81 



<)P>.. The total eflective E. M. F (OC^) that overcomes the total ohmic resistance 

 ( H -Ri) of the circuit, is due to the cyclic magnetization set up by the M. M. F. 

 vector OXq. OX^ is the resultant of OX and XX^ and as shown by the geom- 

 etry of the figure it is 90° in advance of the current, and therefore of A^A, as it 

 should be. The projection of XX^ on OX is the comjwnent of the armature 

 M. M. F. that acts against the field magnetization, /. e., it is « measure of the 

 armature reaction. The projection of XX^ on OA is likewise a measure of the 

 crors-magnetizing action of the armature. 



Having constructed the initial diagram, we can now follow out what takes 

 place when the resistance of the external circuit is varied. Suppose Rj is re- 

 duced to a value Rr- The current vector head B^ will move out along the semi- 

 circle OBoBr until equilibrium is again established in the circuit by the current 

 reaching, its maximum possible value under the new conditions.* The vectors 

 OA and OX retaining their positions, all the other vectors involved will reach 

 their final values corresponding to the new current by following the arcs of the 

 circles passing through their positive extremities to the positions designated by 

 tlie common subscript letter (r). The correctness of the variations indicated can 

 be readily verified by an inspection of the geometry of the figure in connection 

 with equation (7). 



In the present case Rj has been reduced to zero; in other words the sub- 

 scripts (r) indicate what takes place when a machine whose armature inductance 

 is large, as well as constant, is short circuited. A^ moves up to A, and the E. 

 M. F. at the brushes is zero. The current assumes an angle of lag of almost 90° 

 behind the total internal armature E. M. F. OA. the armature reaction almost 

 counterbalances the M.M.F. of the fields, and the resultant M. M. F. OXr is just 

 surticieut to develop the E. M. F. OCr that overcomes the resistance of the 

 armature. 



Returning to the initial conditions, suppose we increase the value of Lj from 

 zero to some value Li. i. e., suppose we introduce inductance into the external 

 circuit. The virtual value of the current will then be ex))ressed by tlie equa- 

 tion 



E (Si 



\ (R + Ri)^ - (L ^ Li )-,r^- 



:ind it will lag behind the internal E. M. F. E or OA, by an angle 



"See Bedell and Crehore's Alternating Current?, luige 223. 

 6 



