ARTIFICIAL ELECTRIC LINES WITH iMUTUAL INDUCTANCE. 203 



we have 



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



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



T2/7 2 4 



- ^ (1 - 2J/Coco2 + UPC'?u^^ ). (21) 



4 



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 ^- to 

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

 provided we can so choose M that 



<p- = LC;i/-, (22) 



and 



(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 co, obtaining 



^^V^- = LMC-ro^\ and (24) 



12 



45 2 



Equation (24) gives 



M = L/12, (26) 



which substituted into (25) gives 



iV45 = LV41. (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. 



