238 METHODS OF CALCULATION 



place in three different magnetic paths; only the direct reaction acts in 

 the main circuit of the field magnets, while the transverse reaction and 

 the stray fields act, in general, upon circuits of low magnetic density., 



The conclusion which I have drawn from the above is that, in 

 general, the direct reaction should be expressed as a counter M.M.F.; 

 that is to say, by a number of ampere-turns equivalent to the demag- 

 netizing effect of the armature. 1 The total armature M.M.F. per 

 complete magnetic circuit or per pair of poles is 



KN T /- 

 IV a , 



2 



where K is a coefficient of reduction and N the armature conductors 

 per pair of poles. I have formally given for asynchronous motors a 

 practical value which is approximately the same for alternators, viz.: 



k being the coefficient of reduction which appears in the formula of 

 E.M.F. written under the form 



2V 2 



Here TV is the number of peripheral conductors for one phase and <u the 

 velocity of pulsation. It is the direct reaction which produces, almost 

 entirely, the variation of terminal voltage. As to the transverse reac- 

 tion and the reaction of stray fields, with the assumption that the 

 armature is unsaturated, as I assumed and as M. Guilbert also 

 assumes, they may be expressed simply by the coefficients of self- 

 induction / and s. 



More recently I have indicated 2 that the transverse reaction could 

 also easily be expressed in ampere-turns. 



The analysis of the phenomena taking place in the alternator leads 

 therefore to a new proposition, formulated in my articles of 1899. 



1 No notice is here taken of one of the cases considered by the author in 1899; 

 namely, that in which all the machine is well below saturation, because it is only 

 susceptible of very rare applications; moreover, it has been treated with more 

 detail by M. Jean Rey in a very interesting communication presented to the 

 Congress of 1000, in which the reader will find an interesting example of a cal- 

 culation of reactive coefficients in a machine actually built by this method, which 

 has since been followed by various authors. 



'"Theory of Synchronous Motors," Vol. I. Paris, Gauthiers-Villars, 1900. 



