450 BELL SYSTEM TECHNICAL JOURNAL 



Case II-B 



When the current is zero at one end and maximum at the other end 



of the line, then, 



sin al/ = ± 1 and cos L = 



or cos .1/ = 1 and sin L = ± 1 

 and the radiated power is: 



P^ = 80P ("^Y watts. (2&) 



Case II-C 



When the current is maximum at each end of the line, then, 



sin il/ = and cos L = ± 1 



and the radiated power is: 



P2 = 40/2 ( y j watts. (2c) 



The approximation for the power radiated by unbalanced currents 

 is essentially the case of a long wire parallel to a perfect earth. The 

 approximation may be obtained from (2) by assuming that power is 

 radiated only in one hemisphere, which divides the numerical constant 

 by a factor of two and by writing for a the quantity 2/?, h being the 

 height of the wire above ground. Equation (7) of the paper is written 

 on the basis that (sin M = ± 1). 



It is of interest to compare some of the above results with those for 

 the case of a single conductor far removed from reflecting surfaces. 

 If the wire is excited so as to bear standing waves of / r.m.s. amperes 

 maximum value the radiated power is: 



P, = 30/2 0.5772 + log, (2L) - COIL) - cos^ M - cos^ (L - M) 



+ 2 cos M cos (L - M) ^-^j^ 1 watts. (3) 



If the wire is "terminated" so that there are no reflections from the 

 ends a uniform current of / r.m.s. amperes may be assumed to exist 

 along the wire. In this case the power radiated is: 



P4 = 60/- 



0.5772 - 1 + log, (2L) - Ci{2L) + ^^^1 watts. (4) 



