Capacity for Induction-coils and Tesla (Joils. 227 



examined by the writer, in which an 18-inch coil was used, 

 the damping was found to be sufficient to reduce the maximum 

 secondary potential by about 25 per cent. It is, however, 

 useful to consider the simpler theory in which the oscilla- 

 tions are regarded as undamped, since it enables us to trace 

 with sufficient accuracy the general nature of the effect of 

 varying one or more of the induction coefficients or capacities 

 of the system. The other effects of the resistances, viz. on 

 the frequencies, initial amplitudes, and phase relations of the 

 oscillations, are generally small, and no serious error is in- 

 troduced by neglecting them. Thus, while the value of the 

 maximum secondary potential given by (8) is considerably 

 in excess of the value found by experiment, the conditions 

 in which it occurs do not differ greatly from those deduced 

 from the simpler theory. For example, in three cases worked 

 out in a former paper*, in which the damping and phase- 

 angles were taken into account, the values of the angle 

 2^/1^ — 6 1 at which the maximum secondary potential occurred 

 were 107°'4, 65°'8, and 74°*3 respectively. The values of cj> 

 tor these cases, calculated as explained above, are 111°*3, 

 H2°'8, and 71°'7. 



The calculation of the most effective primary capacity. 



One important problem connected with the induction-coil 

 is that of determining the optimum primary capacity for a 

 given coil, i. e. the capacity which, connected across the 

 interruptor, allows the greatest secondary potential to be 

 developed, when the induction coefficients of the circuits, the 

 secondary capacity, and the primary current interrupted are 

 all given. 



In considering this problem, and other problems of this 

 kind, it is convenient to express the sum of the amplitudes 

 of the two oscillations in the secondary circuit in terms of 



"(=ETr) and P ( = TTt)" We havo ,hen £or the 



principal maximum 



\ o m =: JttL.Vo . sin (h 



>>o — n r 



= Tftr-Usin*, (9) 



where TTO 1 f 



U 2 = —. -' . . . . (JO) 



* Phil. Mag. xxvii. pp. 572-577 (1914). 

 t Phil. Mag. xxvii. p. 584 (1914). 

 Q2 



