582 Prof. T. R. Lyle on Mechanical Analogy to the 

 Hence the number of oscillations in one surge is 



^-^cot^ 



Zq £ 



which increases and finally becomes infinity as the coupling 

 is loosened. 



Now the efficiency of the secondary circuit as a radiator 

 depends both on the energy of each oscillation and on the 

 number of oscillations that follow each other in a train, and 

 we have seen that when a = b the maximum amplitude, and 

 hence the average energy of an oscillation during one com- 

 plete surge, is independent of the coupling. Hence the best 

 arrangement is to make the coupling as loose as is consistent 

 with the oscillations attaining the maximum amplitude before 

 damping and radiation have reduced them too much. Thus 

 is explained the advantage of the loose coupling in the Marconi 

 transmitter. 



10. In the general case, when the circuits are not tuned to 

 the same natural frequency, we have (see § 5) 



E r 1 



V 1 =— < (s — a) cosayrf -f (s — b) cos co 2 t ?-, 



which may be transformed to 



E / " ~ 



Vi= —a / (s — a) 2 + (s — b) 2 + 2(s — a)(s — b) cos(g) 2 — &i)t 



X COS 



= Ey/ 1— 4-ySin 2 Tfr.sm 3 — ^ — * cosl -^ — l t-\-S) 



a. * b — a. w 2 -&)i 

 tan 6 = tan — =■ t< 



where 

 and 



a 



V 2 — ^2 E(C0S G>j£ - COS C0 2 t) 



c 



which may be transformed to 



TT r»T7i /Kl \/aI) . , . &)«, ft)i , /0)o + CWi 7T\ 



V *= 2E V Si- — Sin *- S1D -'a" ' cos ( 1 '-2> 



showing that in this case (a^b) both the amplitude and the 

 phase of the oscillations of A r j vary with the time, and that 



