ON FARAD AYS LINES OF FORCE. 193 



Electro-magnetism. 



Ampere has proved the following laws of the attractions and repulsions of 

 electric currents : 



I. Equal and opposite currents generate equal and opposite forces. 



II. A crooked current is equivalent to a straight one, provided the two 

 currents nearly coincide throughout their whole length. 



III. Equal currents traversing similar and similarly situated closed curves 

 act with equal forces, whatever be the linear dimensions of the circuits. 



IV. A closed current exerts no force tending to turn a circular conductor 

 about its centre. 



It is to be observed, that the currents with which Ampere worked were constant 

 and therefore re-entering. All his results are therefore deduced from experiments 

 on closed currents, and his expressions for the mutual action of the elements 

 of a current involve the assumption that this action is exerted in the direction 

 of the line joining those elements. This assumption is no doubt warranted by the 

 universal consent of men of science in treating of attractive forces considered 

 as due to the mutual action of particles ; but at present we are proceeding 

 on a different principle, and searching for the explanation of the phenomena, 

 not in the currents alone, but also in the surrounding medium. 



The first and second laws shew that currents are to be combined like 

 velocities or forces. 



The third law is the expression of a property of all attractions which may 

 be conceived of as depending on the inverse square of the distance from a fixed 

 system of points ; and the fourth shews that the electro-magnetic forces may 

 always be reduced to the attractions and repulsions of imaginary matter properly 

 distributed. 



In fact, the action of a very small electric circuit on a point in its neigh- 

 bourhood is identical with that of a small magnetic element on a point outside 

 it. If we divide any given portion of a surface into elementary areas, and 

 cause equal currents to flow in the same direction round all these little areas, 

 the effect on a point not in the surface will be the same as that of a shell 

 coinciding with the surface, and uniformly magnetized normal to its surface. 

 But by the first law all the currents forming the little circuits will destroy 



VOL. I. 25 



