154 PRINCIPLES OF ELECTRICAL DESIGN 



This may be plotted in Fig. 59 as the ordinate OE, making NE 

 represent the armature flux, on the assumption that the whole 

 of this flux component is cut by the "active" portion of the 

 coil ; and this suggests a graphical method of locating the correct 

 brush position when commutating poles are not used, because 

 what may be called the equivalent neutral zone is found when 

 the conductor AA' occupies a position such that the length 

 NE is exactly equal to OM. If this position cannot be found 

 without passing under the tip of the pole shoe (represented by 

 the heavy dotted rectangle), the machine will not commutate 

 perfectly without the addition of a commutating interpole. 



The question of relative magnitude of these end flux e.m.fs. 

 deserves some attention, because it would be foolish to compli- 

 cate the problem of commutation if the correction, when made, 

 is of little practical moment. It is claimed by some writers 

 that refinement of analysis and calculation is always commend- 

 able even when built upon a foundation that is admittedly a 

 mere approximation. With this attitude of mind the present 

 writer has no sympathy; it appears to lack the sense of propor- 

 tion. Apart from any considerations of a mechanical nature, 

 the practical problem of commutation, from whatever point of 

 view it is approached, is, and always will be, the correct determi- 

 nation of the field in which the short-circuited coil is moving, 

 whether this conception of the magnetic condition is buried 

 in the symbols L and M, and referred to as inductance, expressed 

 in henrys, or considered merely as any other magnetic field; 

 and it would surely be a waste of time and mental effort to intro- 

 duce refinements if the percentage correction, when made, is of 

 a small order of magnitude. The question of end fluxes, how- 

 ever, is one of real practical importance; the end flux in actual 

 machines is not of negligible amount, and although it cannot 

 be calculated exactly, it is a factor which should not be left 

 out of consideration. It is true that we do not concern ourselves 

 with the end fluxes when calculating the useful voltage developed 

 in the active coils; but, apart from the fact that in this connec- 

 tion the amount of the end flux is relatively small, it is not difficult 

 to see that the e.m.f.s generated in the end connections as they 

 cut through the end fluxes due to the armature currents balance 

 or counteract each other and have no effect on the terminal 

 voltage. The conception of the end connections cutting through 

 the flux due to the armature as a whole, as indicated in Fig. 59, 



