+ 2B„ sin 6. cos 9. cos 9. 

 ^ 1 1 ' 1 ' 



2 F ^ (9.) cos 9. cos 

 oh 1 1 ' 



(A70) 



"■ h ^ 1 oh 1 



2 A_ cos 9. I cos 9. I sin 9. 

 2 1 ' 1 ' 1 



+ 2 B„ sin^ 9. 

 2 1 



- 2 F , (9.) sin 9. 

 oh X- 1 



= 0. CA71) 



n 

 Since i sin 9. cos 9. | cos 9. | = for an even number of equally 

 i=l 

 spaced intervals 9. summed over a complete wave cycle, the resulting 

 summed expressions for the derivatives set equal to zero are 



n n 



A„ y (cos 9. I cos 9.1)^ - y F , (9.) cos 9. I cos 9. I = (A72) 

 1=1 1=1 



n n 



B, \ sin^ 9, - \ F , (9.) sin 9. = 0. (A73) 



^-i_i 1 ., ohi 1 



i-i 1=1 



These expressions are easily solved for the unknown parameters A„ and 

 B^, yielding: 



n 



y F , (0.) cos 9. I cos 9. I 

 . _ , oh 1 1 ' 1 ' 



A^ = ^ ^ CA74) 



y (cos 9. I cos 9. 1)2 

 1=1 



138 



