558 Mr. Iolo Jones on the Period and Decrement 



Fig. 4. — Variation of n with k-. 

 2700 



2500 



2300 



2100 



1900 

 n 

 1700 



1500 



1300 



1100 



900 



700 











H 



= 100 













R2 /L 2 

 = 500 























// R 2/ L = I000 











































]A 



v^ 



^ 



1500 















^^ 







R 2/L 2 = 2000 







0-5 



0-6 



0-7 0-8 



0-9 0-95 



T//e Condition for Heal Oscillations. 



As shown in the Table, for certain values of P and R 2 /L 2 

 the corresponding values of the frequency become imaginary, 

 which means that no oscillations are produced at these values 

 of P and R 2 /L 2 . This occurs when the coupling is 09 and 

 0*95 and when the ratio R 2 /L 2 is also large. It is clear 

 however, that there must be a real oscillation when R 2 is 

 infinite, in which case there is no induced secondary current, 

 and consequently there must be, at the larger values of P, a 

 certain limited range of values of R 2 /L 2 over which no real 

 oscillations are produced. The extent of this range depends 

 upon the coupling, and it can in fact be shown that there is 

 a* limiting value of A 2 , below which there are real oscillations 

 for all values of R 2 /L 2 , and above which there is a finite 

 range of values of R 2 /L 2 over which no real oscillations are 

 produced. 



Thus, considering the cubic in z given by (6) and writing- 

 it in the form 



