202 TREATISE ON ALTERNATING CURRENTS. 



Equation (1) can then be written 



and the solution of this, giving the steady periodic state, is by 

 (Appendix B) equation (5) 



pe 



sin (pt + I - 0J 



where 



or 



e sin (vt 



.... (2) 

 where 



tan = tan - 



(3) 



APPENDIX D. 



Determination of equivalent resistance, re- 

 actance, and impedance of n mutually reactive 

 circuits in parallel. 



Writing M rr for s r , the equations are (see 47, Chap. VIII.) 



i + kpM n ii + JcpM^ -h kpMi&z + . . . 4- kpM ln i n = e 

 + IffpM^v + IffpM^ + . . . 4- ^pM^ n e 



n = e \ . (1) 



4- r B i n + kM nn i n = e 



