226 Prof. E. Taylor Jones on most Effective Primary 



damping that the potential seldom, if ever, reaches a value 

 equnl to the greatest in the first half-period. 



The principal maximum of V 2 is the maximum which occurs 

 nearest to the first summit of the curve (6), i. e. at the time 

 nearest to t = l/4in- l . The first maximum occurs at the time 



t = , and this is the principal maximum if the frequency- 



n\ -J- n^ 



ratio n 2 jn x is between 1 and 5. If n 2 = 5n l the first maximum 



1 2 



is equal to the second, and they occur at times , . 



^ J n 1 + n 2 ' n ± + v 2 



If n 2 /n 1 is between 5 and 9 the second maximum is the 



2 



principal maximum, occurring at the time . If 



n ± + n 2 



712 = 9^ the second and third maxima are equal, and if ?i 2 /n 1 



is between 9 and 13 the third maximum is the principal 



3 

 maximum, and it occurs at i = ; and so on. 



ni + n 3 



Consequently the principal maximum secondary potential 

 is given by the equation 



Y 2 m = 27rL 21 i — — -.sin<£, .... (8) 



<f> = — ; if — is between 1 and 5, 



T n } +n 2 n x 



9 n x + n 2 " " " ° " y ' 



9 ~n x + n 2 " " " ^ " i5 ' 



If njni has one of the values 3, 7, 11, . . . the maxima 

 of the two oscillations occur simultaneously, the principal 



at the time 1/4??! i<f>= — J, and being- 

 equal to the sum of the amplitudes of the oscillations. These 

 cases may be called the coincidences. 



If the resistances of the circuits were taken into account 

 the value of the maximum secondary potential would be 

 considerably less than that given by (8), chiefly owing to 

 the damping effect of the resistances*. In certain cases 



* The full expression for V 2 , with damping factors and phase-angles, 

 was given in the Philosophical Magazine for April 1914, pp. 565, 574. 

 Several examples of the (V 2 , t) curve were given in the papers referred 

 to above. 



