330 M. I. Pupin — Electrical Oscillations of 



m 



Let a complex harmonic, alternating electromotive force E 

 act upon this cirucit. 



By Fourier's theorem E can be represented by 



Itz 

 E = a 1 sin pt + a 2 sin 2pt + . . +a n sin npt + . . . where p = — 



T being the fundamental period. It is well to observe here 

 that in complex harmonic e. m. forces as produced by ordinary 

 methods the amplitude a t , of the fundamental harmonic is 

 largest and the amplitudes of higher harmonics diminish with 

 the period of these harmonics. 



The current produced in the circuit by the action of this 

 complex e. in. f. will, of course, be a complex harmonic con- 

 sisting of the same number of single harmonics as the e. in. f. 

 and of the same periodicity ; but the ratio of the amplitudes 

 will be different now. The various simple harmonic compon- 

 ents have also different phases. In general every one of these 

 harmonics is a forced oscillation of the circuit, but by tuning 

 the circuit we can bring it (within certain practical limits) in 

 resonance with any one of the harmonics. 



In my work I generally bring the circuits in resonance with 

 the fundamental harmonic. A resonant circuit behaves toward 

 a complex harmonic e. m. f. just the same as an acoustical 

 resonator toward a source of complex sound. It brings out 

 prominently that harmonic with which it is in resonance. To 

 express this numerically, say that the ratio of the amplitude of 

 the fundamental harmonic e. m. force to that of the next higher 

 harmonic (supposing it even to be no higher than an octave) is 

 2 to 1. Then the circuit can be easily brought into resonance 

 with the fundamental harmonic, in such a way as to increase the 

 ratio of the amplitudes of the corresponding simple harmonic 

 currents to 60 : 1. Theoretically (and to a great extent practically 

 also) that ratio can be made anything we please by increasing 

 continually the coefficient of self-induction and diminishing 

 the capacity without destroying the resonance. In other 

 words, we can by proper single tuning weed out the upper har- 

 monics as much as we please. But, as will be indicated later 

 on, it is not always advisable to avail ourselves too much of 

 the means of weeding out the upper harmonics by using very 

 large self-induction. The best method of tuning depends on 

 the nature of the problem before us. I propose to discuss two 

 cases, after stating briefly the experimental method which 

 I consider as the simplest in detecting resonance. Con- 

 sider the circuit represented in fig. 5. Put a telephone in 

 shunt with some part of the circuit between the coil and the 

 condenser ; insert a small auxiliary coil with movable iron core 

 in series with the large coil. Say the fundamental frequency 



