512 WEBER ON THE MEASUREMENT 



of negative electricity, and — «' as its velocity. If now for i and 

 i', in the expression of the force which one element of a current 

 exerts upon another, their values i = aeu, and i' = ae' u' are 

 substituted, we then obtain for them 



'- .aauv!. (cos e — f cos cos 0'). 



If now we first consider in this expression a e . «' e' as the pro- 

 duct of the positive electric masses « e and a' e' in the two ele- 

 ments of the current, and ti vS as the product of their velocities 

 u and m', and if we denote by r the variable distance of these two 

 masses in motion ; and lastly, by s^ and s] the length of a portion 

 of each of the two conducting wires, to which the elements of 

 the cuiTent a and «' just considered belong, estimated from 

 a definite point of origin and proceeding in the direction of the 

 positive electricity, as far as the element of the current under 

 consideration, we then know that the cosines of the two angles 

 and 0', which the two conducting wires in the situation of the 

 elements of the current mentioned form with the connecting 

 right line r^, may be represented by the partial differential coef- 

 ficients of r, with respect to «, and */ ; thus 



^ dr. ^, dr. 



COS0 = -7—' cos 0' = ^, 



d s, ds," 



we then have 



_ ^ ddri dr, d r, 



' ~ ' dsi dsj ds, dsj 



as the cosine of the angle e which the directions of the two con- 

 ducting wires form with each other. Moreover, if the differen- 

 tial coefficients above mentioned be substituted for the cosines of 

 the three angles s, and 0', we have 



(\ dr, dVi ddr^ \ 



2d Si ds,' ~ ^' ds, dsj) 



r,r, 



as the expression of the force with which one element of the 

 current acts upon the other. 



Secondly, if in the above expression, —ue.a'e' be considered 

 as the product oi i\\& positive electric mass « e of one element of the 

 current « into the negative electric mass — «' e' of the other ele- 

 ment of the current a', and —uv! as the product of their velocities 

 u and — III; moreover, if the variable distance of these two moving 

 masses be denoted by r^i and by s, and *'„ the length of a portion 

 of each of the two conducting wires, to which the elements of 



