10" ' 



units per kilometre (about *425 mfds.), i. e. ' jo - ^'^~ 12 

 units for the whole cable. 



Capacity measured between the outer conductor and the 



5 ./7~ 



sheathing, — ■ 10 -1 ° units per kilometre (about '26 mfds.), 



i. e. • 4 . 10 -13 units for the whole cable. 



9 







sn 



2 5+ \/7 10 _i2 



7T 9 



45- 

 n= 



TT 



-^7 10 _ 12 

 9 



r=r f =- 10 13 , 



7T 



TT 2 

 ^"80' 



9tt 2 

 "" 80' 



Ci c 2 ' 3+V7 



c c' 16 ' 



C 2 Cx 



~c~~'~ 



13-v/Y 

 16 



Consider the cable in four cases : — 



Case I. when both conductors are continuous. 



Case II. when the inner conductor is cut in the middle so 



that the cable is in two sections. 

 Case III. when the inner conductor is cut in two places, 



and the outer in one, so that the cable is in four 



sections. 

 Case IV. when the inner conductor is cut in three places, 



and the outer in two, so that the cable is in six 



sections. 



9 . 144 . 7r 2 

 Take a value of co . ^r which makes ft « y integral in 



all cases. This corresponds to about 25 alternations per 

 second. 



Then if the cable be divided into n equal sections the new 

 values of rr'mnfiy are inversely proportional to n, while the 

 values of ja, v are proportional to the square of n. The 



value of-r-| is unchanged in every case. 



