184 Transmission of Power [February, 
the cable c. The other terminals, x and y, are either put 
to earth or connected by a separate conductor. 
Let us suppose that the electromotive force of the current 
which flows is unity. Since by the revolution of b, a 
counter-eleCtromotive force is produced to that of A, the 
electromotive force of the current that flows is manifestly 
the difference of the two. Let the resistance of A and b 
together be equal to unity, and that of the mile of cable and 
connections between them the o*oi of this unit. Then the 
current which flows will be— 
r _E_ 1 
R i*oi* 
If now an additional machine, A', Fig. 2, an additional 
motor, b', and an additional mile of cable, be introduced 
into the above circuit, the electromotive force will be 
Fig. 2, 
doubled, and the resistances will be doubled, the current 
strength remaining the same as— 
Q_ B_ 1 + 1 __ 2 
R roi + i*oi 2*02* 
Here it will be seen that the introduction of the two addi- 
tional machines, a', b', has permitted the length of the 
cable, c, to be doubled, without increasing the strength of 
the current which flows, and yet allowing the expenditure 
of double the power at A a' and a double recovery at B b' of 
power, or, in other words, a double transmission of power with- 
out increase of current. Increase, now, the number of 
machines at A to say one thousand, and of those at b in like 
proportion, and the distance between them, or the length of 
the cable, one thousand, or in the case we have supposed, 
make it 1000 miles, its diameter remaining the same. Then 
although the same current will flow, yet we have a thousand 
times the expenditure of power at one end of the cable, and a 
