Ponderomotive and Electromotive Forces. 257 



second variable, which defines the situation of the particle in 

 the conductor — namely, the distance s r (measured on the curve 

 of the conductor) of the particle from any initial point. Ac- 

 cordingly each coordinate of the particle is to be regarded as 

 a function of t, while, again, s' itself can be considered a func- 

 tion of t> If, then, afy y r , z? are the coordinates of the elec- 

 tricity-particle at the time t, the complete differential coeffi- 

 cient of each of those coordinates with respect to t divides into 

 two terms containing the partial differential coefficients with 

 respect to t and s', so that we obtain for each coordinate an 

 equation of the following form — 



daf Jbaf 5 a/ ds f 

 dt dt d/ dt 



ds r 

 For the differential coefficient -=-, which represents the 



velocity of the currrent, we will introduce a simple symbol ; 

 we will denote by c' the velocity of the flow of the positive 

 electricity, and by — c r i that of the negative electricity, while 

 we then remain at liberty, according to the special assumption 

 we make respecting the behaviour of the two electricities, 

 either to consider the quantities cf and c\ equal the one to the 

 other, or to put one of them =0, or to ascribe to them any 

 values different from one another. With the aid of this nota- 

 tion we get, instead of the preceding equation, the two follow- 

 ing, which refer to the positive and negative electricities : — 



dt - 3* +c V' 



oW _ da/_ , 3^ ' 

 dt ~ ^t Cl d/' 



In a contingent second differentiation with respect to t, we 

 should have to take into account that the quantities c' and c\ 

 are again to be treated as functions of t and s f , because at a 

 fixed point of the conductor the current-velocity can vary with 

 the time if the intensity of the current is variable, and also 

 because at a fixed time the current-velocity can be different at 

 different points of the conductor if the conductor has not 

 everywhere an equal cross section and like quality. 



The distance r between the particle of current-electricity in 

 the conductor / and the unit of electricity in the point x, y y z 

 is likewise to be regarded as a function of t and s f ; and the 

 complete differential coefficients of r with respect to t are 

 therefore to be formed in the following manner for the positive 



