202 PIERCE. 



f 



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



zi = Ri-{- jLico, (9) 



Z2= - j/C^Oi, (10) 



These values substituted into (1) give 



U = vQ/2, (11) 



^ = ^|l-f (l+^^)j, (12) 



in which the following abbreviations are employed 



L = Zi + 2M, R = Ru (13) 



r,= R/Lo:, and Q= ^Z^Jj^,- (14) 



As a further abbreviation, let us write 



^ = 1 - f (1 + V'), (15) 



so that equation (12) becomes 



V = QA/2. (16) 



Then by the general equations (6), we have for <p the value 



if V>0, ^=sin-i J^JJl+ii + l- (17) 



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

 tions and Electric Waves. We now proceed to develop the subject 

 further. 



Confining our attention to this case in which T' is greater than zero 

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

 after transposition and squaring, 



sln^^=QA\l+£,-^, + --] (18) 



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

 parison with the inductive reactance per section that 



T < < 1 and ry^ < < AA^ (19) 



