ARTIFICIAL ELECTRIC LINES WITH MUTUAL INDUCTANCE. 203 



we have 



sinV = QA = Q - Q^/4:. (20) 



Let us now expand the two sides of (20) in series, obtaining 

 6 45 



DCo^0 



(1 - 2MC2C02 + SiPC^^w* ). (21) 



By reference to (8) it will be seen that to make T, the time retarda- 

 tion per section, independent of the frequency, we shall require (p- to 

 be proportional to co^. This requirement will be consistent with (21) 

 provided we can so choose M that 



(22) 



UMCio^' LM^Cic^^ 



2 ' 1 



(23) 

 are both satisfied. 



Equations (22) and (23) are equations from which to determine M. 

 Instead of an exact determination of M we shall content ourselves by 

 an approximate determination of M by substituting (22) into (23) 

 and equating separately terms of the same power of w, obtaining 



Equation (24) gives 



M = L/12, (26) 



which substituted into (25) gives 



Ly45 = Zy41. (27) 



Equation (27) is not true, but since terms in which U enters are of a 

 higher order than terms in L and U, we may consider the difference 

 between the two sides of equation (27) as negligible, and employ (26) 

 as the approximate condition required. 



