NUMERICAL VADUE OF POTENTIAL. 13 



force is perpendicular at all' points ; hence, the lines of force 

 proceed perpendicularly from the conductors, or terminate there 

 perpendicularly. 



26. NUMERICAL VALUE OF POTENTIAL. In all these phenomena, 

 equipotential surfaces are only apparent as differences, and not as 

 the absolute values of the corresponding potentials. We may 

 accordingly add to these potentials any given constant. 



In the expression 



which represents the work corresponding to the displacement of a 

 unit of electricity from an equipotential surface V 1} to an equi- 

 potential surface V 2 , let us suppose that the latter is the earth, and 

 that we agree to take its potential as equal to zero, we shall have 



The numerical value of the potential at any given point, is the 

 number of units of work which corresponds to the displacement of a 



Fig. 2. 



unit of positive electricity from this point, to the earth, by any path 

 whatever. The sign of the potential is that of the work of the 

 electrical forces in this displacement. 



In other words, the potential at a point, is the work which must 

 be done to bring unit mass of electricity from the earth, or from a 

 body in connection with the earth, to this point. 



27. POTENTIAL IN THE CASE OF THE LAW OF THE SQUARE OF 

 THE DISTANCES. We have hitherto left undetermined the law, 

 according to which the action of electrical masses varies with the 

 distance. We shall assume in future that this law is the inverse of 

 the square of the distance, conformably to the experiments of Coulomb. 

 In this case, the potential is expressed simply as a function of the 

 masses and of the distances. 



Let us suppose, in the first place, that the electrical system is 

 reduced to a mass + m placed at a point O. If a mass equal to 

 unity placed at a point M (Fig. 2) at a distance r from the former, is 



