1891.] 



On the Theory of Electrodynamics. 



523 



rF. Let a be the surface density of the charge conducted to a plate ; 

 then the effective electrification along that plate will be of surface 

 density a = a *F ;> therefore, by Coulomb's principle, 



F = 47T</ 



= 47T <7 



so that 



i-F. 



47T 



Thus the current is not circuital, but there is an excess of the surface 

 density conducted to the surface over the displacement current from 

 the surface, which is equal to' F/4 IT. 



The specific inductive capacity, as determined by static experi- 

 ments on capacity, is here measured by-/*, the coefficient in the 

 expression 1 for a. 



In addition to this discontinuity at the' face of a condenser plate, 

 the induction in the mass of the dielectric will not be circuital unless 

 the electric force is itself circuital, which it is not in the general 

 electrodynamic theory to be presently discussed. 



The current becomes more nearly circuital the greater the value 

 of ft.. If yt, and therefore *c, were infinite we should attain the limit 

 when the cui-rents are circuital. If the values of yt for all dielectrics 

 were multiplied by the same infinite constant, so as to keep their 

 ratios unchanged, the distribution of electric potential would not be 

 altered, provided the charges on all conducting surfaces were also 

 increased in that ratio ; the displacement or induction, which is now 

 the essential quantity in the theory, thus maintaining its original 

 value. This comes to the same thing as measuring the actual charges 

 in a unit which is diminished in that ratio. 



In this way the Maxwell scheme of circuital currents reveals itself as 

 a limiting case of the more general polarisation theory. The infinite di- 

 electric constant makes the excited polarisation of very great amount in 

 comparison with the exciting cause ; so that in the limit we may, in 

 a sense, imagine the system as one of self-excited circuital polarisa- 

 tion, a point of view which approaches somewhat to that of Maxwell 

 himself. 



This mode of connecting the two theories was pointed out by von 

 Helmholtz. But his scheme takes for the new unit of charge the elec- 

 trostatic unit corresponding to vacuum with its new infinitely great 

 dielectric constant, so that this unit is reduced proportionally to the 

 square root of the infinite ratio ; the displacement is then infinitely 

 great, and the potential infinitely small, according to the square root 

 of this ratio. 



(This, however, should be expressed more precisely as follows : 



VOL. XLIX. 2 N 



