the GoldscJimidt Dynamo. 765 



The current generated by reaction from this, back into the 

 stator, is 



p 2 W p 2 M 2 



P 2 M 2 9 . 



= " Ej/° C ° S P 



The current which this now generates in the rotor is 



p*W „ . . # , 2/> 3 M» . , 



= tfrrp- yo cos 2pt sin ;?£ + g%-^-^o sin 2/tf cos p£ 



# 3 M 3 

 = yv -p -p i/o{ sll i 3^ + sin 2p£ cos^} 



» 3 M 3 

 = RTTrT ^ 1 2 sm 3 J^ + i smpO- 



The current which # 3 now generates in the stator is 



■Mi, 



M dz~ pM 



= R 4 C0S ^s--ir/ 3Sm ^ 



p 4 M 4 f 41 cos 3p£ cos pt + i cos 2 /rt — sin 3pt sin pH 



""BiRjEsR/ L -sin 2pt cos pt sin pt J 



= A{4^ cos Zpt cos pt — sin 3^ sin pt + \ cos 2 pt — ^ sin 2 2p£}. 



Employing the identity cos 2 A— sin 2 B = cos (A + B) cos (A— B) 

 this becomes 



?/ 4 = A(4 cos Zpt cos pt + cos 3p£ cos pi — sin 3p£ sin pt) 



= A(4 cos ?>pt cos pt + cos 4p£) 



= A {2 (cos 4p£ + cos 2p£) +cos 4p£} 



» 4 M 4 

 ~ STRJ^R ^ 3 cos 4 ^ + 2 cos 2 ^)' 



