ANALYSIS OF CURVES. 423 



to the previous half wave, but with the same sign instead 

 of the opposite sign. That is, any two ordinates of the 

 curve half a period apart will be equal, and on the same side 

 of the horizontal axis. Examples of such curves are 

 sometimes met with, as in curves of variation induced in 

 the exciting circuit of an alternator by the armature 

 current. (See Fig. 104, page 224.) 



Curves containing both odd and even harmonics are 

 not symmetrical in any ordinary sense of the term. Such 

 a curve is the one shown in Fig. 203. 



Form of the Wave. It is important to notice the effect 

 of the addition of a harmonic to a fundamental wave upon 

 the shape of the resulting curve. If the two curves are 

 coincident in phase when the fundamental harmonic passes 

 through its zero value, as in Fig. 201, the resultant curve 

 is flattened at the top. If, on the other hand, the two 

 curves are in opposition of phase at this point, i.e., they 

 cross the axis in opposite directions, as shown in Fig. 200, 

 the resultant curve becomes peaky. In either case the 

 half waves are symmetrical about a vertical line. If the 

 harmonic is intermediate in phase, like that shown in Fig. 

 202, the curve becomes irregular, having one side flattened 

 and the other raised to a peak. 



FIG. 202. THIRD HARMONIC OUT OF PHASE. WAVE DISTORTED. 



Fin. 203. CURVE CONTAINING BOTH ODD AND EVEN HARMONICS. 



In analysing a curve, the number of harmonic waves 

 which must be considered will depend on the extent to 

 which the wave form difters from a simple sine curve, 

 and the degree of accuracy with which it is necessary to 

 express the true shape. Usually it is sufficient to 



