in connexion with the lheory of Electro-statics. 465 



condition to allow of the possibility of electric equilibrium ; 

 the condition is satisfied when the three conductors belong to 

 the so-called tension series. 



We have next to examine what will occur when this con- 

 dition is not satisfied. At a particular moment the distribu- 

 tion of the free electricity in the system will be a certain one ; 

 I leave it undetermined whether this free electricity exists only 

 at the surface of the conductor, or whether it has penetrated 

 into its interior. Let its potential in regard to any point of 

 one of the conductors be u\ this u is not constant, but a func- 

 tion of the coordinates of the point to which it relates; hence 

 the forces which are exerted by the free electricity upon 

 a particle of electricity existing at any spot within the con- 

 ductor will not retain a state of equilibrium, but produce a 

 definite resultant. Let us imagine the existence of an element 

 of space, v, within the conductor, and let us denote the above 

 resultant for any point in v by R. If t; contains no free elec- 

 tricity, the neutral electric fluid contained in it becomes de- 

 composed; the positive electricity will be moved in the direc- 

 tion of R, the negative in the opposite direction ; the quanti- 

 ties of positive and negative electricity excited in the element 

 v, and also their velocities, must therefore be the same. I shall 

 assume that the quantity of either fluid, which is moved in a 

 unit of time through a section off, perpendicular to the direc- 

 tion of R, and the magnitude of which may be denoted by 

 dw, is = dwkB., in which k denotes the conducting power of 

 the substance. To determine what takes place when v contains 

 free electricity, I shall assume that no motion of the electric 

 fluids can occur in a conductor, except when equal quantities 

 of the two electricities pass in opposite directions through each 

 surface-element of it simultaneously. Hence it follows, even 

 when v contains free electricity, that as much positive electricity 

 passes in a unit of time through dw in the direction of R, as 

 negative electricity in the opposite direction. As regards the 

 quantity of the electricities flowing through dw, I assume that 

 it is again = dwkR. 



If to these assumptions, most of which have been already 

 put forth by Weber in his elect rodynamic measurements, we 

 further assume that the difference in the values of the poten- 

 tial of the total amount of free electricity in the case of two 

 points lying in immediate proximity to each other on the 

 proximal and distal sides of the surface of contact of two con- 

 ductors remains the same, whether a current flows through 

 the conductor, or the electricity is at rest in them ; we arrive, 

 on the supposition that the electric condition of the system 

 has become stationary, at the same equations for the po- 



Phil. Mag. S. 3. Vol 37. No. 252. Dec. 1850. 2 H 



