h+i'= 



368 Dr. Barton and Mr. Lownds on Reflexion and 



have 



BQ 1- . • (13) 



Q=<k + 0'=O, for« = 0. ! 



On elimination of Q and the i's these equations yield 



(l+I*S ^)f=(l-L*S ^)ft; . . (14) 



which is equivalent to Heaviside's expression for reflexion at 

 a terminal condenser. 



27. Writing for the incident wave-train 



£ 1 =e--*p*cos 0^ + 0? 

 the solution of (14) may be written 



<f> f — Ce ~ *P* cos (p£ + i + 7) — (cos t -{- C cos 1 + 7)6 -i></Xo ; j 

 where C cos 7 - 1 ~^~ k V = c , j 



Csin7= :Z i= 2L °=c', I ,_. 



Ao \ (15) 



tan 7 = — = 2 \ 9 9 . 



Xo = Lv$ p, and A = 1 + ^ 2 - 2£% + /c 2 %0 2 . ; 



Or, if we ignore, as before, the exponential term and let 

 the incident wave-train be the real part of e^-k^P 1 , then the 

 solution is 



f = ( C + c^ l3 (16) 



the c's having the values given in equations (15). 



In the case of a terminal condenser we see that if k = Q, 

 C = l for all values of Xo- This simple relation is slightly 

 disturbed by the damping wdien present. 



28. This theory of the terminal condenser has been given 

 for the sake of dealing with the reflexion which occurs at the 

 oscillator at the beginning of the line. It may be approxi- 

 mately treated as a condenser simply, because the interval 

 elapsing between the launching of the wave-train along the 

 line and its return after traversing about 300 metres is so 



