Experiments with Alternating Currents. 239 



we may put 



._gco^-B_® cos ^-^J 



*- x + y x + Y " " - k) 



Substituting in (1) and rearranging, 



dhi , /' . Jc 2 k 3 Y\du , 9 Jc 2 Q cos pt 

 & + [*i+ x + Y)dt + nu = "X+Y • 



Let 



X + Y 



*i+#^=*, .......... (3) 



x^f= E W 



We have 



d?u t .. du 9 ^ 



a¥ di + /lM = Ecos i ? *i 



the solution of which is 



Esine , x , M 



M= "P _C0S (^"" e )' ( 5 ) 



where 



tane=^- — s (6) 



rr—p 



Supposing, as before, that k is great in comparison with 



T? — p' Z . 7T 



— , e will nearly equal ~ . 



p ^ A 



Differentiating (5), 



du E sin e . , , -. /r . x 



Tt = _ sm (^_ e) , ....... (7) 



Substituting in (2), 



.. , #3 YE sin e . >' • x 

 (r cosp£ + — — y sm Q?£ — e) 



* = XTY~ • 



E.M.F. at D=iX 



X, f- .. & 3 YEsine ■ \ 



= X+Yi ° sp k sin ^~~ e )j 



^ rr . . & 3 YE sine cose . & 3 YE sin 2 e I 



= ii (ScospH t — sm.pt j cos pt r. 



E.M.F, at B — b(icospt. 



