1903.] The "Hunting" of Alternating-Current Machines. 



same order of magnitude as the opposite effect which is dependent on 

 those terms. The result is : 



= 0, 

 and 



ap + Lpx + pfi = 0, 

 whence 



\L (L + \)p* + /> 2 } ft + Lp* (A - Aa ) f + app = 0, 

 and 



|L (L + A)jp 2 + /o 2 } a + a (L + X)p 2 -pp(A- Aa ) g = 0. 



These give a and ft in terms of and a, and substituting in (7), we 

 find 



whence it follows that 



a = a Q sin (8t + c), 



where 



tan e = - 



1 + 



and 



The small periodic term in the torque, produced by the oscillation, 

 is found, as before, to be 



J {aft + ( A - Xa ) ft - ( A - Xa ) a f } . 



The value of this when t = or = 0, that is when the motor is in 

 the position of steady motion, though not moving with the steady 

 velocity, is 



which from (8) is equal to 



8o 2_ ^y(A-Aao) 2 r 



jL (L + A) j9 2 + /) 2 } : /q \ 



-7= 7r \\ / -j 2 ^ 



5 2 + 1 1 + j /x, ^^ /+ 2 } 



The velocity at this moment is -,-, '(o sin St) L _ Q or go 8. 



The oscillation about the state of steady motion is, therefore, 

 VOL. LXXII. s 



