a' 





m' 



b' 





r/ 



k 







/e 







a 



m 







b 



92 M. E. Edlund on the Nature of Electricity , 



the relative velocity. The circumstances, on the contrary, are 

 different if one of the molecules is on one side of the direction 

 of the other. Suppose two molecules, m and w!, the first of 

 which is in motion on the line a b (fig. 3), and the other, m'j at 

 rest. The distance r between the mo- 

 lecules is then equal to ^ oc'^+p^ ', and ^ig* ^* 

 their relative velocity (that is, the ve- 

 locity on the line of junction) 



dr __x dx 

 dt r dt 



Therefore the relative velocity dimi- 

 nishes as m approaches the point o, 



where it is =0. When, on the contrary, the distance between 

 the molecules increases, their relative velocity increases simulta- 

 neously. The variations of the relative velocity are obtained by 

 differentiating the last expression, which gives 



dh^ __ dx'^ x^ dx^ 

 df~'Vd?'^^'d?' 



X 



or if we introduce the cosine of the angle in the place of -, and 



dx 

 h in place of -^, we obtain 



^V h^ .- , ., 



__=_(l_cos^^). 



The variation of the relative velocity, therefore, is proportional 

 to the square of the velocity of the molecule in the circuit ; it 

 presents its maximum at the point o (fig. 3), and diminishes as 

 the molecule moves away from it. By corresponding substitu- 

 tions we obtain for the expression of the relative velocity 



J=coseA. 



If the molecule m moves with a constant velocity on the line 

 ah (fig. 3), in which case the relative velocity varies in relation 

 to the fixed molecule rn!, the repulsion between the two molecules 

 for a determined distance r is, according to what precedes, 

 greater than if the relative velocity were constant. This is so, 

 whether m recedes from, or whether it approaches the point o. 

 To the expression denoting the repulsion between the two mole- 

 cules when their relative velocity is constant we must therefore 

 add a term constituting a function of the variation of the velocity. 



We will designate this function by ^/r | — [1 — cos^ 6'] ]. We 



know beforehand, with respect to this function -v/r, that it must 



