ELECTRIC OSCILLATIONS AND ELECTRIC WAVES. 227 



In the following discussion this increase of capacity and re- 

 sistance is ignored. The effect of loading a line (increase of L) 

 is to decrease the value of the current for a given value of voltage 

 in a wave, according to equation (9) of Art. 116, and therefore 

 the rate of loss of energy because of wire resistance is decreased. 

 A clear idea of the effect of loading may be obtained by consider- 

 ing a particular example : 



Fig. 162. 



1. A battery of voltage E is connected across the end of a 

 line for one one-hundred-and-eighty-six-thousandth of a second, 

 thus producing a rectangular wave pulse one mile long. 



2. The total energy of the wave is JZJ 2 + | CE?. 



3. The rate of loss of energy in the wires is R W P watts. 



4 The rate of loss of energy in the insulation is (E?/Ri) 

 watts. 



5. The time of transit of the wave from end to end of line is, 

 say, / seconds. Therefore: 



6. The actual loss of energy in the wires is R w Pt joules. 



7. The actual loss of energy in the insulation is (E?/Ri)t joules. 

 Suppose now that L is quadrupled by loading. Then the 



wave velocity is halved according to equation (8) of Art. 116 

 and the current in the wave is halved according to equation (9) 

 of Art. 1 1 6, voltage in wave being unchanged. The following 

 statements are therefore easily seen to be true : 



1 . The battery will have to be connected for two one-hundred- 

 and-eighty-six-thousandths of a second to give a wave one mile 

 long, and, supposing this to be done, then: 



2. The total energy of the wave is the same as before. 



3. The rate of loss* of energy in the wires is one quarter as 

 great as before. 



