212 ME. G. H. LIVENS ON THE 



the vector I, as the vector P, is attached to the matter and moves with it. The last 

 two equations contain, therefore, an explicit expression of the effect of the motion so 

 that they are in a sense more convenient than the equations 



D = E + P, H = B-47rI, 



47T 



defining merely the values of D and H at any point : they are, of course, ultimately 

 consistent with these equations for, taking the second one as an example, we have 



div H = 4 div B-47r4 div-4ir div Curl [L-J, 

 dt at at 



or 



|-div(H-B + 47rI) = 0. 



d/L 



With the possible exception of the equation denning dtl/dt it is now generally 

 agreed that the scheme here presented provides a completely effective specification of 

 the kinematical connexions in the electromagnetic field. 



To obtain some idea of the effect of these connexions on the dynamical processes 

 operative in the field a further assumption is necessary, and this may take one of 

 several forms which will be reviewed in the sequel. For the present we are concerned 

 merely with these equations as effective representatives of the electromagnetic 

 processes. They are sometimes given another form, by the introduction of a scalar 

 potential $ and a vector potential A, these being such that 



B = Curl A, E=--~ -grad 0, 



C Cf/t 



with the other two equations 



Curl H = C, div E = 4irp. 

 c 



The first two of these equations are equivalent to the remaining fundamental 

 equation of MAXWELL'S theory which they replace, but they suffer from the serious 

 disadvantage that the quantities A and <f> specified in them are not completely 

 denned by the equations as given and require additional data to fix them. 



4. We have just noticed that an additional assumption of a dynamical character is 

 necessary to render the Maxwellian electromagnetic scheme completely effective as an 

 electrodynamic theory. The simplest and most direct form of this assumption may be 

 taken to be that expressing the force of electrodynamic origin acting on an arbitrarily 

 moving element of charge, this force being, per unit charge equal to 



F=E+-[>B] 

 c J 



