Relations between Electrical Measurements. 4*4*7 



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 cur- 

 rents 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 con- 

 stant condition. The above definitions, in mathematical lan- 

 guage, give W=EC/, or 



*=s < 5 > 



where E is the electromotive force, and W the work done. Thus 

 the electromotive 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 electricity 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 ; electro- 

 motive 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 electromo- 

 tive 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 Prof. W. Thomson 

 " On the application of the principle of Mechanical Effect to the 

 Measurement of Electromotive Forces," published in the Philo- 

 sophical Magazine for December 185L 



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 



