4:2 PROCEEDINGS OF SECTION A. 



When t = 0, let 



FiorOi =Ei, Fa or 02 = ^2 



Ci or ^1 = 0, C-z or d^ = 0, 

 that is, both condensers are charged, or both pendulums are deflected 

 at the instant at which motion begins. 



Proceeding as in § 5 we find that the motion that ensues is given by 



Fi or 01 = - [{{s - a)Ei + fihE^} cos wji 

 c 



+ {{s - b)Ei -pjfiEz] cos wgf] 

 Vz or 02 = -,- [{s -h){{s-a)Ei +pibE2} cos u)it 



PlOC 



- {s - a){{s - h)Ei - pibE^} cos u^t] 

 with (7i = K^DVi, C2 = K0DV2, 



all the symbols having the same significations as before. 



Now, if the initial P.D.s or deflections be such that 

 {s - a)Ei + p^hE^ = 0, 

 the component whose frequency is wi disappears and the resultant 

 motion is a pure harmonic motion in both circuits whose common 

 frequency is w2j the higher of the two resultant frequencies of the 

 system. In the pendulum system this motion is unstable, and it is 

 therefore probably unstable in the coupled circuits. 



Again, if the initial values Ei and E2 be such that 

 {s - h)Ei - p^hEz = 

 the component whose frequency is W2 disappears, and the resultant 

 motion is a pure harmonic motion in the circuits whose common 

 frequency is wj, the lower of the two resultant frequencies of the 

 system. 



In the pendulum system this motion is stable, and it is therefore 

 likely to be stable in the electrical system. Its stabiUty increases if 

 the friction of the beam is increased ; in fact, if there is much frictional 

 resistance to the motion of the beam any kind of motion of the 

 pendulums, even when they differ much in length, quickly degenerates 

 into this motion. 



This suggests that the pendulum model might be used to illustrate 

 some of the problems that arise in the paralleling of alternators. 



Substituting from the equation of condition 



{s -b) El - pihEz = 



in the general expressions for Fj and F2 we find that the equations of 



motion take the simple forms 



Vi = El cos Wit, Fo = E2 cos ojit 



Cj = — (jJiKiEi sin Wit, C2 = — W1K2E2 sin wit. 



