524 



Mr. J. Lannor. 



[May 14, 



The absolute dimensions of electric charge and electric displacement 

 in K are both K,', those of electric force (static) K a ~'. These dimen- 

 sional relations mast persist when the transition is made from von 

 Helmholtz's system to Maxwell's, so that the changes in the units are 

 as von Helmholtz indicates ; and the ratio of the electrostatic to the 

 electrokinetic unit of quantity in an ideal absolute medium with K. 

 unity will now be the ascertained value of this constant for air or 

 vacuum multiplied by the square root of the value of K, for air. The 

 electric pressure in a fluid dielectric, however, depends, in this limit- 

 ing form of the theory, on the square of the value of the electric 

 displacement, as may be proved : thus the circumstances of ordinary 

 cases of statical electrification are those of finite numerical value of 

 the displacement, notwithstanding the smallness of this absolute unit 

 of charge.) 



Generalised Electrodynamic Theory. 



To obtain the general type of the modification of which the theory 

 of electrodynamics is susceptible owing to the existence of non- 

 circuital currents, we start, following von Helmholtz, from the 

 ascertained laws for circuital currents, which may be developed 

 in the manner of Neumann and Maxwell from the electrodynamic 

 potential 



The value of T with the sign here given to it is to be reckoned as 

 kinetic energy ; the mechanical forces are to be derived by its 

 variation due to any virtual displacement of the system, a force acting 

 in the direction of the displacement producing an increment of T ; 

 the electric forces are derived according to Lenz's law or Maxwell's 

 kinetic theory. The equations of the field are thus all expressible in 

 terms of this function T. When non-circuital currents are con- 

 templated, the currents , i', now varying with *, ', must be placed 

 inside the integral signs ; and to T must be added the most general 

 type of expression that will vanish when either current is circuital. 

 Thus we must write 



where * is a function such that 



i.e., it is, so far, any function which has no cyclic constant round 

 either circuit. The distribution of the energy between the pairs of 



