255, 256] ELECTROMAGNETIC WAVES. 551 



cases we wish to know what goes on in a line of finite length, when 

 the ends are connected to any electromagnetic systems whatever, 

 both when the systems are left to themselves and when electro- 

 motive-forces are applied. Space is lacking for more than the 

 briefest possible treatment of this matter, which is very fully 

 treated in Heaviside's papers on wires to which reference has 

 already been made. 



The method of procedure is the same in every case. 



We shall make use of the equations 



<> 



si ,,dv 

 < 2 > -te = K di- 



Let us seek particular solutions of the form 

 (3) 



Inserting in (i) we have 

 (4) 



and if we put 



(5) 



we have the equation for u, 

 (6) , 



The solution of this is 

 (7) u = A cos fjLO) + B sin IJLX, 



where A and B are constants to be determined. From (2) we 

 obtain 



-=- = R\u K\ (A cos fjLX + B sin /JLX), 



(8) 



K\ 

 w = (B cos fjux A sin fix). 



The functions (3) are solutions of the differential equations 

 whatever the value of X. The values of X that are admissible are 

 determined by the terminal conditions. We shall take as an 

 example one of the simplest cases possible. Let us suppose that 

 at one end, where x = I, the two wires are connected, while at the 



