Rupin — Resonance Analysis of Alternating Currents. 485 



theory underlying these upper harmonics may be, the bare fact 

 which the engineers have to face is : There is no cure against 

 harmonics as long as the circuits contain iron. Hence, con- 

 struct lines in such a way that conditions favoring resonance 

 with the frequency of the fundamental or with one of its odd 

 upper harmonics will seldom occur, and whenever they do 

 occur the resonant rise of potential should not be capable of 

 producing any damage. Avoid slotted armatures and arma- 

 tures with projecting pole pieces and Iceep the magnetization 

 down as much as possible. 



VII. Analysis of rotary magnetic fields. 



Before closing this paper I will describe briefly the applica- 

 tion of the resonance method of analysis to the study of the 

 intensity fluctuations of a rotary magnetic field. The investi- 

 gation was carried out by two students of the Electrical 

 Department of Columbia College, at my suggestion, and will 

 be published in the near future. The method, briefly stated, 

 is this : A suitable number of turns of wire are subjected to 

 the induction of a rotary magnetic field. These turns form 

 part of a resonator. Whatever fluctuations there be in intensity 

 of the rotary field they will be periodic, their period bearing 

 a perfectly definite relation to the periodicity of the current 

 which produces the rotary field. For instance, in a three- 

 phase combination of alternating currents the intensity of the 

 rotary field will, according to theory, show six maxima and 

 six minima during each complete revolution, the maxima dif- 

 fering from the minima by about 14 per cent. A circuit, sub- 

 ject to the inductive action of such a field should have a 

 periodic electromotive force induced in it whose frequency 

 will be either three or six times the frequency of the funda- 

 mental, according to the shape of the curve of fluctuations. 

 Similarly in a rotary magnetic field produced by a two-phase 

 combination of alternating currents. If such electromotive 

 forces were induced the resonator would detect them, and 

 from the resonant rise of potential the extent of the fluctua- 

 tions producing these electromotive forces could be estimated. 



JNo electromotive forces of this type were detected in either 

 a triphase or a two phase combination. Hence the inference : 

 Rotary magnetic fields produced by reasonably well constructed 

 machines are not accompanied by fluctuations in their intensity. 



Electrical Engineering Laboratory, 

 School of Mines, Columbia College, New York, May 10, 1894. 



