202 PIERCE. 



We shall then have (compare El. Osc. and El. Waves, p. 316) 



21 = i?i + jIiOJ, (9) 



22 = - J/C2CC, (10) 



These values substituted into (1) give 



U = vQ/2, (11) 



Q { Q ) 



T^ = ||l-f (1+T)|, (12) 



in which the following abbreviations are employed 



i = Li + 2M, R - /?!, (13) 



,= /?/Lc., and Q=^^rtRj~^- (14) 



As a further abbreviation, let us write 



^ = 1 - I (1 + rf), (15) 



SO that equation (12) becomes 



T' = QA/2. (16) 



Then by the general equations (6), we have for tp the Aalue 



if ^'>0, ^=sin-i /^ /^/l+^ + l- (17) 



This equation is the equivalent of (142), p. 317, of Electrical Oscilla- 

 tions and Electric Wares. \Ye now proceed to develop the subject 

 further. 



Confining our attention to this case in which V is greater than zero 

 (that is, A positive), and expanding the inner radical in (17), we obtain, 

 after transposition and squaring, 



sinV=<?j|l + ^-j|^ + ...j (18) 



If now we consider the resistance per section to be so small in com- 

 parison with the inductive reactance per section that 



ri- <<\ and y]' < < 4.4^ (19) 



