70 Mr. W. A. Price on Alternating 



This = - . -^- (1 - mvr) {sin (tot + a)fM + cos {at + a)f 2 {(3) } 



to fJb — V 



+ - . UL ( 1 _ m/ ir) { sin (tot + a)t\ (7) + cos (tot + a)f 2 (7) } 



tO V — fJb 



L {sin (at + h)f z (j3) + cos [at + &)/ 4 (/8) } 

 sin (cot + b)f 3 (y) + cos (at + b)f A (7) }. 



a ' n (/J, — v) 

 B v 



a ' (v—fi)n 

 The potential of the concentric conductor at B is ~(s + s'). 



This = - . -r^—r { sin (at + a)f 3 (/3) + cos (tot + a)/ 4 (/3) } 

 a n(fi — v) 



A v 



+ — . -7 r {sin (tot + a)f z (y) + cos (tot + a)/\(y) } 



a n(v — /jb) 



+ 5 .J^(l-«i/ir){Bin (^ + A)/'i(/3)+cos(^ + A)/ 2 (/3)} 



+ _ . i^Z_ (i _ mvr ) £ s in. (ft,{ + 6 ^ ( 7 ) + cos (w/ + b)f 2 (7) } . 

 a v — //. 



§ 9. Consider a system of circular conductors, of which 

 fifteen are shown in fig. 4. 



Of these Nos. 1, 5, 6, 10, 11, 15 have each a resistance 

 SJtjt ; they represent the central conductors of such concentric 

 cables as we have been considering. Nos. 2, 4, 7, 9, 12, 14 

 have each a resistance 2tjt'. They represent the outer or 

 concentric conductors. Nos. 3, 8, 13, have no resistance, 

 and are maintained always at zero potential throughout. 

 They represent the water or sheathing of the cables. 



The capacity measured between each of the pairs 1, 2 : 



4, 5 : 6, 7 : 9, 10 : 11, 12 : 14, 15 respectively is 27rc, where 

 c = m; and between the pairs 2, 3 : 3, 4 : 7, 8 : 8, 9 : 12, 13 : 

 13, 14 is 2rrrc f , where c'=-n. The capacity between the pairs 



5, 6 : 10, 11 is zero. 



At B conductors 2, 4 are connected by a piece having no 

 resistance or capacity. 



Similarly at C, conductors 5, 6 are connected ; at D, 7, 9 ; 

 at E, 10, 11 ; at F, 12, 14, and so on. The series may be 

 indefinitely extended. 



