11 II 



y [F (G.) - F C9-)]^ = I [A^ cos 20. + B, sin 20. + C, + D, cos 0. 

 _L <- V "■ ±-' ov 1 -* .^, ■- 1 1 1 ill 1 



1=1 1=1 



+ E.sin 0. |sin0.| - F (0.)]^ (A23) 



1 i' i' ovi 



To minimize the sum of squares of the differences, the derivative of 

 this expression is taken separately with respect to each of the five 

 unknown parameters A , B , C , D , and E , and the resulting expressions 

 are set equal to zero, yielding a system of five simultaneous equations 

 with five unknowns. The system of equations is then summed for each 

 interval, i, over a complete wave cycle, and the resulting expressions 

 are solved for the values of the unknown parameters A, , B , C, , D , and 

 E which thus minimize the sum of squares of the differences. The 

 de r i vat i ve s are : 



9[Fy(0.) - F (0.)]^ 



i-^^-r — — — - — = 2A,cos^ 20. + 2B,sin 20. cos 20. 



oA 1 ill 1 



+ 2C,cos 20. + 2D, cos 0. cos 20. 

 1 1 1 1 1 



+ 2ETsin0. I sin 0.1 cos 20. 

 1 1 ' 1 ' 1 



- 2 F (0.) cos 29. = (A24) 



ov 11 ^ -^ 



8[F (0.3 - F (0.)]' 

 "■ v^ 1-^ ov 1 -" 



= 2A,cos 20. sin 29. + 2B,sin2 20. 

 1 1 1 1 1 



+ 2C,sin 20. + 2D, cos 9. sin 29. 

 1 1 1 1 1 



+ 2E,sin 9. I sin 9. I sin 20. 

 1 1 ' 1 ' 1 



- 2F (0.) sin 20. = rA25) 



ov 11 ^ -^ 



'[^^9.) - F^^(0.)] 



^„ = 2A,cos 20. + 2B,sin 20. 



oC 1 1 1 1 



+ 2C, + 2D cos 9. 

 Ill 



+ 2E,sin 9. sin 9. 

 1 1 ' 1 ' 



- 2F (0.) = (A26) 



ov 1 ^ ■' 



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