272 Maxwell. 



that, in fact, " the physical lines of magnetic force are 

 currents." 



The comparison with the lines of flow of a liquid is 

 applicable to electric as well as to magnetic lines of force. In 

 this case the vector which corresponds to the velocity of the 

 fluid is, in free aether, the electric force E. But when different 

 dielectrics are present in the field, the electric force is not a 

 circuital vector, and, therefore cannot be represented by lines 

 of force ; in fact, the equation 



div E = 

 is now replaced by the equation 



div(eE) = 0, 



where g denotes the specific inductive capacity or dielectric 

 constant at the place (x, y } z\ It is, however, evident from 

 this equation that the vector cE is circuital ; this vector, 

 which will be denoted by D, bears to E a relation similar to 

 that which the magnetic induction B bears to the magnetic 

 force H. It is the vector D which is represented by Faraday's 

 lines of electric force, and which in the hydrodynamical 

 analogy corresponds to the velocity of the incompressible fluid. 



In comparing fluid motion with electric fields it is necessary 

 to introduce sources and sinks into the fluid to correspond to 

 the electric charges ; for D is not circuital at places where there, 

 is free charge. The magnetic analogy is therefore somewhat 

 the simpler. 



In the latter half of his memoir Maxwell discussed how 

 Faraday's "electrotonic state" might be represented in mathe- 

 matical symbols. This problem he solved by borrowing from 

 Thomson's investigation of 1847 the vector a, which is defined 

 in terms of the magnetic induction by the equation 



curl a = B ; 



if, with Maxwell, we call a the electrotonic intensity, the. 

 equation is equivalent to the statement that " the entire 

 electrotonic intensity round the boundary of any surface 

 measures the number of lines of magnetic force which pass, 



