Mb maxwell, ON FARADAY'S LINES OF FORCE. SS 



In the following investigation we shall have occasion to treat of magnetic quantity and 

 intensity in connexion with electric. In such cases the magnetic symbols will be distinguished 

 by the suffix 1, and the electric by the suffix 2. The equations connecting a, b, c, k, a, fi, y, 

 p, and p, are the same in form as those which we have just given, a, b, c are the symbols of 

 magnetic induction with respect to quantity ; k, denotes the resistance to magnetic induction, 

 and may be different in different directions; a, /3, y, are the effective magnetizing forces, con- 

 nected with a, b, c, by equations (B) ; jo, is the magnetic tension or potential which will be 

 afterwards explained ; p denotes the density of real magnetic matter and is connected with 

 a, b, c by equations (C). As all the details of magnetic calculations will be more intelligible 

 after the exposition of the connexion of magnetism with electricity, it will be sufficient here to 

 say that all the definitions of total quantity, with respect to a surface, and total intensity with 

 respect to a curve, apply to the case of magnetism as well as to that of electricity. 



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 neighbourhood 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 



