188 REPORT—1863. 
electric couple; but the term is also used independently of the source of 
power, to express the fact that, however caused, a certain force tending to do 
work by setting electricity in motion does, under certain circumstances, 
exist between two points of a conductor or between two separate bodies. But 
equal quantities of electricity transferred in a given time do not necessarily or 
usually produce equal amounts of work ; and the electromotive force between 
two points, the proximate cause of the work, is defined as proportional to the 
amount of work done between those points when a given quantity of elec- 
tricity is transferred from one point to another. Thus if, with equal currents 
in two distinct conductors, the work done in the one is double that done in 
the second in the same time, the electromotive force in the first case is said 
to be double that in the second; but if the work done in two circuits is 
found strictly proportional to the two currents, the electromotive force acting 
on the two currents is said to be the same. Defined in this way, the electro- 
motive force of a voltaic battery is found to be constant so long as the 
materials of which it is formed remain in a similar or constant condition. 
The above definitions, in mathematical language, give W=EC¢, 
or Hee Riyia va aild st Tarastgaegegee om 
where E is the electromotive force, and W the work done. Thus the elec- 
tromotive force producing a current in a conductor is equal to the ratio 
between the work done in the unit of time and the current effecting the 
work. This conception of the relations of work, electromotive force, current, 
and quantity will be aided by the following analogy :—A quantity of elec- 
tricity may be compared to a quantity or given mass of water; currents of 
water in pipes in which equal quantities passed each spot in equal times 
would then correspond to equal currents of electricity ; electromotive force 
would correspond to the head of water producing the current. Thus if, with 
two pipes conveying equal currents, the head forcing the water through the 
first was double that forcing it through the second, the work done by the 
water in flowing through the first pipe would necessarily be twice that done 
by the water in the second pipe; but if twice as much water passed through 
the first pipe as passed through the second, the work done by water in the 
first pipe would again be doubled. This corresponds exactly with the 
increase of work done by the electrical current when the electromotive force 
is doubled, and when the quantity is doubled. 
Thus, to recapitulate, the quality of a battery or source of electricity, in 
virtue of which it tends to do work by the transfer of electricity from one 
point to another, is called its electromotive force, and this force is measured 
by measuring the work done during the transfer of a given quantity of 
electricity between those points. The relations between electromotive force 
and work were first fully explained in a paper by Professor W. Thomson on 
the application of the principle of mechanical effect to the measurement of 
electromotive forces published in the Philosophical Magazine for December 
1851. 
17. Meaning of the words “ Electric Resistance.” —It is found by experiment, 
that even when the electromotive force between two points remains constant, 
so that the work done by the transfer of a given quantity of electricity 
remains constant, nevertheless, by modifying the material and form of the 
conductor, this transfer may be made to take place in very different times ; 
or, in other words, currents of very different magnitudes are produced, and 
very different amounts of work are done, in the unit of time, The quality of 
