ii-A] 



WAVE ANALYSIS. 



333 



3. Equation (4) is the most convenient for plotting and for 

 general use. The phase angles a 3 , a 5 , etc., are measured from the 

 zero of the fundamental in the same angular scale as the funda- 

 mental wave, as in Fig. I ; that is, 180 always represent half a 

 wave of the fundamental and not half a wave of each particu- 

 lar harmonic. (On the other hand, < 3 , < 5 , etc., are measured 

 each to the scale of the particular harmonic; the scale for <f> 3 

 measures 180 for a half-wave of the third harmonic, the scale 

 for <f> 5 measures 180 for a half-wave of the fifth harmonic, etc.) 



A positive phase angle indicates a leading wave, as the third 



y= Ci sinJC+Ca sin 3 (a7+a 3 )+C 5 sin 5 (C+ 5 ) 

 = 100 sin X -*-30 sin 3 (<C-1-30 )-M5 sin 5(X 15) 



FIG. i. Complex wave composed of a fundamental, a leading third and a 

 lagging fifth harmonic. Phase angles a s and a 5 are measured from zero of the 

 fundamental. 



harmonic in Fig. I ; a negative phase angle indicates a lagging 

 wave, as the fifth harmonic in Fig. I, this being the usual notation 

 in alternating currents. 



Note that in measuring to or from a zero of a wave the zero 

 selected is always one where the wave changes from negative 

 to positive. 



