Relations between Electrical Measurements. 453 



lines of magnetic force due to all the currents, magnets, &c, in 

 the field, supposing the strength of each current or magnet to 

 be reduced from its actual value to unity. Call the number 

 of lines of force due to a circuit or magnet, which pass through 

 another circuit, the potential coefficient between the one and the 

 other. This number is to be reckoned positive when the lines 

 of force pass through the circuit in the same direction as those 

 due to a current in that circuit, and negative when they pass in 

 the opposite direction. 



If we now ascertain the change of the potential coefficient due 

 to any displacement, this increment multiplied by the product 

 of the strengths of the currents or magnets will be the amount 

 of work done by the mutual action of these two bodies during 

 the displacement. The determination of the actual value of the 

 potential coefficient of two things, in various cases, is an import- 

 ant part of mathematics as applied to electricity. (See the 

 mathematical discussion of the experiment, Appendix D. Brit. 

 Assoc. Reports, 1863, p. 168.) 



25. Electromagnetic Measurement of Electric Quantity. — A 

 conducting body insulated at all points from the neighbouring 

 conductors may in various ways be electrified, or made to hold a 

 quantity of electricity. This quantity (§ 14) is perfectly definite 

 in any given circumstances ; it cannot be augmented or dimi- 

 nished so long as the conductor is insulated, and is called the 

 charge of the conductor. Its magnitude depends on the dimen- 

 sions and shape and position of the insulated and the neighbour- 

 ing conductors, on the insulating material, and finally on the 

 electromotive force between the insulated and the neighbouring 

 conductors, at the moment when the charge was produced. The 

 well-known Leyden jar is an arrangement by which a consider- 

 able charge can be obtained on a small conductor with moderate 

 electromotive force between the inner and outer coatings, which 

 constitute respectively the " insulated" and "neighbouring" 

 conductors referred to in general. We need not enter into the 

 general laws determining the charge, since our object is only to 

 show how it may be measured when already existing ; but it 

 may be well to state that the quantity on the charged insulated 

 conductor necessarily implies an equal and opposite quantity on 

 the surrounding or neighbouring conductors. 



We have already defined the magnitude of a current of elec- 

 tricity as simply proportional to the quantity of electricity con- 

 veyed in a given time, and we have shown a method of measu- 

 ring consonant with this definition. The unit quantity will 

 therefore be that conveyed by the unit current as above defined 

 in the unit of time. Thus, if a unit current is allowed to flow 

 for a unit of time in any wire connecting the two coatings of a 



