M. E. Edliind on the Nature of Electricity. 97 



positive. This is only possible by one means alone, viz. that the 

 function (f> contains^ besides the term into which the square of 

 the relative velocity enters, a term into which an odd power of 

 that velocity enters, and that the value of the latter term is 

 greater than that of the former. We will now suppose the odd 

 power to be the first — which is the only correct supposition, as 

 will be seen when we consider two parallel currents in opposite 

 directions. This gives us 



0( — A.cos 6)= —ah . cos^ — iM^cos^^,'^ ,,^. 



(!>{-{- h. cos 0)=+ ah. co-^e-ikh'^cos^e J 



in which a is a constant. We have therefore obtained the same 

 result as if we had imagined the function (f) developed in a series 

 according to ascending powers of the relative velocity, and re- 

 tained only the first two terms of that series. 



We now pass to the case in which the molecules m and m! 

 move in opposite directions in parallel circuits. We suppose that 

 the molecule m' moves towards the point a', while m advances 

 towards the point b (fig. 3). It is evident that in this case the 

 relative velocity of m and m' must be twice as great as if one of 

 the molecules were to rest while the other moved with the same 

 velocity h as before. 2h, then, must be written in the place of 

 h; and the same applies equally to the variation of the velocity. 

 It makes no difference whether the molecules are approaching or 

 receding from one another. Employing formulae (1), (7), and 

 (10), we obtain in this way, for the direct action between two 

 molecules in motion (case 1) : — 



- ^ [1 -2ah cos 61 - i . Uh^ cos^ ^ + J . 4M^(1 - cos^ 6) ] . 



For the action to which no. 2 refers (viz. the repulsion, taken 

 with the contrary sign, between the molecules m' and m, the 

 former considered in motion, and the other in the state of repose) 

 we obtain 



+ ^li-~ahcosO-lkh^cos^0 + iW{l-'Cos^e)]. 

 We get, for the action foreseen in no. 3, 

 _^[l-«/iCosl9-lM2cos^^ + iM^(l-cos^-^)l; 



and for no. 4, 



)nm' 



r^ 

 Phil Mag, S. 4. Vol. 44. No. 291. Aug, 1872. H 



