ELECTRIC OSCILLATIONS AND ELECTRIC WAVES. 223 



equal to the electric energy per unit length of line 

 according to equation (9) or equation (10) of Art. 116. Such a 

 wave is called a pure wave. 



When \ Li 2 is not equal to f Ce* we have what is called an 

 impure wave, and an impure wave is always resolvable into two 

 pure waves traveling in opposite directions. For example, the 

 first two laps of the ribbon wave in Fig. 153 give voltage = 2E 

 and current equal to zero over the whole line, and this condition 

 is resolvable into the two oppositely moving waves, namely, the 

 first lap (+ E, + /) and the second lap (+ E, - /). This 

 resolution may be made in any case as follows : Let A be the 

 voltage across the line and B the current in the line at any 

 point, and let it be required to resolve this state of affairs into a 

 pure wave ET traveling to the right and a pure wave E"I" 

 traveling to the left. Then we have 



y=+a (i) 



E" 



JT7= ~ a (2) 



E' + E" = A (3) 



/' +1" = B (4) 



where a is written for *\j-^ . These four equations determine 



E', E", I' and I". Of course either E" or I" must be 

 negative if both E' and I' are positive. 



122. Immediate effects of wire resistance and poor insulation 

 on a wave on a transmission line. When an electric current 

 dies away in an ordinary circuit of wire (after the electromotive 

 force of a battery, for example, has ceased to act) the magnetic 

 energy of the circuit (see Art. 35) is slowly converted into heat 

 in the wire in accordance with Joule's law, and if we imagine 

 that a pure wave has suddenly entered upon a transmission line 

 of which the wire resistance is not negligible, then the immediate 



