

ADDITIONS TO THE THEOKY. SECOND APPLICATION 97 



We thus obtain the line of reference BY, which represents the 

 mdition when the current is in phase with respect to 2- The locus 

 )f the characteristic point A\ is a straight line DQ perpendicular to 

 , while the locus of the point O\ is the straight line OX. For 

 :h value I w , we therefore know the two straight lines at which the 

 rector AiOi, equal to the supply E.M.F. 1} should always terminate. 

 All loads corresponding to the values I w will therefore be determined 

 :>y taking points such as A\,A\',A"\, etc., on DQ, and by drawing circu- 

 arcs of radius E l . The respective intersections Oi,O\,O\", of these 

 lines with O\A<z, give some E.M.F.'s values, 2, which are proportional 

 Oi, AzOi', A^Oi", while the corresponding reactive -currents, 

 I d , are proportional, respectively, to the lengths DA\, DA\, DA\". 

 For each pair of values of I d and 2, the corresponding exciting 

 ipere-turns F will then be obtained by referring to the excitation- 

 irve. Let us take, on this curve, the point M, which has for its 

 jrdinate the resultant E.M.F. 2, thus determined. The correspond- 

 ig abscissa, Om, measures the resultant ampere-turns. 



F- F KN'I d . 



V2 



It is therefore sufficient to subtract, from this abscissa, the counter- 

 ampere-turns of the armature, =KN'I d , in order to obtain the abscissa, 

 Om' F, which represents the excitation, and, consequently, represents 

 2, the E.M.F. induced on open circuit which would be obtained with 

 this excitation. 



It must not be forgotten that the reactive current I d is demagnetizing 

 and positive if counted to the right of the axis YY', and magnetiz- 

 ing and negative if counted to the left (see page 94). The upper 

 signs in the above formulae apply in the first case, and the lower signs 

 in the second case. We will therefore have 2 < 2 if the point A\ 

 to the right of the point D and, on the contrary, E^ > 2 if it is to 

 ic left. 



In the particular case where a motor is connected directly, without 

 additional rheostat or self-induction, on a constant potential circuit 

 of great output, and, when the impedance z of its leakage is negligible, 

 D coincides with B, and the line QD then passes through the point 

 B itself; which simplifies the diagram still further. 



The diagram which has just been explained is most precise in the 

 case of an alternator working at the knee, or above the knee of the 



