M. E. Edlund on the Nature of Electricity . 91 



distance between thein increases, the function F being such that 

 it becomes =1 for A = 0, is < 1 for a negative value, and >1 

 for a positive value of h. These expressions may conveniently 

 be written in the form 



the function <f)[h) being such that it becomes =0 when A = 0, 



has a negative value when h is negative, and a positive value 



when h is positive. 



What has just been said applies exclusively to the case in 



which the velocity is constant. We will now suppose that m 



approaches m\ and makes the same way Ar in the same time A^ 



as before, but with diminishing velocity, so that the velocity is 



greater when m is nearer x (fig. 1) than when it has arrived aty. 



Although m makes the same way during the same space of time. 



At* 

 and consequently -r— has the same value in this as in the former 



case, the repulsion at the point y can no longer be the same. 



The molecule m has moved more rapidly in the vicinity of x 



than when nearer to y, and has therefore remained longer where 



the repelling force is stronger than where it is weaker. The 



result must evidently be that the repulsion at y will be stronger 



than if the velocity had been constant. The repulsion, then, 



Ar AV 



depends not only on -r— , but also on -r-^. If we now pass to 



the limit, we thus find that the repulsion does not depend 

 merely on the velocity, but again on the variation of the velocity, 



-7-, the latter dependence augmenting, in the present case, the 



quantity of the repulsion-force. 



If the molecule m increase its distance from m' while its velo- 

 city augments, but in such a way that the determined path Ar is 

 traversed in the fixed time A^, the repulsion in this case, as in the 

 preceding, will be greater than if the velocity were constant. 

 Here also the molecule will remain longer at the points where 

 the repulsion-force is greater, than at those where it is less. It 

 is therefore necessary to add to the expression representing the 

 amount of the repulsion under constant velocity a term depen- 

 dent on the variation of the velocity. 



The electric molecule moves in its course with a constant ve- 

 locity ; as was said above, variations in the intensity of the cur- 

 rent exert no influence in this respect. If, therefore, a molecule 

 approaches or recedes from another which is on the straight line 

 in which the movement takes place, there can be no variation in 



