: 
ON STANDARDS OF ELECTRICAL RESISTANCE. 145 
lent to work done, will be the same, and equal to EQ. Hence the electro- 
motive force between two points is unity, if a unit of mechanical work is spent 
(or gained) in the transfer of a unit of electricity from one point to the other, 
This general definition is due to Professor W. Thomson. 
The direct measurement of electromotive force would be given by the mea- 
sure, in any given case, of the work done by the transfer of a given quantity 
of electricity. The ratio between the numbers measuring the work done, and 
the quantity transferred, would measure the electromotive force. This mea- 
surement has been made by Dr. Joule and Professor Thomson, by determining 
the heat developed in a wire by a given current measured as in (§ 18)*. 
28. Indirect Measurements of Electromotive Force.—The direct method of 
measurement is in most cases inconvenient, and in many impossible ; but the 
indirect methods are numerous and easily applied. The relation between the 
eurrent, C, the resistance, R, and the electromotive force, KE, expressed by 
Ohm’s law (equation 6), will determine the electromotive force of a battery 
whenever RK and C are known. A second indirect method depends on the 
measurement of the statical force with which two bodies attract one another 
when the given electromotive force is maintained between them. This me- 
thod is fully treated in Part IV. (43). The phenomenon on which it is based 
admits of an easy comparison between various electromotive forces by electro- 
meters. This method is applicable even to those cases in which the electro- 
motive force to be measured is incapable of maintaining a current. The laws 
of chemical electrolysis and electromagnetic induction afford two other indirect 
methods of estimating electromotive force in special cases (54 and 31). 
29. Measurement of Electric Resistance—We have already stated that the 
resistance of a conductor is that property in virtue of which it limits the 
amount of work performed by a given electromotive force in a given time, 
and we have shown that it may be measured by the ratio ro the elec- 
tromotive force between two ends of a conductor to the current maintained 
by it. The unit resistance is, therefore, that in which the unit electromotive 
force produces the unit current, and therefore performs the unit of work in 
the unit of time. If in any circuit we can measure the current and electro- 
motive force, or even the ratio of these magnitudes, we should, cpso facto, 
have measured the resistance of the circuit. The methods by which this 
ratio has been measured, founded on the laws of electromagnetic induction, 
are fully described in Appendix D. Other methods may be founded on the 
measurement of currents and electromotive forces, described in 18, 19, 20, 27, 
and 28. Lastly, a method founded on the gradual loss of charge through very 
great resistances will be found in Part IV. (45). The equation (25) there 
given for electrostatic measure is applicable to electromagnetic measure when 
the capacity and difference of potentials are expressed in electromagnetic units. 
30. Electric Resistance in Electromagnetic Units is measured by an Absolute 
Velocity.—The dimensions of R are found, by comparing those of E and C, 
to be 2 or those of a simple velocity. This velocity, as was pointed out by 
Weber, is an absolute velocity in nature, quite independent of the magnitude 
of the fundamental units in which it is expressed. The following illustration, 
due to Professor Thomson, will show how a velocity may express a resist- 
ance, and also how that expression may be independent of the magnitude of 
the units of time and space. 
® Phil. Mag. vol. ii, 4th Ser, 1851, p. 551. 
1863, L 
