Capacity for Induction-coils and Tesla Coils. 239 



consequently 



1 n v 2 12 — i n v 2 



-L<21 



i. e. the maximum electrostatic energy in the secondary coil 

 is equal to the initial energy in the primary condenser. 



In Drude's adjustment, therefore, the efficiency is unity 

 if the resistances are negligible. This result may also be 

 seen from the expression (13) for the primary potential, 

 which reduces, i£ cos 27rn x t= — 1, cos 27rn 2 t = l } to 



m — 1 



V] = Y ° V {m-lY^Uchn ' 



and therefore vanishes when m = l. At the moment when 

 the secondary potential reaches its maximum value, there- 

 fore, the primary condenser is uncharged, and, since 



<*Vx n dV 2 . . . 



-77- =U, — 77- =u, there is no current in either circuit, so 



that the whole of the energy exists as electrostatic energy in 

 the secondary coil. 



In this kind of variation, in which L x alone is varied, the 

 initial energy supplied to the system is constant, and the 

 adjustment which gives maximum efficiency must also give 

 the greatest secondary potential. But when the primary 

 capacity is increased the energy supplied to the system 

 becomes greater, and the secondary potential may be in- 

 creased to a certain extent beyond the point corresponding 

 to maximum efficiency. 



Both forms of the problem may present themselves in 

 practice. If, for example, the Tesla coil is given, and ample 

 energy is available for charging the condenser, the capacity 

 of the condenser may always be adjusted to the "optimum " 

 value, whatever be the value of P. But if, on the other 

 hand, the energy is limited and it is required to construct a 

 Tesla coil which will make the fullest use of it in generating 

 high secondary potential, the primary capacity is then con- 

 stant, viz. : the greatest that can be charged to the required 

 sparking potential with the energy available at each dis- 

 charge of the induction-coil. In this case maximum efficiency 

 and small secondary capacity should be the chief considera- 

 tions borne in mind in the construction of the Tesla coil. 



Bangor, May 1915. 



