•152 Messrs. Watson and Burbury on the Law 



2. On these canons Ave make the following observations. 



With regard to L, it will be observed that it consists, first, 

 of a statement of fact — namely, that a reversal of one current 

 reverses the effect ; secondly, of an inference supposed to fol- 

 low from the observed fact — namely, that an element of one 

 current has no effect on an element of another which lies in 

 the plane bisecting the former at right angles. Let the first 

 element be at the origin in direction x, and the second any- 

 where in the plane of y, z. If, when the first element is in 

 the positive direction, the second is attracted, it follows, by 

 the general principle enunciated, that were the first element 

 in the negative direction, the second would be repelled. Now 

 we cannot imagine any reason why in the former case the 

 force should be an attraction and in the latter a repulsion, any 

 more than the converse. Hence it is concluded, no doubt 

 rightly, that there can be no force tending to move the second 

 element in the plane of ?/, z. 



But it should here be observed that the reasoning would not 

 apply to a couple tending to turn the second element round 

 an axis without changing the position of its centre. The hy- 

 pothesis, for instance, that the first element tends to turn the 

 second into a position parallel to the first, agrees with the 

 general law enunciated in I., and is not open to a priori objec- 

 tion. 



II. is equivalent to the principle, which is universally 

 assumed in all treatises on the subject, that any elementary 

 current may be replaced by its components, the middle points 

 of the components being identical with that of the element. 



IV. leads to the conclusion, as shown in Maxwell's c Elec- 

 tricity,' vol. ii., that the forces of attraction between two ele- 

 ments are inversely proportional to the square of the distance 

 between them. 



V. It follows from Oersted's experiments, that the mutual 

 action of two closed electric circuits is the same as that of two 

 magnetic shells bounded by the circuits. It must therefore 

 have a potential ; and such potential must be of the form 



fdi f \ 1 — — dsds'*, 



in which i, V are the strengths of the currents, and e is the 

 angle, and r the distance between an element ds of the one, 



* We take the positive sign in the same way as it is usual to say the 

 potential of unit mass of matter at distance r is - 



