90 M. E. Edlund on the Nature of Eledricmj . 



Let two molecules of aether^ m and m', be at a distance r from 



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one another. If both are at rest, their reciprocal repulsion is — g-. 



On the contrary, the case of m approaching or receding with a 



constant velocity gives rise to other ratios. If m be at first at as 



(fig. 1), at the distance r-|- Ar from m', and then during the time 



A/ approach m! by the distance Ar, the reciprocal repulsion in- 



„ mm! ^ mvpi , ^ 



creases from ^^rp^^ ^o -^; but pig. i. 



if the velocity of approach be suf- ^ \ '^ 



ficient, the repulsion has not time ^ ^ v^ » ' 



to acquire that augmentation, and 

 therefore at y is inferior to that 



which corresponds to the distance r. This diminution, all cir- 

 cumstances being equal, is a function of the constant velocity h. 



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The repulsion at y may therefore be expressed by -^-f[h), where 



the value of /(A) is less than 1. If, on the contrary, m recedes 

 from m' with the same constant velocity h, passing in the time 

 A^ through the distance y — os^ (fig. 5i) =Ar, the repulsion at 

 the moment when m arrives at y 

 must be greater than that which ^^' ^, 



corresponds to the distance r, pro- ! — /, 



vided the repulsion cannot be di- , 



minished with the velocity of the ^ 



increase of the distance. Therefore the repulsion may in this 



case be expressed by — ^-^(A), where F(A) is greater than 1. If 



in the first case, in which the distance between the molecules is 

 diminished, the velocity be considered negative, it must be po- 

 sitive in the second. Concerning the functions f[h) and F(A) 

 we know nothing beforehand, except that the former must be 

 less, and the latter greater than 1, and that both approach I as 

 h diminishes. But as the causes which retard or accelerate the 

 development of the repulsion at the time of the approach, must 

 have the same eff"ect upon its disappearance when the molecules 

 recede from each other, it is probable that the two functions have 

 the same form, or that the development of the repulsion follows 

 the same law as its disappearance — and that both can be ex- 

 pressed by the same function of the velocity, if we take care to 

 put the latter negative in one case and positive in the other. 

 We have thus, for the repulsion between two aether molecules, 



the expression — 2-F( — A) if the molecules approach each other 

 with a constant velocity A, and the expression — g- F( + A) if the 



