Triode Generator with Two Degrees of Freedom. 713 



This is in complete agreement with the experimental 

 results. 



We saw (i.) that when a vibration is possible at all the 

 system will automatically start vibrating in some form. It 

 cannot, however, produce stationary oscillations in both 

 frequencies at the same time (ii.), so that only one of the 

 two coupling frequencies will build up. Which one this 

 will be depends on the circumstances and can be found from 

 a consideration of 



iii. a s 2 = a 2 , b s 2 =0j 



iv. a s 2 = 0, h 2 = b 2 . 



These cases may be conveniently treated together. Before 

 considering, however, in detail the stability of the system 

 when oscillating in one mode of vibration only, we shall 

 first determine the conditions for which such an oscillation 

 is "possible" at all, apart from its stability. Moreover, 

 as the peculiar discontinuities, described in the introduc- 

 tion, occur when the natural frequency of the secondary 

 circuit is altered, we shall leave all parameters unaltered 

 except the detuning of the secondary and consider how 

 these possible amplitudes a and b vary as a function of 

 this detuning. For the circuit under consideration this 

 variation of co 2 is brought about by varying L 2 (fig. 4), 

 which is equivalent to a variation of the secondary capacity 

 in a case where the electrostatic coupling here considered is 

 replaced by its electromagnetic equivalent. 



Now (9 a) can be written 



(16) 



where 



and 



i 7 ^ 2 = ^- /i( ^), 



«2 «2 



"1 



f 7 - = ~ -/n<>2 h 



a 2 2 



i 

 J 



2 9 



ft 2\ ©r — ©i ©i 

 ji(©2 ) — ~r~ "~ "i • ;r~2 



0)1 — C0 2 &>2 





f / 2^ ©I 2-- ffl H 2 w i 2 

 /ll(,©2 ) — „ 2 v. 2 " ~2 

 (0-2 — ©II ©o 



i 

 •J 



(17) 



These functions fi and/n are the coefficients with which 

 the damping coefficient of the secondary must be multiplied 

 in order to transpose the secondary damping to the primary 



