D. C. COMMUTATING MACHINES 197 ration coefficient, the field excitation required to produce the e.m.f . e (1 + p) is Fo (1 + sp) ; thus an additional excitation of spF0 is required at load, due to the armature resistance. 2. The demagnetizing effect of the ampere-turns armature reaction of the angle of shift of brushes TI requires an increase of field excitation by riFa. (Section VII.) 3. The distorting effect of armature reaction does not change the total m.m.f. producing the magnetic flux. If, however, mag- netic saturation is reached or approached in a part of the mag- netic circuit adjoining the air gap, the increase of magnetic density at the strengthened pole corner is less than the decrease at the weakened pole corner, and thus the total magnetic flux with the same total m.m.f. is reduced, and to produce the same total magnetic flux an increased total m.m.f., that is, increase of field excitation, is required. This increase depends upon the saturation of the magnetic circuit adjacent to the armature conductors. 4. The magnetic stray field of the machine, that is, that part of the magnetic flux which passes from field pole to field pole with- out entering the armature, usually increases with the load. This stray field is proportional to the difference of magnetic potential between field poles; that is, at no load it is proportional to the ampere-turns m.m.f. consumed in air gap, armature teeth, and armature core. Under load, with the same generated e.m.f., that is, the same magnetic flux passing through the armature core, the difference of magnetic potential between adjacent field poles is increased by the counter m.m.f. of the armature and by saturation. Since this magnetic stray flux passes through field poles and yoke, the magnetic density therein is increased and the field excitation correspondingly, especially if the magnetic den- sity in field poles and yoke is near saturation. This increase of field strength required by the increase of density in the external magnetic circuit, due to the increase of magnetic stray field, depends upon the shape of the magnetic circuit, the armature reaction, and the saturation of the external magnetic circuit. Curves giving, with the amperes output as abscissas, the ampere-turns per pole field excitation required to increase the voltage proportionally to the current are called over-compounding curves. In the increase of field excitation required for over- compounding, the effects of magnetic saturation are still more marked. 13 198 ELEMENTS OF ELECTRICAL ENGINEERING XL Characteristic Curves 60. The field characteristic or regulation curve, that is, curve giving the terminal voltage as function of the current output at constant field excitation, is of less importance in commutating machines than in synchronous machines, since commutating machines are usually not operated with separate and constant excitation, and the use of the series field affords a convenient means of changing the field excitation proportionally to the load. The curve giving the terminal voltage as function of current out- put, in a compound-wound machine, at constant resistance in the shunt field, and constant adjustment of the series field, is, how- ever, of importance as regulation curve of the direct-current generator. This curve would be a straight line except for the effect of saturation, etc., as discussed above.