M. E. Edlund on the Nature of Electricity . 93 



be =0 when cos^ = l, since in this case the molecule m moves 



in the line of junction between m and m! , and consequently the 



relative velocity of the two molecules is constant. We know 



moreover that the value of the function y^ is always positive, 



w^hether the molecule m approaches or recedes from m'. It may, 



besides, be remarked that the value of the function may depend 



h^ 

 not only on the amount of the variation, — (1 — cos^^), but also 



on the distance r between the molecules, and consequently r may 

 enter under the sign of the function at the same time that the 

 same variable enters into the expression of the quantity of the 

 variation. 



The complete expression of the repulsion between two mole- 

 cules of aether m and w! , the latter of which is fixed, and the 

 former, m, moves with a constant velocity h in a line forming 

 the acute angle 6 with their line of junction, will therefore be : — 



When m approaches m', 



-^'[l + </>(-/i.cos^)+,/.(^[l-cos^e])]; (1) 

 When m recedes from m', 



-"^\\+<i>{+h.co.e) + f{^^[\-^o.^e]j\. (2) 



What has just been said we shall first apply to the case of two 

 molecules m and m' moving with equal and constant velocity in 

 the same direction in parallel lines (see fig. 3). 



According to the principles established by W. Weber*, we 

 shall admit that the effect of the reciprocal action between two 

 molecules is entirely communicated to the circuits in which they 

 move. The motions only of the circuits can be observed in the 

 reciprocal action of two currents; and the empirical formulae 

 founded on the observations relate to those motions. Now, in 

 order to find the variation produced in the distance between two 

 circuit- elements by the reciprocal action of the sether molecules, 

 one of the elements may be regarded as fixed, and the other 

 alone as free. We suppose, in the present case, that the element 

 in which m! moves is free, and that which belongs to m is im- 

 moveable. If in the whole mass of aether the molecule m' were 

 alone in motion, it could not be admitted, in the same manner 

 as if it were at rest, that the repulsions exerted upon it by the 

 whole of the surrounding aether annul each other; on the con- 

 trary, those repulsions might have a resultant S not =0. The 

 repulsion exerted on the moving molecule m' by all the sur- 

 rounding aether with the exception of m should therefore be ob- 



* Ahhandlungen uber elekirodynamische Maashestimmungen, p. 309. 



