DETERMINATION OF WAVE FORM 665 



Therefore, 



[F' 



3 = i^j S [Fa]' approximately 



5 ]' 



A, = - M 2 [F 7 ]' 

 A 9 = J* S [7,]' 

 F/ = A! - A 3 + A 5 



When dealing with waves containing only the odd harmonics, 

 it is necessary to plot only one-half the wave, since the second 

 half is like the first with the algebraic sign of the ordinates 

 reversed. Suppose the half wave has been divided into 2k parts, 

 equivalent to dividing the whole wave into 4/b parts, then the 

 ordinate [FJi is identical with [F 4 jt]i. The relation of the num- 

 IHT, .V 4Jt , of any ordinate when the whole base is divided into 4A; 

 parts to the number of the same ordinate, N k , when the whole 

 has been divided into k parts is given by 



1) + l = 4N fc - 3 = Nt k . 

 ( lonsequently 

 #3 = l /3 [[Fidi + [Yi*]* + [Fi 2 ] 9 ] = M [[Fiji + [FiJ, - [Fiji] 



^s = ! 5 [[i' 20 ]i -f [F 20 ]5 + [r 20 ] 9 - [r 20 ] 3 - [F 20 ] 7 ] 



B 7 = i 7 [[y 28 ]! + [7 28 ]5 + [F 28 ] 9 + [F 28 ] 13 - [F 28 ] 3 - [F 28 ] 7 



- [F 28 ]n]. 



\\ hen the sine coefficients are determined, the ordinate [FJ'i is 

 identical with [F 4 *W if or when the sine terms are determined the 

 initial ordinate is transferred k spaces to the right. In this case 

 tin* nimitxjr of any ordinate, N, k) when the whole base has been 

 divided into 4fc parts is related to the number of the same 

 ordinate, AT',, when the whole base has been divided into k 

 parts, as follows: 



4 (#' fc _ i) + k + 1= N' k - 3 + k = Nu. 



A 3 = - ', [[F 12 ] 4 + [F 12 ] 8 + [FiJiJ - 



A, = ', |[>- 10 ], - [r 20 ], + (Yn}* - [Y 



- 7 1 - ir s ], + [r]4 - [yl. 



