512 



Prof. H. C Plummer on the Action of 



3. If initially the currents are zero, e 1 = e 2 = ; if at the 

 same time the charges are a=a, ?/ = 0, (2) give immediately 



x— X^y — a cos p\~ l t, x~\ 2 y = a cosp 2 _1 £. 



The equations (3) hardly exhibit the variations of p u p% 

 with 7 very clearly. The quadratic in p 2 , 



/-(P 1 »+P,V.+lVP^(W)-o > 



is no better in this respect, and its solution conveys the rela- 

 tions even more obscurely. There seems, therefore, to be 

 some excuse for a graphical representation. 



Figr l. 



On OA, the diameter of a circle (fig. 1), let OD represent 

 P x 2 , and DA represent P 2 2 . The perpendicular BD re- 

 presents PiPjj. Take G on BD so that GD/BD = 7 . Let 

 ECGF be the diameter through G. Then 



EG + GF = OD + DA=P 1 2 + P 2 2 ; 



EG . GF = BG . GB' = P,P 2 n-7) . PiP 2 (l + 7 ) 

 = P 1 2 P 2 2 (l- 7 2 ). 



Hence EG represents p 2 and GF represents p 2 2 . Thus as 

 the coupling increases from D to B, the squares of the 

 periods OD, DA change in a way easily apprehended until 

 one disappears and the other is represented by the diameter 

 of the circle. 



