380 Prof. Thomson on the Dynamical Theory of Heat. 



some elementary properties, and to define various terms, adapted 

 for specifications of systems of electric currents and electromotive 

 forces distributed in any manner whatever throughout a solid. 



142. It is to be remarked, in the first place, that any portion 

 of a solid traversed by current electricity may be divided, by 

 tubular surfaces coinciding- with lines of electric motion, into an 

 infinite number of channels or conducting arcs, each containing 

 an independent linear current. The strength of a linear current 

 being, as before, defined to denote the quantity of electricity 

 flowing across any section in the unit of time, we may now define 

 the intensity of the current at any point of a conductor as the 

 strength of a linear current of infinitely small transverse dimen- 

 sions through this point, divided by the area of a normal section 

 of its channel. The elementary proposition of the composition 

 of motions, common to the cinematics of ordinary fluids and of 

 electricity, shows that the superposition of two systems of cur- 

 rents in a body gives a resultant system, of which the intensity 

 and direction at any point are represented by the diagonal of a 

 parallelogram desci-ibed upon lines representing the intensity and 

 direction of the component systems 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 I'espectively ; 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 given. 



143. The term electromotive force has been applied in what 

 precedes, consistently with the ordinary visage, to the whole force 

 urging electricity through a linear conducting arc. When a cur- 

 rent is sustained through a conducting arc by energy proceeding 

 from sources belonging entirely to the remainder of the circuit, 

 the electromotive force may be considered as applied from with- 

 out to its extremities ; and in all such cases it may be measui'cd 

 - — electrostatically, by determining 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 infi- 

 nitely gi'cater resistance (practically, for instance, a long fine 

 wire used as a galvanometer coil), and determining the strength 

 of the current which branches into it when it is so applied. These 

 tests may of course be regarded as giving either the amount of 

 the electromotive force with which the remainder of the circuit 

 acts on, or the whole of the electromotive force efficient in, the 



