Capacity for Induction-coils and Tesla Coils. 237 



which the resistances are included, was given by Drude in a 

 well-known paper*, but the above expressions will serve for 

 the present purpose. 



Drude considers the problem in which the secondary coil 

 is given, and in which it is required to find what arrangement 

 of the primary circuit gives the highest secondary potential! • 

 After remarking (I. c. p. 539) that it is necessary to dis- 

 tinguish between the two cases in which (a) the capacity Q 1 

 is varied, and (b) the self-inductance L x is the variable 

 quantity, he apparently comes to the conclusion (p. 540) 

 that in either case the highest secondary potential is attained 

 when 1j\Gi is equal (or nearly equal) to L 2 C 2 , i. e. when the 

 periods of the primary and secondary circuits, separated from 

 each other, are equal. This is the case of so-called " re- 

 sonance," and all the subsequent calculations and conclusions 

 given by Drude, including the tables and curves (/. c. 

 pp. 546-551), are based on the assumption that this con- 

 dition (L 1 Ci = LjOa) is satisfied. Drude finally arrives at 

 the result that, if the damping of the oscillations is small, 

 the secondary potential is greatest when the coupling co- 

 efficient is 0*6 and the primary capacity is so adjusted as 

 to bring the primary circuit into " resonance " with the 

 secondary, this adjustment of the system giving the frequency- 

 ratio n 2 /w 1 = 2. 



The reasoning by which Drude arrives at the above result 

 is, I think, not perfectly clear, and the result does not hold 

 in case (a). Denoting the ratio L 2 C 2 /L 1 Ci by m, the expres- 

 sion (12) for V 2 becomes 



V2= W(i-»o"+i/A« (cos27rni<_cos2,r " 2<) - • (14) 



If the primary capacity C 2 alone is varied (L 1? L 21 , k 2 , V , 

 and L 3 C 2 being constant), the denominator of this expression 

 has a minimum value when 



m=l-2P (15) 



If also n Y and n 2 are suitably related, the maxima of the 

 two waves in the secondary coil will occur simultaneously, 

 so that at time l/2n lf cos 2-7™^= — 1, cos2w7i 2 £=l. This 

 happens, for example, when P = 0*265 J, ??i = l — 2& 2 = 0*47, 

 which adjustment makes the frequency-ratio n a fn x equal to 2. 

 It follows from (14) that if k 2 = 0*265 the most effective 

 primary capacity is that .which makes m = 0*47, i. e. 

 LjC^ 2*128 L 2 C 2 . At this degree of coupling, therefore,. 



* P. Drude, Ann. d. Physik, xiii. p. 512 (1904). 



t The primary sparking potential V\> is also supposed to be given. 



I More exactly A 2 = 9/34. 



