254 METHODS OF CALCULATION 



and in dotted lines the position corresponding to the reactive current, 

 that is to say, the axis of the pole facing the zero of the curve. 



The reaction is then deduced from the figure by determining the 

 mean useful ordinate of the curve. Theoretically this ordinate would 

 be obtained by evaluating the area of the shaded curve situated in 

 front of the pole, and dividing this by the breadth of the pole; but 

 the result so obtained is not practically useful, because it takes no 

 account of the expansion of the lines of force, which greatly broadens 

 the flux, particularly as the air-gap is made larger and the angles 

 of the pole pieces are more rounded. To determine the direct reaction, 

 one must take instead of the breadth of the pole, the breadth of the 

 field-magnet flux which issues from it; and to determine the mean 

 ordinate in this breadth. A similar determination is made for the 

 transverse reaction. It must be observed that the flux which forms 



rut. 

 BfUnd. 



1st. phase -X/ 



phase K/o 

 1 3rd. phase X-/o 



LJ 



FIG. 9. 



it is established not only under the poles, but also around them, 

 although with a lesser density. Consequently, this flux occupies 

 a greater breadth in which the mean reaction should be determined. 

 There is, therefore, a large individual liability to error in the appre- 

 ciation of these reactions, and this should give preference to the com- 

 plete method of operation here indicated for the employment of 

 theoYetical coefficients, which do not take account of the special con- 

 ditions in each machine. If the breadth of the flux is equal, for example, 



2 / V^ \ 

 to the pitch, Figs. 8 and 9 show the mean ordinates l/o I 



and /o for the direct reaction, and similarly for the transverse 

 reaction. The values give those of the coefficients K and K t them- 

 selves, if the ampere-turns obtained are compared with the ampere-turns 

 which would be obtained with the three bobbins united in a single 

 pair of slots and traversed by a current 7 . The curve of potential 



2N i 2 \/ T. \ N 



gives - I --/o ) instead of /oX3- The ratio gives the coeffi- 

 3 2 / 2 



'2 Vf, 



1 1=0.384. 



