48 Mr maxwell, ON FARADAY'S LINES OF FORCE. 



When a solenoidal magnetized circuit returns into itself, the magnetization does not 

 depend on difference of tensions only, but on some magnetizing force of which the intensity is F. 



If i be the quantity of the magnetization at any point, or the number of lines of 

 force passing through unit of area in the section of the solenoid, then the total quantity 

 of magnetization in the circuit is the number of lines which pass through any section 

 / = 2idyd«, where dydss is the element of the section, and the summation is performed over 

 the whole section. 



The intensity of magnetization at any point, or the force required to keep up the 

 magnetization, is measured by hi =f, and the total intensity of magnetization in the circuit 

 is measured by the sum of the local intensities all round the circuit, 



where dw is the element of length in the circuit, and the summation is extended round 

 the entire circuit. 



In the same circuit we have always F = IK, where X is the total resistance of the 

 circuit, and depends on its form and the matter of which it is composed. 



On the Action of closed Currents at a Distance. 



The mathematical laws of the attractions and repulsions of conductors have been most ably 

 investigated by Ampere, and his results have stood the test of subsequent experiments. 



From the single assumption, that the action of an element of one current upon an 

 element of another current is an attractive or repulsive force acting in the direction of 

 the line joining the two elements, he has determined by the simplest experiments the 

 mathematical form of the law of attraction, and has put this law into several most elegant 

 and useful forms. We must recollect however that no experiments have been made on 

 these elements of currents except under the form of closed currents either in rigid conductors 

 or in fluids, and that the laws of closed currents only can be deduced from such experiments. 

 Hence if Ampere's formulae applied to closed currents give true results, their truth is not 

 proved for elements of currents unless we assume that the action between two such elements 

 must be along the line which joins them. Although this assumption is most warrantable and 

 philosophical in the present state of science, it will be more conducive to freedom of investi- 

 gation if we endeavour to do without it, and to assume the laws of closed currents as the 

 ultimate datum of experiment. 



Ampere has shewn that when currents are combined according to the law of the 

 parallelogram of forces, the force due to the resultant current is the resultant of the forces 

 due to the component currents, and that equal and opposite currents generate equal and 

 opposite forces, and when combined neutralize each other. 



He has also shewn that a closed circuit of any form has no tendency to turn a 

 moveable circular conductor about a fixed axis through the centre of the circle perpendicular 

 to its plane, and that therefore the forces in the case of a closed circuit render Xdx+ Ydy+Zdz 

 a complete differential. 



