300 Mr. W. B. Morton on the Propagation of 



the wave -train in the wires is at any insfcant^u^Zy simple har- 

 monic throughout. 



Numerical Values. — To obtain an estimate of the import- 

 ance of the small terms of (13) and (14) I shall take the 

 numbers given by Dr. Barton in his last paper (loc. cit.). 

 Judging from his diagram (fig. 2) in that paper, the ampli- 

 tude of the second positive maximum of the wave-train is 

 about half that of the first. This would give 



e p =2 or q—^-~p^ — 



We have roughly 



p = 2tt x 35 x 10 6 = 22 x 10 7 , q = 2± x 10 6 , 

 B = 69-5xl0 5 , L=19; 

 .-. ^ = 37x10*, and er = 0. 

 These values give for the velocity of propagation 

 v{l --00000035} , 

 and for the attenuation 



^{1+-000091}, 



so that the corrections are quite negligible. We see from 

 the expressions (13), (14) that the damping q only affects 

 the value of the small terms introduced by the inequality of 

 p and a. 



Effect of a Terminal Resistance. — To find the effect on the 

 incident waves of a resistance (without inductance) inserted 

 between the ends of the wires, we put in the complex values 

 in the expression (7) for the reflexion-factor. We then get 



V 2 _ (p — q + vfix) +i(p — V*oc) 

 Vi (—p + q + v/3x)—i(p + vax) 



=f+ig, say. 



Therefore to an incident wave e ipt corresponds a reflected 

 wave {f+ig)e i P t \ or, taking real parts, with incident cos/?£ we 

 have reflected 



/cos pt—g §\npt = */f 2 +y i cos (pt + 6), 

 where 



tan<9 = ^,; 



