Coupled Circuits used in Wireless Telegraphy. 579 



pendulum makes ( = n say) between 11 points of rest, that is 

 during 5 periods of amplitude change, then 



5 (D 2 — a>i 



giving the ratio of: co 1 to co 2 . 



Jnow measure in the usual way the period of the individual 

 swings of the second pendulum, which is equal to 



4i7T 



co 2 -\-o) 1 



From these two results oy l and co 2 can be deduced, and the 

 values so obtained can be compared with those computed by 

 means of the triangle formulae given in § 1. 



In this connexion it is interesting to note that if the 

 pendulums are of the same length /, and have bobs of equal 

 mass m, then one of the resultant frequencies is always the 

 same as that of an ordinary simple pendulum of length I 

 with a rigid point of suspension, that is, it is equal to s/ g\l, 

 no matter what the coupling may be. 



For in this case (see § 3) 



. in 



and 



and as the " triangle " is isosceles, 



s = a(l + sin^r), s— c=a(l — sim|r) 



but 



hence 



„ ab 9 ab 



- ™* -,-e 



„-i-9 , ,!_ 1 +- sin 'f 9 



COi — j, (0 2 — 



/' 2 "l-sin-fT 

 for all values of sin \/r, the coupling. 



9. The surging of the energy forwards and backwards 

 between two coupled circuits is very well illustrated by the 

 model. 



TVhen the P.D. of the condenser in a circuit is at the full 

 amplitude for a particular oscillation, the current in that 

 circuit is zero, and all the energy in the circuit at the instant 



2 R2 



