AND MODEHN PHYSICS. 187 



which arc linked with any closed circuit are made 

 to vary, an induced electromotive force is brought 

 into play round that circuit. This electromotive force 

 is, according to Faraday's results, measured by the 

 rate of decrease in the number of lines of magnetic 

 induction which thread the circuit. Maxwell applies 

 this principle to all circuits, whether conducting or not 



In obtaining equations to express in symbols 

 the results of the fourth principle just enunciated, 

 Maxwell introduces a new quantity, to which he gives 

 the name of the "vector potential." This quantity 

 appears in his analysis, and its physical meaning is 

 not at first quite clear. Professor Poynting has, how- 

 ever, put Maxwell's principles in a slightly different 

 form, which enables us to see definitely the meaning of 

 the vector potential, and to deduce Maxwell's equations 

 more readily from the fundamental statements. 



We are dealing with a circuit with which lines 

 of magnetic induction are linked, while the number 

 of such lines linked with the circuit is varying. Now, 

 let us suppose the variation to take place in con- 

 sequence of the lines of induction moving outwards 

 or inwards, as the case may be, so as to cut the circuit 

 Originally there are none linked with the circuit As 

 the magnetic field has grown to its present strength 

 lines of magnetic induction have moved inwards. 

 Each little element of the circuit has been cut by some, 

 and the total number linked with the circuit can be 

 found by adding together those cut by each element 

 Now, Professor Poynting's statement of Maxwell's 

 fourth principle is that the electrical force in the 

 direction of any element of the circuit is found by 



