1903.] Tlic " HuntiiKj " of Atternating-Churrent Mm-ltim*. 251 



probal)ly somewhat less than 7. The motion is only just stable with this 

 load, however, and can be made unstable by a very small reduction of 

 /3 , and I think the figures are a proof that there is an element of 

 instability other than a possible negative value of y. 



To get an approximation to the absolute value of 7, we note that 



-, nearly. 

 '}' 



Hence 



4MpS _ A*p (L + K ) P * _. 4 x (70)' x 3-5 x 314 _ 



' T(L~+W +PP 2 ~ 13-6 x (17)* 

 and 



1 = 4A fe! = about 5-7 sees., 

 7 960 



which is the sort of magnitude one would expect from the rate of 

 development of the oscillations when the motor is unloaded and 7' is 

 small or slightly negative. 



Note Added June 28th, 1903. 



It is useful to consider the effect of increasing the dimensions of 

 the machine on the results here obtained. Suppose that the linear 

 dimensions of every part except the field coils are increased n-fold, 

 that the speed remains the same. Then : 



A becomes 7i 2 A, 



P P/ n , 

 L nL, 



K ,, 11K, 



M 7i 5 M. 



The rated output is multiplied by between n 3 and 7i 4 . To get the 

 same magnetisation we require 7i-times the ampere turns in the field- 

 coils. Hence if the number of turns in the field-coils and the current 

 density be kept the same, we require 7t-times the section of wire, 

 and the wire is 7i-times as long. Since all the other linear dimensions 

 of the coils and of the magnetic circuit are increased 7i-fold, it readily 

 follows that p (if the magnets are completely laminated and there are 

 no amortisseur coils) is increased 7?-fold. 



Taking these values, we find that 



becomes 



