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



tained by deducting from S the repulsion whicli takes place 

 between m and m! — or, what comes to the same thing, by adding 

 to S the latter repulsion taken with the opposite sign. The 

 question now is, w^hat is the motion impressed on the circuit- 

 element in which m^ moves by the molecule m being put in 

 motion ? 



In the same way as for electrostatic phenomena, we have to 

 take into consideration the four following circumstances : — 

 1, the direct reciprocal action of the two molecules ; 2, the dif- 

 ference between the action exerted upon m! by the whole of the 

 surrounding sether when m is supposed at rest and the action 

 exerted upon the same molecule m' by all the aether with the ex- 

 ception of m ; 3, the action of m upon the space occupied by m' ; 

 and, 4, the action upon the same space of all the surrounding 

 sether with the exception of m. The difference mentioned at 

 no. 2 is evidently equal to the repulsion, taken with the oppo- 

 site sign, between m, supposed immoveable, and the molecule ?n'; 

 and the action indicated at no. 4 is identical with the repulsion, 

 taken with the opposite sign, between the molecule m regarded 

 as immoveable and the space in question. If we add the actions 

 upon m!j foreseen in the first two cases, and if we subtract the 

 corresponding sum of the last two, we obtain, in accordance with 

 Archimedes^s principle, the action upon rn! sought, or upon the 

 circuit-element in which m' moves. 



In order to understand more clearly the accuracy of the above 

 process, let us state the problem thus : — To find the motion pro- 

 duced in the molecule m!, or in the circuit-element in which m' 

 is found, by the molecule m being put in motion. Now the 

 motion sought depends evidently on the modification induced in 

 the repulsion between m' and m by the circumstance that the 

 latter has been put in motion. The expression of the motion of 

 the circuit-element of m! is therefore obtained by subtracting 

 from the repulsion between the molecules m' and m (the latter 

 being regarded as in motion) the repulsion between the same 

 molecules when m is considered to be at rest. The remainder 

 thus obtained is in reality the sum of the first two cases above 

 stated. The effects of repulsion to w^hich the last two cases 

 relate are obtained in an analogous manner. It is now easy to 

 find the algebraic expression of the reciprocal action of two ele- 

 ments of a current. If the two molecules m and m' move in 

 parallel lines in the same direction, as, for example, towards b 

 and b', their reciprocal distance will undergo no modification, 

 provided they move with the same velocity. Their direct action 

 upon each other wall thus be the same as if they were both at 

 rest. We have, therefore, for the action belonging to case 1 : — 



