DYNAMICAL THEORY OF HEAT. 153 
connected with them by conducting arcs of the same metal, and insulated from ihe 
remainder of the circuit. 
The electro-motive force so defined may be determined either by determining, 
by some electro-statical method, the difference of potentials in the two conductors 
of standard metal mentioned in the definition; or by measuring the strength of 
the current produced in a conducting are of the standard metal of infinitely 
greater resistance than the given conducting arc, applied to connect its extre- 
mities, when insulated from the remainder of its own circuit. 
145. With reference to the distribution of electro-motive force through a solid, 
the following definitions are laid down :— 
Der. 1. The intrinsic electro-motive force of a linear conductor at any point 
is the actual intrinsic electro-motive force in an infinitely small arc through this 
point, divided by its length. 
Der. 2. The efficient electro-motive force at any point of a linear conducting 
circuit is the sum of the actual intrinsic electro-motive force in an infinitely small 
are, and the electro-motive force produced by the remainder of the circuit on its 
extremities, divided by its length. 
Der. 3. The intrinsic electro-motive force at any point in a solid, in any di- 
rection, is the electro-motive force that would be experienced by an infinitely 
thin conducting arc of standard metal, applied with its extremities to two points 
in a line with this direction, in an infinitely small portion insulated all round 
from the rest of the solid, divided by the distance between these points. 
Der. 4. The electro-motive force efficient at any point of a solid, in any direc- 
tion, is the difference of the electro-motive forces that would be experienced by an 
infinitely thin conducting arc of standard metal, with its extremities applied to 
two points infinitely near one another in this direction, divided by the distance 
between the points, in the two cases separately of the solid being left unchanged, 
and of an infinitely small portion of it containing these points being insulated 
from the remainder. 
146. Principle of the superposition of thermo-electric action. It may be assumed 
as an axiom, that each of any number of co-existing systems of electric currents 
produces the same reversible thermal effect in any locality as if it existed alone. 
§§ 147-155. On Thermo-electric Currents in Linear Conductors of Crystalline 
Substance. 
147. The general characteristic of crystalline matter is that physical agencies, 
having particular directions in the space through which they act, and depending 
on particular qualities of the substance occupying that space, take place with 
different intensities in different directions, if the substance be crystalline. Sub- 
stances not naturally crystalline may have the crystalline characteristic induced 
in them by the action of some directional agency, such as mechanical strain or 
