DETERMINATION OF WAVE FORM 



651 



Here is measured on the same scale as 6 and the zero point 

 of any component is where it first passes from a negative to a 

 positive value. A positive value of a n indicates a leading com- 

 ponent. The constant term is usually absent in alternating- 

 current waves. 



The effect of the odd and even harmonics and of their phase 

 displacements is illustrated in Fig. 412. Odd harmonics produce 

 a wave the second half of which is like the first with the algebraic 

 signs of all the ordinates reversed. Even harmonics produce 

 an asymmetrical wave. 



< xl.l Harmonics Even Harmonics 



FIG. 412. Illustrating the effects of odd and of even harmonics. 



The integrals in (10) and (11) are proportional to the areas 

 under the curves which would be obtained if each value of 

 f(0) were multiplied by the corresponding value of sin kd or 

 cos ke and new curves plotted on the same base, 2ir. 



Therefore, 



A k = twice the average ordinate of curve /(0) sin kd (10o) 

 /** - twice the average ordinate of curve f(0) cos kd 



The integration could be performed by a planimeter. 



The labor involved in carrying out the process just indicate 



