130 SYNCHRONOUS MOTORS 



may be neglected. The expression for P is therefore practically 

 equal to the following: 



i i r T \ n r / _\ T 9 



... (3) 



Consequently, by making p very low, as was done by Hutin and 

 Leblanc, the permanent expenditure of energy due to the current of 



frequency j^ + j^- can be reduced, at the same time that the damping 



effect due to the current of frequency jrj^ is amplified. 



When the pole-pieces are solid, they already, by themselves, play 

 the role of a damping circuit, and, their resistance p being very small, 

 it can be readily understood that the effect thus obtained would be 

 already quite appreciable. 



At synchronism, we have T'= TI, and the preceding expressions 

 (i) and (2) (p. 128) reduce to the form 



and 



The armature-reaction then produces two fluxes in the field-coils, 

 one being constant, which represents the mean reaction, and the other 

 having a frequency which is double that of the alternators. 



Long-Period Oscillations. Long-period oscillations, characterized 

 by periodical variations of current which can be observed on an ampere- 

 meter, may occur in consequence of causes which are apart from the 

 peculiarities of the motors themselves. For example, a motor which 

 drives a machine-tool subjected to a variable load, or a motor connected 

 to a generator whose speed varies periodically (for example, a generator 

 driven by a steam engine having a single cylinder), will itself undergo 

 the same corresponding oscillations of currents, which are much slower 

 than the preceding. These slow oscillations have, moreover, the 

 incidental effect of keeping up the real oscillations, and thus they are 

 often the cause of the machines falling out of synchronism. 



Other causes more complex, and which are still less well understood, 

 can bring about the systematic and periodic production of this phenom- 



