460 ."^^ Messrs. Watson and Burbury on the Law 



tho current-element ihz and one of the solenoid currents, whose 

 strength is i r , would be 



.,« Tcose , , 

 i'oz 1 ds\ 



J r 



the integration being taken round the elementary circuit. 

 By Stokes's theorem this becomes 



P 7 



where A is the area of the solenoid-section, /, m } n the direc- 

 tion-cosines of its normal, and r the distance of its centre from 

 8z. Therefore the potential energy between the whole infinite 

 current and this section of the solenoid is V, where 



V = AW 1 / 2? "2^2x 3 dz 



=An'^=^- 

 ar + tf 



And the potential of the whole solenoid is 



dx j cly 



K ,.,C ds ds _ 



An \ o— : — o — . dz, 



or 



Aw' { tan" ^- tan- 1 -}. 

 C on a) 



16. Again, it is generally stated that the action of a par- 

 ticle of imaginary magnetic matter upon a current-element 

 varies as the sine of the angle between the distance of the 

 particle from the element and the element directly, and as the 

 square of that distance inversely, and is perpendicular to the 

 plane passing through the particle and the element. For the 

 reasons mentioned in the case of the solenoid, it is obvious 

 that no such law of action as this can be experimentally proved 

 to exist between a current-element and a magnetic pole ; but 

 the equivalent law of action between an infinite current and a 

 particle of imaginary magnetic matter may be deduced from 

 the law of current-action now proposed, combined with the 

 experimental fact that the potential of a current-circuit and a 

 magnetic shell is equivalent to that between the circuit and 

 the current bounding the shell of suitable intensity. For if i 

 be the intensity of a current in the axis of z, and i' that in the 

 bounding circuit of a plane magnetic shell of very small area 

 A it will follow, as in the case last considered, that the poten- 



