36 PROCEEDINGS OP SECTION A. 



For in this case (see § 3) 

 sini// = V73jP2 = 



M + m' 



and as the " triangle " is isosceles 



s = a (1 + sin -d/), s - c — a {\ - sin \^) 



, . ^ ah ^ ah 



but Wi^ = — , (,J2 = > 



s s - c 



\. •> 9 o 1 + sin v// o 



hence ^,2 = ^ wo^ = z ; — i . ; 



^ r ^ 1 - sm v// / 



for all values of sin 4^, the coupling. 



9. The surging of the energy forwards and backwards between 

 two coupled circuits is very well illustrated by the model. 



When 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 is hKV^ Avhere K is the 

 capacity and F the P.D. of the condenser. Hence the square of the 

 amplitude of the condenser P.D. at any time may be taken as propor- 

 tional to the energy in the circuit at that time. The analogous state- 

 ment for the pendulums is obvious. 



Let us consider the surging of the energy between two coupled 

 circuits (or coupled pendulums) that have been tuned so that their 

 natural frequencies are equal. 



Then a = h, s - a = s -& = ^c and the equations (I) of § 5 

 giving the F's or d's become 



Vi = ^E (cos Wit + cos W2O 



V2 = ^E / ^ (cos o)it - cos W2O 



^ P. 



where = fr- = ^ for the circuits 



Pi K2 Li 



= i for the pendulums. 



These equations can be written as 

 Vi = E cos -^-^ 



^ I Vt. ■ (3)2 — (ai /w" + w\ 7r\ 



Fi = E cos -^-^ — - t cos -^ — t. 



Pi 



