EQUIVALENCE OF A CURRENT AND A MAGNETIC SHELL. 449 



The factor G is the action at the point P of the circuit, when it 

 is traversed by a current of unit strength. We may represent this 

 action by a straight line PG proportional to G, and making angles 

 A, /x, v with the axes. 



467. EQUIVALENCE OF A CURRENT AND A MAGNETIC SHELL. 

 The action of a magnetic field on a current element being identical 

 with that of the same field on the corresponding element of the edge 

 of a shell bounded by the current, it follows that the action of the 

 current on a pole is identical with that of a shell of strength I, the 

 positive face of which is on the left of the current. 



The magnetic potential of a current at a point P is then, to 

 within a constant, equal to the product of the strength I by the 

 angle w, under which we see from this point the positive side of a 

 surface bounded by the circuit that is, the face on the left of an 

 observer who is going with the current, and looking towards the 

 interior. The angle to represents also the flow of force which a 

 mass equal to unity, placed at the point P, would send towards 

 this surface. 



As the components of the force are equal and of opposite signs 

 to the partial differentials of the potential, we see that the solid angle 

 corresponding to a surface ^<o, seen from the origin of the co- 

 ordinates, is given as a function of the contour by the equations 



t)o> Cydz zdy 



(8) 



c)co Czdx xdz 



*y~ "J ^ 



<)a> Cxdy -ydx 



^T J ^ 



468. ACTION OF Two ELEMENTS OF A CURRENT. The action 

 of two elements of a current may be established by an analogous 

 method by the aid of some principles and of facts taken from 

 experiment. 



I. Equality of action and reaction. This principle does not 

 allow of experimental verification in the case of two elements of 

 currents. It must be regarded as a fundamental hypothesis ; it 

 carries with it the necessary consequence that the action of two 

 elements is along the right line which joins them. On the other 

 hand, the reciprocal action of two elements of current is obviously 



G G 



