CHAFFEE. — IMPACT EXCITATION OF ELECTRIC OSCILLATIONS. 293 



considered as an intermittent function, could be analyzed into har- 

 monics. Instead, however, of analyzing the current wave, the equiva- 

 lent problem of expanding the resulting e. m. f. wave into harmonics 

 can easily be done if, as is seen by reference to Figure 14 to be roughly 

 true, the e. m. f. curve be assumed to be an intermittently repeated 

 sine cycle. 



FiGUKE 15. 



Suppose the particular case of a discharge every two secondar}'' 

 oscillations (I. C. F. = 2) be considered in detail Figure 15 indicates 

 the conditions of the problem. The full line sine curve, marked in 

 represents the secondary oscillation which has thus far been considered, 

 or in other words, the primary harmonic of maximum intensity. The 

 other full line, marked ii, is the primary discharge, and the dotted 

 line the approximate e. m. f. wave which was referred to above. 



The function 



7r/2 



e = 







77/2 



e = ^ sin 2x 



is to be developed into a Fourier series of the form 



e= ai sina: + a^ sin 1x ■\- a^ sin 3.r + 



where any coefficient a^ is given by the expression 



am = - \ /M sin mx dx = - \ E sin 2x sin mx dx 

 rr J IT Jq 



The result is expressed below. 



e^=: E (.43 sin ^4- .50 sin 2x+ .26 sin 3.r — 



.061 sin 5x+ .028 sinT.i- — .017 sin 9.r + . . 



