Low Frequency and their Resonance. 429 



-=j sin apt by resonance. The rise of potential according to 



formula (8) is given by 



apL 



To show how this rise of potential compares to the rise ob- 

 tained by resonance to the fundamental harmonic, let a = 5 

 and let the coefficient of self-induction be the same as before.* 



p> 



= 



pL 



- — a 

 R > 



P B 



= 



5»L 

 -R a - 



p, 

 p. 



= 



5a/ 



Hence 



It is a well known fact that well made alternators are con- 

 structed in such a way that a l is generally larger than 5 a b ; 

 hence, P x will be generally considerably larger thau P B . This 

 was confirmed by the above experiment. 



(It is well to observe that this suggests a rather interesting 

 method of analysing a complex harmonic e. m. f. into its com- 

 ponent harmonics and of determining the relative value of the 

 amplitude of each component.) 



The bearing of this on the method of producing a simple 

 harmonic current by electrical resonance, described in the first 

 part of this paper (1. c.) needs, I venture to say, no further dis- 

 cussion. 



The study of resonance in electrical systems consisting of a 

 primary and a secondary circuit with localized self-induction 

 and capacity presents several features which deserve careful 

 attention ; a brief discussion of these together with a descrip- 

 tion of several experiments bearing upon the theory of low 

 frequency resonance will be given in my next paper. 



Electrical Engineering Laboratory, School of Mines, 

 Columbia College, April 15th, 1893. 



[To be continued.] 



* In the experiment described above the capacity was the principal variable ; 

 for. the first approximation to resonance was obtained by plugging the condenser 

 until the vicinity of resonance was reached. The maximum point was finally ob- 

 tained by a, comparatively speaking, slight variation of the coefficient of self- 

 induction. 



