382 Pujyin — Itesonance Analysis of Alternating Currents. 



then it can be easily shown* that the current in the resonator 

 will be : 



oo ha + 1 . 



y=a2~ T- , ■■ sui[(2flr+l)j?< + g>2a + l] 



V V ;y ( (2a + l)yO f 



If, therefore, the capacity C is adjusted in such a way that 



\ -L=0 



(2a+l)yC 



then the circiut will be in resonance with the harmonic of fre- 

 quency ^ ^- ; and if L is sufficiently large and R sufficiently 



small (two conditions which are very easily fulfilled) the cur- 

 rent y will in general to within a small fraction of a per cent 

 be given by 



y = — x> — sin {2a + l)pt 



The amplitude of the potential difference in the condenser 

 which is measured by the voltmeter e is then given by 



In the same way we obtain for the fundamental frequency 



■^2a+l " *2a+l 



Hence 



P 



p va + i) ^ 



This gives the ratio of the amplitude a 9a + l of the harmonic of 



frequency L^ ^ to that of the fundamental. Let a = 2, then, 



i T\Jh = <\ 



The voltmeter readings which give P 5 and J > 1 magnify that 

 ratio five times, in the case of the fifth harmonic, and it can 

 be easily seen that a similar relation holds true for other har- 

 monics. This is a very desirable feature of the method, con- 

 sidering that the amplitudes of the upper harmonics are gener- 

 ally small in comparison to the amplitude of the fundamental, 

 especially when the secondary circuit of the transformer carries 

 a load. 



* For further information see author's paper cited above. 



