206 



LORD RAYLEIGH. 



It is easy to see that the intégral, representing the potential at the 

 secondary terminais, is a maximum when U is concentrated at some 

 one time t' , and t is such that 



sin n (f — t') = 1, 



that is, when the break is absolutely sudden and the time considered is 

 one quarter period later. If the break be not sudden, sin n [t — f') will 

 départ from its maximum value during part of the range of intégration, 

 and the highest possible value of u will not be attained. 



The theory is substantially the saine if v, be finite. There is some 

 value of t — t') for whieh 



is a maximum ; and the greatest value of u will be arrived at by con- 

 centrating U at some time f, and by so choosing t that (f, — t') has the 

 value aboyé defined. The conclusion is that if the primary current fall 

 to zéro from its maximum value without oscillation, the potential at 

 the secondary terminais will be greatest when this fall is absolutely 

 sudden, and that this greatest value begins to be sensibly departed frorn 

 when the break occupies a time comparable with one of the time- 

 constants of the secondary circuit. In the case of no résistance we have 

 to deal merely with the time of secondary oscillation; but if the résis- 

 tance is high, the other time-constant, N\S, may be the smaller (see 

 équation (2) ). 



It is here that the character of the secondary coil, especially as 

 regards the number of its windings, enters into the question. On the 

 supposition of an absolutely sudden break, we arrived at the rather 

 paradoxical conclusion that the limit of spark-length depended only 

 upon the capacity of the secondary without regard to the number of 

 windings— a number which could be changed in a high ratio without 

 sensibly influencing the capacity. We see now, at any rate, that a 

 réduction in the number of windings, and the accompanying diminution 

 in the time of oscillation, would necessitate a greater and greater sud- 

 denness of break, if the full effect is to be retained. 



We will now consider the action of the primary condenser, a ques- 

 tion, the reader may be inclined to think, already too long post])oned. 

 For it is well known that in most actual coils the condenser is an 



