188 JAMES CLERK MAXWELL 



dividing by the length of the element the number of 

 lines of magnetic induction which are cut in one 

 second by it. 



Moreover, the total number of linos of magnetic in- 

 duction which have been cut by an clement of unit 

 length is defined as the component of the vector 

 potential in the direction of the clement; hence (ho 

 electrical force in any direction is the rate of decrease 

 of the component of the vector potential in that 

 direction. We have thus a physical meaning for the 

 vector jK)tential, and shall find that in the dynamical 

 theory this quantity is of great importance. 



Professor Poynting has modified Maxwell's third 

 principle in a similar manner; he looks upon tho 

 variation in the electric displacement ns duo to tho 

 motion of tubes of electric induction,* and tho mag- 

 netic force along any circuit is equal to the number 

 of tubes of electric induction cutting or cut by unit 

 length of the circuit per second, multiplied by 4?r. 



From the equations of the field, as found by 

 Maxwell, it is possible to derive two sets of sym- 

 metrical equations. The one sot connects the rate of 

 change of the electric foroo with quantities depending 

 on the magnetic force; tho other set connects in a 

 similar manner the rate of change of the. magnetic 

 force with quantities depending on the electric force- 



* For an exact statement an to tho ivlition between tho directions 

 of tho lint's of electric displacement and of tho magnetic force, refer- 

 ence must lx) undo to Professor Poyntin;'s paper, 7'/nV. 7V<i;i., 1SH5, 

 I'urt II., pp. 280, 281. Tho ideas arc further developed in u series of 

 articles in tho Electrician, September, 1895. He Terence should also ho 

 nude to J. J. Thomson's " Kmnt IJe*e:irehe.s in Electricity nnd 



