72 Mr. W. A. Price on Alternating 



The potential at the point C on the conductor 5 has been 

 expressed in terms of Ce, BA ; and the potential at the point 

 C on the conductor 6 in terms of Cc, Dd. These two are 

 equal for all values of t, and we have an equation which can 

 be separated into two others between W>, Cc, Dd. In the 

 same way we obtain two equations at A, B, D, E, and F, and 

 between these all the quantities required can be obtained. 



In the particular case where to Ins such a value that /3 and 

 y are integral, and the currents at all the points are in the 

 same phase, let us write in § 8, 



r ;(l-iWTVi08) + -^- (l-m/^yifr) as P, 



fJ, — V V — fl 



'''(I -»'/"■)/. 0) + r ! T,(l-»>')/ 1 (7) ^ E, 



V 



J? 





j) 



55 



)•> 



c 



» 



V 



» 



D 



55 



V — fl^ '" fl — V 



remembering that when /3 7 are integral, f\{@) =/2(/3), and 

 /3(/3) = /4(/3), and the same with 7. 



The condition at A gives AP = BQ, 



B „ (A + C)Q = 2BR, 

 (B + D)Q=2CP, 



(C + E)Q=2DR, and so on. 



If the known current is introduced at B, and A is kept to 

 earth, the ratio of the amplitude of the received current to 

 the sent current is given by 



B _ P 

 A~ Q 



If the known current is introduced at C, we have 



5 = 2^-1 .... Case II. 



If the known current is introduced at E, we have 



a =8 (qO -8 q* + 1 • • CaseHI - 



If the known current is introduced at G, we have 



Case I. 



, /PR\ 3 ../PRN 2 , PR A n TT7 



