ON FARADAY'S LINES OP FORCE. 183 



the total quantity of magnetization in the circuit is the number of lines which 

 pass through any section, I=*S,idydz, where dydz 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 kif, and the total intensity of 

 magnetization in the circuit is measured by the sum of the local intensities all 

 round the circuit, 



where dx 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 K 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 can only 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. 



