438 Prof. A. W. Porter and Mr. R. E. Gibbs 



on 



that for which two of the roots are given by +ip. This 

 condition gives the two equations 



P 2 = \ 

 whence eliminating p, 



9 9 



Whatever value of x satisfies this equation, other values 

 will also satisfy it, provided that 2qx is greater than at first 

 by 2w times an integer, at least for points so distant that 

 a 2 can be treated as constant. 



But in any usual case a. 2 and therefore fi will be very small 

 compared with KL-f?*R, so that 



p 2 -Jl9~(v/9) *Jjlg, 



where the second term on the right is small ; and 



u= -fSin lax, 

 mh 



and therefore p 2 is subjected to a small harmonic variation 

 (dependent on x) about its average value n*. own* 



The equations become somewhat modified bit at the same 

 time more symmetrical if the electrical circuit possesses 

 a capacity S. 



Each of the systems is now " elastic" and possesses a free 

 vibratory period of its own. 



The equations are, for the circuit 



and for the membrane 



( cP d tA 



K m w+ r dt +K P=°> 



leading to the auxiliary equation 



dQ_^f d 2 d 



