500 



THE ELECTROMAGNETIC FIELD. [PT. III. CH. XII. 



take for ^ and q z the charges of the two condensers, so that the 

 currents are 



(1 ) ^ = ^f' /2 = W' 



We accordingly have 



T: 



(2) F 



r~i+i 



-*K^* KZ' 

 and the differential equations for the free oscillations are 



(3) 



The equation for the frequencies is 



(4) 



M\* 



= 0, 



or 



(5) 



+ 



+ + + 



As this equation is of the fourth degree, we shall treat only the 

 case of no damping, which, as we have seen, will not cause a large 

 error in the determination of the frequencies. Putting then 

 JJj = E 2 = the equation becomes 



^ "^ 



_ 



\ v > 



or, as we may otherwise write, 

 (7) 



-\ 4 ' V~.i A i m-~"Tt/ -\2 



If the two roots of this quadric are 



A !_ 



V' V' 



= 0. 



