Pupin — Resonance Analysis of Alternating Currents. 385 



mental and the 1st odd harmonic, that is the harmonic of three 

 times the frequency of the fundamental. The resonance dia- 

 gram has, of course, as many peaks as there are harmonics in 

 the inducing current* The dotted curve (flat-peaked) in fig. 2 

 was plotted on an enlarged scale from the readings taken in 

 detecting the first harmonic represented by the sharp peak of 

 the resonance diagram, and represents this peak spread out, so 

 as to show how the various readings fit into a well defined and 

 symmetrical curve such as required by theory. It also shows 

 that a condenser of small subdivisions should be employed in 

 detecting higher harmonics. 



III. Description of Experiments. 



The resonance diagram obtained by the method of fig. l b 

 gives the number of harmonics which are present in the induc- 

 ing current. It does not give the exact value of the ampli- 

 tudes of these harmonics. It would be somewhat premature to 

 discuss the theory of the resonance diagram obtained by this 

 arrangement and to show how the ratio of the amplitudes of 

 the harmonics to that of the fundamental frequency in the in- 

 ducing current, that is the exact color of this current, could be 

 calculated from the ratio of the height of the j3eaks in the 

 resonance diagram. Suffice it for the present to mention only 

 that the peaks of this diagram represent the amplitudes of the 

 harmonics magnified about proportionally to the square of the 

 frequency. For instance, the resonance diagram of fig. 2 tells 

 us that the amplitude of the 1st odd harmonic in the inducing 

 current is about one-ninth of the amplitude of the fundamen- 

 tal. The determination of the exact value of this ratio was not 

 the object of the following experiments. Their aim was to 

 detect the presence of harmonics, to trace their origin and to 

 study their variation with the variation of the load, and of 

 other variable elements of the circuit on which these harmonics 

 seein to depend. 



Preliminary Tests. 



In order to form an estimate in how far the experimental 

 data obtained by the arrangement of fig. l b agreed with the 

 theory the following tests were applied : 



*I have never detected an even harmonic in alternating current waves pro- 

 duced by ordinary commercial alternating current apparatus, and conclude, there- 

 fore, that these harmonics do not exist in such cases. For asymmetrical machines 

 this would obviously not hold true. Alternators with slotted armatures give 

 waves in which all the odd harmonics up to the harmonic of nine times the fre- 

 quency of the fundamental can be detected. As a rule the first odd harmonic is 

 the strongest. 



