Cady and Vinal — Electric Arc. 93 



§ 6. The net result of the glow-arc pulsations is the trans- 

 formation of a portion of the direct current energy into that 

 of an alternating current, giving rise to an alternating current 

 superposed upon the direct current. In this respect the dis- 

 charge behaves like a microphone contact, or like a current 

 interrupter. Such cases may be treated either as pulsating 

 resistances or as alternating electromotive forces.* Suppose, 

 for example, that a constant electromotive-force E sends a 

 current / through a circuit of self-inductance Z, constant 

 resistance R, and pulsating resistance aR cos pt. Then 



E = L — + IE (1 + a cos pt). 



CI o 



This case is discussed by Barkhausen (1. c), who by a pro- 

 cess of successive approximations arrives at the conclusion that 

 the current wave is of a form represented by a fundamental 

 vibration with a system of higher harmonics. The equation 

 has been exactly solved for another purpose by Mr. L. Cohen, 

 to whom the writers are indebted for his kind permission to 

 make use of the solution. In a paper shortly to be published 

 by Mr. Cohen it will be shown that 



E\ 



Ea 



E'a 2 cos (2pt -^-^) 

 V(^ 2 + y^ 2 ) {E* + Jip 2 IJ) 



where <£, yfr x , <^r 2 , are constants. 



For the present purpose the most noteworthy feature about 

 this solution, beside the existence of the harmonic terms, is the 

 fact that the greater the value of a, that is, the greater the ampli- 

 tude of the variable resistance, the more slowly does the series 

 converge. This helps account for the intensity of the higher 

 harmonics that are recorded below (§ 25). The equation just 

 quoted fails to take into account two facts : first, that the 

 capacity of the circuit plays an important part in the case of 

 oscillations of high frequency, and second, that the resistance 

 of the electric discharge does not pulsate sinusoidally, but in 

 a much more complex manner. 



§ 7. Of the relative durations of the arc and glow phases 

 we know little, but the shorter one of these is in relation to the 

 other, the more pronounced must the harmonic terms become. 

 In any event the presence of a complex wave form, involving 



* Barkhausen, Das Problem der Schwmgungserzeugung, Leipzig, 1907, 

 p. 19. 



