266 METHODS OF CALCULATION 



/! when the poles are crossed, and an inductance of A' when they are 

 coincident, behaves under load, when the real dephasing is for 

 example, as though the active current 7 cos ^ traversed an inductance 



, the reactive current / sin d> an inductance , and the total cur- 



rent 7 a parasitic inductance - equal to the mean of the two 



preceding. 



In order to take into account the Foucault currents of the arma- 

 ture produced by the rotating reaction, it is sufficient to apply a 

 reducing coefficient m to its inductance, which is less than unity, 

 evaluated according to the conditions of 'construction, and at the same 

 time to increase the apparent resistance of the armature in accordance 

 with the energy lost in these Foucault currents, since it is furnished 

 by the armature. It is for this reason that we attribute to this 

 resistance a value r' > r in all of our diagrams. 



If the field magnets or the armature of the alternator are saturated, 

 the direct and transverse self-inductances will be replaced by equiva- 

 lent back ampere-turns, again calculated as in my theory of rotating 

 field: the sinusoid of the amplitude o.27rw7 presents the mean ordinate 



2 nl 1 2 \ 2 



times smaller and is consequently equivalent to I ) ampere- 



TT io\7r/ 



/2\ 2 



turns. The value of K and K t will therefore be I I for a single 



bobbin if it has the same breadth as the flux. If the winding com- 

 prises several straddling coils, the coefficients should be multiplied 

 by the straddling factor of the winding k; finally if the flux of the 

 poles is narrower than the pitch, it should be multiplied by the factors 



J . /7rr)\ . Jf ficd\] 



-r-sml -j I and -T i cos I -7 1 , respectively the coefficient of 



direct reaction and the coefficient of distortion for the conditions 

 analyzed above. 1 



1 It is of course easy to pass from a single-phase machine to a polyphase 

 machine of two phases, observing that each phase gives a fixed reaction and a 

 rotating reaction of the same amplitude. I have shown in my theory of rotating 

 fields, already alluded to, that the fixed reactions unite in space and are added 

 algebraically while the q rotating, parasitic reactions give rise to a resultant /ero. 

 The coefficients K and K t are then themselves theoretically expressions in all 

 the machines independent of the number of phases (N designating always the 

 total number of peripheral wires); but the rotating, parasitic self-inductance 

 disappears in polyphase machines. In this manner the return is made to the 

 theoretical coefficients of the polyphase machines. 





