114 ELECTRICAL MEASUREMENTS 



mi = a + jb, m* = a j6 



where 



k 2X 2r 



a = TTF* = -^ ana o = -a? 



These values of mi and ra 2 when substituted in (8) give 

 r, -at r /' /' 1 



C 6 I (a j)bt ,. ;to I ( a -f >&)<,. I ,, . 



0=-^-- : ** lee d - e lee (tt (14) 



rP 2jb I Jo Jo 



but 



fji* = cos 6< + j sin 6* 



and 



t * = cos or ^ sin ot. 

 Hence 



^ = ^^[(sin 60 f'ee a< cos btdt - (cos 60 fee* sin &tcft] (15) 

 rro Jo Jo 



The method of dealing with this equation when e falls sensibly 

 to zero before the first elongation is reached is similar to 

 that just employed in the nonperiodic case. . See page 112. 



Let R and S be defined as follows: 



ee*'cos btdt 

 'o 



p t = e , a constant (16) 



I edi 



Jo 



r 



_ Jo 



I 



Jo 



a constant (17) 



edt 



Jo 



Then when t y t' 



r_ 



bt-Scosbt] (18) 



1C 



ft ft 



To find B i determine ti by placing -r = and substitute the result 

 in (18). Neglecting the constant coefficient 



[(- aR + bS) sin bt + (aS -f- &#) cos 6<] = 



sin fch a/S + 6^ \S + 7rl2 



cos6^ = tan6 ^ = oF^65 = XTT^S 



