0(>4 ELECTRICAL MEASUREMENTS 



Similarly by dividing the base into seven and into nine equal 

 parts, 



[F 7 ], + [F 7 ], + [F 7 ], +...+ [F 7 ] 7 

 [F,]i + [F,], + [F 9 ], + . . .+ [F,], 



It is convenient to erect the first ordinate at the point where 

 the curve crosses the axis. In that case YI = and 



B l + B 3 + #5 + B 7 + . . . = 



In practice the process is somewhat simplified, for except in 

 special cases the harmonics above the seventh are not important. 

 So 



BI = % 2 [F 3 ] approximately 



5* = H s irj 



When these approximations are used, by appropriately divid- 

 ing the base, tests may be applied to detect the presence of 

 higher harmonics. If they are present the approximate values 

 of the lower harmonics may be corrected ; for instance, if the 9th 

 be present, then 



B, = y3*(Y 3 ]-B 9 



To find Ai, A 3 , etc. 



As these are the coefficients of the sine terms, which will have 

 their maximum values a quarter period from the initial ordinate 

 [F P ]i, draw the first of the new set of ordinates [Y P ]\ a quarter 

 period from [Y P ]i. At this point, all the cosine terms are zero 

 and consequently add nothing to the value of the ordinate. 



The initial ordinate of the fundamental, as well as that of the 

 fifth and of the ninth harmonic, is positive, while the initial 

 ordinate of the third and of the seventh harmonic is negative. 



F'i = A 1 - A, + A 6 - A 7 + A,... 



When the base has been divided into three, five, seven, etc., 

 equal parts, by the rules already given, 



[FJ'i + [F,]', + [F,]', = 3 [- A 3 + A, - An. . ..] 

 IFJ'i + [FJ', + [FJ', ... + [FJ' 5 = 5 [A 5 - A. . .] 

 [Fy]'! + [F 7 ]' s + [F 7 ]', . . . + [F 7 ]' 7 - 7[- AT + A,,.. .] 

 [FJ'! + [FJV+ [F 9 ]'i + ...-+ [F,]', = 9 [A, - 



