ON STANDARDS OF ELECTRICAL RESISTANCE. 115 
system, starting from an effect produced by electricity when at rest. The 
units based on these four equations are precisely those called by Weber elec- 
trostatical units, although it may be observed that he chose those units 
without reference to what is here called the third fundamental equation, or, 
in other words, without reference to the idea of work, introduced into the 
system by Thomson and Helmholtz*, 
The four equations are sufficient to determine the four units, and into this 
system no new relation can be introduced. The first three equations may, 
however, be retained, and a distinct absolute system established by substi- 
tuting some other relation between electrical and mechanical magnitudes 
than is expressed in equation (4); and, indeed, the electrostatical system just 
defined is not that which will be found most generally useful. It is based on 
a statical phenomenon, whereas at present the chief applications of electricity 
are dynamic, depending on electricity in motion, or on voltaic currents with 
their accompanying electromagnetic effects. Now the force exerted on the 
pole of a magnet by a current in its neighbourhood is a purely mechanical 
phenomenon. This force (f) is proportional to the magnetic strength (m) of 
the pole of the magnet, and to the strength of the current C; and if the con- 
ductor be at all points equidistant from the pole, or, in other words, be bent 
in a circle of the radius k round the pole, the force is proportional to the 
length of the conductor (L): it is also inversely proportional to the square of 
the distance (/) of the pole from the conductor, and is affected by no other 
circumstances than those named. Hence we have 
faces salle 3°18 lesGrar futrbalane Cy 
From this equation it follows that the unit length of the unit current must pro- 
duce the unit force on a unit pole at the unit distance. Ifthe equations (1), (2), 
(3), and (5) are adopted as fundamental, they give a distinct absolute system 
of units, called by Weber the electromagnetic units. Equations (4) and (5) are 
incompatible one with another, if equation (2) be considered fundamental ; but 
the electromagnetic units have a constant and natural relation to the elec- 
trostatic units. It will be seen that in the fundamental equation (5) of the 
electromagnetic system, besides the measurements of time, space, and mass, 
alone entering into the other equations, a fourth measurement (m) of a mag- 
netic pole is required; but this measurement is in itself made in terms of the 
mechanical units, forthe unit pole is simply that which repels another equal 
pole at unit distance with unit force. Thus in the electromagnetic as in the 
electrostatic system all measurements are ultimately referred to the funda- 
mental units of time, space, and mass. The electromagnetic units are found 
much the more convenient when dealing, as we have now chiefly occasion te 
do, with electromagnetic phenomena, 
The relations of the electromagnetic units one to another and to the 
mechanical units may be summed up as follows :—The unit current conveys 
a unit quantity of electricity through the circuit in a unit of time. The unit 
current in a conductor of unit resistance produces an effect equivalent to the 
unit of work in the unit of time. The unit current will be produced in a 
circuit of unit resistance by the unit electromotive force. The unit current 
flowing through a conductor of unit length will exert the unit force on a unit 
pole at aunit distance. (In the electrostatic system all the above propositions 
hold good except the last, for which the following must be substituted :—the 
unit quantity of electricity will repel a similar quantity at the unit distance 
with a unit force.) 
. * Vide Appendix C. § 31. 3 
I 
