284 APPENDIX A 



A 



and the /.COX= Z.AOX= . This corresponds to the equations 

 for e\ and 62 on page 16, which show that when / = o, e\ has a phase 



A 



H and 2 falls short of exact opposition (180) by the same angle 



q 



, where is the angle between E\ and Ez projected backwards. 



EZ may be said to lag behind E\ by i8o+0, or to lead E\ by 180 6. 



The current produced in the circuit of the two armatures will 

 be, I=E/Z and will lag behind E by the angle y whose tangent 

 is X+R; where R, X and Z, ( = V^ 2 +X 2 ), are respectively, the 

 resistance, the reactance, and the impedance of the whole circuit, 

 including the impedance of the connecting line and the synchronous 

 impedance of the two armatures; and X=2xZ,=o>Z,, where L 

 is the inductance of the whole circuit. 



By trigonometry 



B = Vi 2 -j-jB 2 2E\Ez cos 0, 

 and since 



=/Z, and 7=j, 

 we have 



E_ VEi 2 +E 2 2 - 2EiE 2 cos 

 Z~ Z 



and the current-phase (referred to OX} is -K p y. 



These two relations stated algebraically, give as the instantaneous 

 value of *, 



V~2VEi 2 +E 2 2 -2EiE 2 cos 

 -- 



sin 



which is the same as the value of i given at the top of page 17. 



The other forms of equations for i and / given on page 17 are 

 deducible from the diagram of Fig. A. 



