520 WEBER ON THE MEASUREMENT 



we shall denote by [R], we may also say that the potential of 

 the mass E, in regard to the situation of the mass E', is 



= |(i-[R?); 



for the partial differential coefficients of this expression, with re- 

 spect to the three coordinates x, y, z, yield the components of 

 the decomposed accelerating force in the directions of the three 

 coordinate axes. 



Lastly,if by the reduced relative velocity of the masses E andE', 

 we understand that relative velocity which these magnitudes, — 

 the distance of which apart at the moment supposed was R, the 



relative velocity -773 and the acceleration , .^ , if the latter were 



constant, — would possess at that instant in which both, in accord- 

 ance with this supposition, met at one point, and if V denoted 

 this reduced relative velocity, the above expression. 



EE'/ rfR2 ^^.ddR\ 

 RR V ~ dt^' + ^^^'dWJ' 



becomes converted into the following, 

 EE' 



which may be verbally expressed as follows : — The diminution 

 arising from motion of the force with which two electric masses 

 would act upon each other when they are at rest, is in proportion 

 to the square of their reduced relative velocity. 



Thus the expressions given for the determination of the force 

 which two electric masses exert upon one another are now con- 

 firmed — 



1st. As regards the entire domain of electro-statics ; 



2nd. As regards that domain of electro-dynamics the object of 

 which is the consideration of the forces of the elements of the 

 current when invariable and undisturbed ; hence 



3rdly. Its confirmation, as regards all that domain of electro-dy- 

 namics which is not limited to the invariable and undisturbed state 

 of the elements of the current, is all that remains to be desired. 



Theory of Voltaic Induction. 



It has already been mentioned that the principle of electro- 

 dynamics laid down by Ampere refers mei'ely to the special case. 



