Action of a Galvanic Coil on an external small Magnet. 191 



tive force varies nearly as the inverse cube of the distance from 

 the centre of the magnet, which law results from the joint action 

 of an attractive and a repulsive force expressed thus, 



-Vr 2 (r + 8r)*J' 



(r -f o>)' 



9 £ 



the differential force being nearly — 3—, which for a given value 



of 6> varies inversely as the cube of the distance. 



'23. The whole preceding argument points to the conclusion 

 that the assumed attractive and repulsive magnetic forces have 

 only a hypothetical existence, and that what really exists is hy- 

 drodynamical pressure. 



24. Proceeding now to discuss in a similar manner the pro- 

 blem of the action of a galvanic coil on a small magnet, I propose, 

 first, to solve it according to the principles of the hydrodyna- 

 mical theory of galvanism, and then to inquire how far the same 

 theory will account for the facts and hypotheses on which Am- 

 pere's empirical solution of the problem rests. The hydrodyna- 

 mical considerations will differ in some essential respects from 

 those applicable to magnetism. 



25. First it will be necessary to ascertain what motions of the 

 sether correspond to the transmission of a galvanic current along 

 a fine wire. For this purpose certain hydrodynamical theorems 

 will be employed, the principles and the proofs of which I have 

 discussed in various antecedent researches. I consider it to be 

 an axiom that^ whatever be the motion of a fluid mass, the lines 

 of direction of the motion may at all times be cut by a surface 

 made up of portions, either finite or indefinitely small, of differ- 

 ent surfaces of continuous curvature, so joined together that the 

 tangent planes at the points of junction of two contiguous por- 

 tions do not make a finite angle with each other. The reason 

 for the latter condition is a dynamical one, whereby infinite forces 

 are excluded. The other is an abstract geometrical condition of 

 continuity, to which the directions of the motion of a fluid 

 assumed to be continuous are necessarily subject, and in virtue of 

 which the motion admits of being calculated. If any one thinks 

 that there are motions of a fluid which this condition does not 

 embrace, let him calculate them if he can ; I do not concern 

 myself with them. 



26. It follows from the foregoing theorem that the general 

 differential equation of the above-defined surfaces of displacement 

 is (according to the usual notation) udac + vdy-{-wdz = } and 

 that consequently the left-hand side of this equality is either in- 

 tegrable of itself or by a factor. Reasoning on the principle 

 that this must be the case always and lit all points of the fluid, 



