350 KENNELLY-NABESHIMA— ESTABLISHING A 



value at A, t seconds after switch closing, will be 



eA=EAs\ncct volts. (14) 



As shown in Appendix I., the vector voltage at P in the final steady- 

 state will be^^ 



sinh dp 

 ^* " ^sinhX ^^^' ^^'' ^'°^^^" ^' ^^^'^ 



The size of Ep^ is the size of this planevector quantity, and may be 

 represented by \Ep^\. H its slope is — (3°, then the instantaneous 

 value at P in the steady state, after t seconds, is 



Pp^ = I £p« I sin (cot — /S°) inst. volts. (16) 



It is also shown in Appendix I. that at P, after the passage of the 

 ^th reflection from B, and before the arrival of the (k -\- i)th re- 

 flection from A, the max. cyclic vector voltage is 



Epk =Ep^ (i -e--**-^) =Ep^ -26-*^^ sinh kb^ max. cy. volts. Z . (17) 



If the size of this planevector quantity be denoted by | £pj. |, and its 

 slope is — Pk° ; then at any time t between the ki\\ and (fe + i)th 

 reflections, the instantaneous e.m.f. at P will be 



epk = I Epk I sin (co/ — ^l) inst. volts. (18) 



The slope — Pk° changes abruptly at each succeeding increment. 



Graphical Development of Initiating Transients. — A rotatory 

 vector diagram of the voltage developed at the B end of the line in 

 the case represented by Fig. 3, is indicated in Fig. 17, for the first 

 four reflections. The line — XOX is the projection axis. Pro- 

 jections on this axis from a rotating vector e.m.f. indicate the in- 

 stantaneous e.m.f. at the end B of the line, with the oscillograph load 

 of 9900 ohms. 



The vector OA represents the first reflected wave of 239.5 max, 

 cy. volts at B, at the instant of its arrival there, and when its 

 instantaneous value is still zero. This vector OA then rotates 



11 Bibliography 30. 



