THE ARMATURE REACTIONS OF ALTERNATORS 251 



preferable to employ the diagram Fig. 7, which lends itself better to 

 determining the different elements without complications. 



If it is desired to solve the inverse problem, that is, to determine 

 the fall of potential under constant excitation as a function of the 

 load, the preceding diagrams do not give a direct solution, but it is 

 easy to employ them for an indirect solution, particularly in assuming 

 constant the external dephasing <, and taking successively different 

 values of the reactive current; for each value of Id the preceding 

 construction will be followed in the opposite direction, and thus will 

 be obtained the voltage at the terminals, the values of ^ and of /,. 

 Thus may be traced a curve of voltage u as a function of Id, and of 7 

 which is obtained therefrom. It is only necessary to seek upon this 

 curve the point corresponding to the conditions required and the 

 dephasing angle. 



The problem is solved no longer for a single point, but along a 

 complete curve, which is also comparatively easy. 



Local Corrections of the Air-gap Due to Saturation (Second 

 Approximation). The diagram Fig. 7 is established by supposing that 

 the reactions act en bloc, and are represented by coefficients. The same 

 is true of the diagram Fig. i. But if it be desired to follow the reality 

 somewhat closer, it is well, once the diagram is determined by the 

 aid of the coefficient K (the calculation of which is explained later), 

 to calculate upon the drawing the flux-density of the resulting field 

 at each point along the air-gap, by the aid of magnetic potential 

 curves (to be explained later) and of the local reluctance. In par- 

 ticular, if the teeth of the armature are saturated, they develop marked 

 variations of the reluctance per unit of surface along the air-gap, and 

 the flux calculated according to a mean value of reluctance may be 

 sensibly modified thereby. This is the case not only for the trans- 

 verse reaction, as has already been remarked by certain authors, but 

 also for the direct reaction, which should not be set aside in this 

 correction. The effect of this latter is to reduce the resultant flux. 

 The curve of the diagram is, in fact, a solution of the first approxi- 

 mation necessary in order to determine the dephasing of the values 

 of the active currents from the reactive currents. After these values 

 have been obtained, a second approximation may be arrived at 

 by tracing the flux-densities from point to point for determining the 

 real flux. la general, however, the precision of the calculations is 

 not sufficiently great to proceed upon this correction unless ample 

 time may be afforded for the study. 



