240 METHODS OF CALCULATION 



(where / is the transverse self-inductance and aj( = 2^f) the speed of 

 pulsation); and of a part of the stray field reaction 



GB=0)Sl COS 1 = (,)$/, 



where 5 is the self-induction of the stray fields. 



The segment GD perpendicular to / represents the E.M.F. of 

 reaction of the stray fields, wsl, and the segment 



ED = wsl sin </ = 



represents the second component of the stray-field reaction; thus in 

 OD is obtained the value of the effective E.M.F. e, which should be 

 obtained by the resultant excitation. 



The value of the angle '</> is determined by expressing simply the 

 relations between the elements of the figure. Let us analyze the 

 broken line OPAB into components upon OB, and BA; whence 



e-=r'I cos <f>+ Ul sin (<[><}>) 



aj(l+s)I sin </> = r'I sin. </>+U sin (^' </>) 

 and 



U s 



U cos<f)+r'I 



The angle of real dephasing ^ is thus determined solely by a 

 knowledge of the transverse reaction. This equation, which was 

 given by the author in 1899, is evidently equivalent to the following 

 construction. 



From the point A a perpendicular AH is drawn to the direction 

 of the current /, and a segment AF is drawn upon this line equal 

 to wsl; then a segment FT=u)lI; finally the point O is joined to 

 the point T, and thus is obtained the angle ^ and the position of the 

 required vector OD representing the total effective E.M.F. e. To 

 determine the necessary ampere-turns for the production of this E.M.F., 

 it is only necessary to employ the open circuit characteristic or 

 saturation curve of the alternator. 



1 The segment BT intercepted by OT will evidently be equal to 

 BD+ DT= toll sin <f>+ wsl sin <J>. 



