152 PROFESSOR W. THOMSON ON THE 
respectively. Hence we may define the components, along three lines at right 
angles to one another, of the intensity of electric current through any point of a 
body, as the products of the intensity of the current at that point into the cosines 
of the inclination of its direction to those three lines respectively; and we may 
regard the specification of a distribution of currents through a body as complete, 
when the components, parallel to three fixed rectangular axes of reference, of the 
intensity of the current at every point are specified. 
143. The term electro-motive force has been applied, in what precedes, con- 
sistently with the ordinary usage, to the whole force urging electricity through a 
linear conducting are. When a current is sustained through a conducting arc, by 
energy proceeding from sources belonging entirely to the remainder of the circuit, 
the electro-motive force may be considered as applied from without to its extre- 
mities; and in all such cases it may be measured—electro-statically, by determin- 
ing in any way the difference of potential between two conducting bodies, insulated 
from one another and put in metallic communication with the extremities of the 
conducting arc;—or electro-dynamically, by applying to these points the extremities 
of another linear conductor, of infinitely greater resistance (practically, for instance, 
a long fine wire used as a galvanometer coil), and determining the strength of the 
current which it conveys when so applied. These tests may, of course, be regarded 
as giving either the amount of the electro-motive force with which the remainder 
of the circuit acts on, or the whole of the electro-motive force efficient in, the 
passive conducting arc first considered. On the other hand, the electro-motive 
force acting in the portion from which the energy proceeds is not itself deter- 
mined by such tests, but is equal to the whole electro-motive force of the sources 
contained in it, diminished by the reaction of the force which is measured in the 
manner just explained. The same tests applied to any two points whatever of a 
complete conducting circuit, however the sources of energy are distributed through 
it, show simply the electro-motive force acting and reacting between the two 
parts into which the circuit might be separated by breaking it at these points. 
In some cases, for instance some of thermo-electric action which we shall have to 
consider, these tests would give a zero indication to whatever two points of a circuit 
through which a current is actually passing they are applied, and would there- 
fore show that there is no electric action and reaction between different parts of 
the circuit, but that each part contains intrinsically the electro-motive force re- 
quired to sustain the current through it at the existing rate. An actual test of 
the electro-motive force of sources contained in any part of a linear conductor is 
defined, with especial reference to the circumstances of thermo-electricity, in the 
following statement :— 
144. Der. The actual intrinsic electro-motive force of any part of a linear 
conducting circuit is the difference of potential which it produces in two insulated 
conductors of a standard metal at one temperature, when its extremities are 
