538 A DYNAMICAL THEOnY OF THE ELECTROMAGNETIC FIELD. 



If there are many bodies connected with A and H in & similar way but 

 with different values of p and q, we may treat the question in the same way 

 by assuming 



L = 2 (Cjaf), M= 2 (Cpq), and N= X (Cf), 



where the summation is extended to all the bodies with their proper values of 

 C, p, and q. Then the momentum of the system referred to A is 



Lu + Mv, 

 and referred to B, Hu+Nv, 



and we shall have ^~ 



(2), 



where X and Y are the external forces acting on A and B. 



(25) To make the illustration more complete we have only to suppose 

 that the motion of A is resisted by a force proportional to its velocity, which 

 we may call Ru, and that of B by a similar force, which we may call Sv, R and 

 S being coefficients of resistance. Then if and 77 are the forces on A and B, 



If the velocity of A be increased at the rate -j- , then in order to prevent B 

 from moving a force, "n = -f. (Mil) must be applied to it. 



This effect on B, due to an increase of the velocity of A, corresponds to 

 the electromotive force on one circuit arising from an increase in the strength 

 of a neighbouring circuit. 



This dynamical illustration is to be considered merely as assisting the 

 reader to understand what is meant in mechanics by Reduced Momentum. The 

 facts of the induction of currents as depending on the variations of the quantity 

 called Electromagnetic Momentum, or Electrotonic State, rest on the experiments 

 of Faraday*, Felicif, &c. 



Experimental Kesearctits, Scries i., ix. t Annales de CMmie, sr. 3, xxxiv. (1852), p. 64. 



