Coujoled Circuits used in Wireless Telegraphy. 581 



this maximum amplitude is only attained in the time t 

 given by 



0)o — ft>i 7T 



and as the " triangle " is isosceles it is easy to deduce that 



cos yjr T 



sin yjr/2 4 



2tt 

 where T= — — = the natural period of either circuit. 



It will be seen from this expression for t that as the 

 coupling (sin i/r) diminishes the time t required for Y 2 to 

 attain its maximum amplitude increases, and when the 

 coupling is zero (i.e. when ^ = 0) it requires an infinite- 

 time for the maximum to be reached. 



The above can be very effectively demonstrated by the- 

 model, the coupling being regularly reduced by loading the 

 beam and if necessary diminishing the masses of the bobs. 



From the remarks at the beginning of this paragraph, we 

 may write the energies in the two circuits at the time t as 

 being equal to 



and 



iK^cos 2 -^*^ 



2 2 



-JE^E 2 sin 2 — ~ — - 1 respectively. 



These expressions show that -^K^E 2 , the whole of the 

 energy in the system, passes from either circuit to the other 

 and back to the original one in the time t s given by 



• ^ t,= 'ir, 



so that t s , which we shall call the period of the surges, is 

 given (easily by the triangle) by 



cos^jr T 

 s ~~ sir7^72 2' 



where T is the natural period of either circuit. 



On the other hand, we have seen that the frequency of 

 the resultant oscillations in either circuit is ^{d) 2 + g>i), and 

 if t be their period, we easily find by geometry that 



_ COS\/r 

 cos yjr/2 



