654 ELECTRICAL MEASUREMENTS 



Accordingly, by the aid of (18) the value for A n may be 

 written, 



^ 11 = H [(2/i + 2/n) sin 15 - (2/2 + 2/10) sin 30 + (i/ 3 + 2/9) sin 

 45 - (2/4 + 2/s) sin 60 + (y b + y 7 ) sin 75 - y, sin 90]. 



Applying the rules, 



^3 = M [f(2/i + 2/n) 4- (2/3 + 2/9) - (2/5 + 2/7)) sin 45 + 



{(2/2 '+ 2/io) - 2/6 } sin 90] 

 ^9 = ^[|(2/i + 2/n) + (2/3 + 2/9) - (2/5 + 2/7)) sin 45 - 



1(2/2 + 2/io) - 2/6 1 sin 90] 

 4 6 = YQ [(i/i + 2/11) sin 75 + (2/2 + y 10 ) sin 30 - (y s + t/ 9 ) 



sin 45 - (1/4 + 2/s) sin 60 + (2/5 + 2/7) sin 15 + t/ 6 sin 90] 



^7 = M 1(2/1 + 2/n) sin 75 - (2/2 + 2/10) sin 30 - (1/3 + 2/9) 



sin 45 + (2/4 + 2/s) sin 60 + (t/ 5 + 2/7) sin 15 - y, sin 90]. 



Cosine Terms. The cosine terms may be treated in a similar 

 manner. 



4 /O \ "" tflKlT / 1 r\\ 



As cos (2n m) ~ = cos -~ 



the differences of the ordinates are involved 

 The equation corresponding to (18) is 



. . mir . mir 



-f cos (2n k) 7,- = cos k ^ (20) 



Zn Zn 



The sign of the left-hand member is + if m is even and if 

 m is odd. Applying the above and, for convenience, expressing 

 the results in terms of the sines, of the angles, the values of B 

 are 



Bi = 1 A [2/0 sin 90 + (y l - y n ) sin 75 + (y 2 - y lo ) sin 60 + 



(2/3 - 2/9) sin 45 + (2/4 - 2/s) sin 30 + (2/5 - 2/7) sin 15] 

 #11 = H [2/o sin 90 - (2/1 - 2/n) sin 75 + (2/2 - 2/io) sin 60 - 



(2/3 - 2/9) sin 45 + (2/4 - 2/s) sin 30 - (2/5 - 2/7) sin 15] 

 B* = H[{(yi - 2/n) (2/3 -- 2/9) - - (2/5 - 2/7)! sin 45 + 



!2/o - (2/4 - 2/8))sin90] 

 #9 = H [{- (2/1 - 2/n) + (2/3 - 2/9) + (2/5 - 2/ 7 )| sin 45 + 



(2/0 - (2/4 - 2/s)J sin 90] 

 #5 = M [2/o sin 90 + (2/1 - 2/11) sin 15 - (2/2 - 2/io) sin 60 - 



(2/3 - 2/9) sin 45 + (2/4 - 2/s) sin 30 + (2/5 - 2/7) sin 75] 

 Bi = M [2/o sin 90 - (2/1 - 2/n) sin 15 - (2/2 - 2/io) sin 60 + 



(2/3 - 2/9) sin 45 + (2/4 - 2/s) sin 30 - (1/5 - 2/7) sin 75]. 



