ACTION OF A POLE ON A CURRENT ELEMENT. 441 



463. ACTION OF A POLE ON A CURRENT ELEMENT. FUNDA- 

 MENTAL PRINCIPLES. We will start from the following principles, 

 some of which may be regarded as evident axioms, and others as 

 experimental facts : 



I. Equality of action and reaction. The action of a magnet on 

 a current is equal and directly opposite to the action of the current 

 on the magnet. This general law of Nature is experimentally verified 

 in the present case ; for if the magnet and the current are connected, 

 the system if made free does not move. 



II. The action changes its sign with the sign of the pole and 

 with the direction of the current. This fact is a result of experi- 

 ment. The action remains the same when the sign of the pole and 

 the direction of the current are simultaneously changed. 



III. Principle of sinuous currents. The action of a sinuous 

 current on a magnet is identical with that of a rectilinear current 

 which has the same terminals. 



In order to verify this principle, Ampere showed that two con- 

 ducting wires terminating at the same ends, one straight and the 

 other sinuous, have no action on any magnet when they are tra- 

 versed by the same current in opposite directions. 



Some limitations are here necessary; the sinuous current must 

 be of the same order of magnitude as the rectilinear current, and be 

 but little distant from it; nor must it turn about the rectilinear 

 current This principle, moreover, will only be used to replace an 

 element by its three projections. 



IV. The action of any given magnet, and therefore of a pole, on 

 a current element, is perpendicular to the element. 



Ampere established this principle in the following manner. A 

 metallic arc of a circle, movable about an axis passing through its 

 centre, and perpendicular to its plane, can glide on two drops of 

 mercury by which the current traversing it enters and leaves. Any 

 given magnet placed in the vicinity leaves the arc at rest. The 

 action of the magnet is then in the plane which passes through 

 the axis of rotation, and is therefore perpendicular to the movable 

 current. The arc, moreover, begins to move when the axis no longer 

 passes through the centre. 



V. The action of a magnet on an element of current is applied 

 to the element. This results from the following experiment, due to 

 M. Liouville. Part of the rectilinear current is made movable 

 about its axis ; with this object, its ends dip in two small mercury 

 cups by which the current enters. The rectilinear element does not 

 rotate at all, in whatever manner the magnet is presented to it. 



