M. E. Edlmid on the Nature of hledricity. 177 



of the repulsion between two molecules of which only one is in 

 motion, we obtain : — 



-'^[l--ahco^e+^^h^(l^^cos^ey\. . (12) 



If m is receding from m', the angle is obtuse and the second 

 term becomes positive. 



Formula (1.2) expresses the direct repulsion between m and 7n', 

 the first being in motion and the second at rest. Now the 

 molecule m is also repelled by all the rest of the mass of aether 

 which surrounds it. At the first instant, before the molecules 

 have been able to change their positions of equilibrium, the re- 

 sultant of the repulsions exerted upon m! by the rest of the sur- 

 rounding sether will be equal to the repulsion between m (con- 

 sidered at rest) and m', but will have an opposite direction. 

 This comes out evidently from the fact that the resultant of the 

 repulsions exerted upon m' by all the surrounding mass of aether 

 was =0 when the molecule m was still at rest. We obtain, then, 

 the sum of the forces which, at the first instant thatm is put in 

 motion, act upon the molecule ??i', if we subtract from the repul- 

 sion expressed by formula (12) the repulsion between m and m' 

 when the former is at rest. It follows from this that at theirs/ 

 instant the molecule m' is repelled along the line of junction be- 

 tween m and w^ with a force which is expressed by 



+ !^Lacos6>-|a2A__|cos^6>)] (13) 



If this expression be negative, the molecule 7n' will tend to 

 remove itself from m in the direction of their line of junction; 

 if, on the contrary, it be positive, an approach will be effected 

 along the same line. If m recedes from m', the angle is 

 greater than a right angle, and consequently the first term is 

 negative ; if, on the contrary, an approach takes place, that term 

 is positive. 



If, then, fj, designate the quantity of aether in motion in the 

 unit of length of the conductor in which m moves, and ds be the 

 element of that conductor, m will be equal to fids. Now fih is 

 equal to the intensity i of the current. In an analogous manner 

 in' may be replaced by fjy'ds'. We thus obtain instead of for- 

 mula (13);— 



+ '^T«cos6>-^//l-|cos^6>)]^5^5'. . . (14) 



Formula (14) is the expression of the force with which an 

 element of the inducing current whose intensity is i tends at tlie 

 first instant to move, in the induced circuit, the quantity of 

 eether /jJds' along the line of junction between the two elements. 



Phil. Mag, S. 4. Vol. 44. No. 292. Sept. 1872. N 



