ELECTRICAL TRANSMISSION OF ENERGY. 183 



used, and a voltage E between the common return and either of 

 the other two wires, then the current in the common return is 

 \/2I, where / is the current in either of the other two wires ; and, 

 working at the same current density throughout, if the resistance 

 of either outside conductor is E, that of the common return 



T> 



is i=. The loss in the lines is therefore 



PR + PR + 2/ 2 -^L 



...... (4) 



Also the total power transmitted is - 



2/JS 



If the same power is transmitted by a mono-phase system at 

 the same voltage, with the same loss, the mono-phase current /' 

 is given by 



1'E - ZIE 

 or 



J' = 2/ ........ (5) 



If R' is the resistance of each mono-phase line-wire, we must 

 have 



2E'I" 2 = R'P(2 + v/2) 

 that is by (5) 



SR'P = PR(2 + \/2) 

 or 



o 



Thus each outside wire is ^ ^- times as large as each 



mono-phase wire, and the common return ^ - -j=. times as large. 



Thus, taking the amount of copper in the mono-phase, or in the 

 direct-current, system as unity, that required for the di-phase 

 system with common return under the same conditions is 



8 8\/2 



or, for the same power transmitted and loss in the line, di-phase 



