ON ELECTRICAL THEORIES. 133 
solution only refers to the propagation of a disturbance in a conductor, 
while Maxwell’s refers to the propagation of such a disturbance in the 
dielectric. 
Maxwell considers the effect of the motion of the medium on the elec- 
tromotive force; he shows that the electromotive force parallel to the 
axis of « ot 
= cw — bw wnat aaa 
where w, v, w are the components of the velocity of the medium conveying 
electric action. Here y is not the electrostatic potential merely; it is 
equal, as Helmholtz has shown,! to the electrostatic potential plus the 
term 
Fu + Gv + Hw. 
We must remark here that u, v, w are the components of the velocity of 
the medium conveying the electric action, i.e. the ether, and this need 
not necessarily be the same as the velocity of the dielectric. 
v. Helmholtz’s Dielectric Theory. 
y. Helmholtz, in the paper? to which we have so often referred, con- 
siders the effect of the polarisation of the dielectric; he supposes that 
when an electromotive force X, parallel to the axis of «, acts on an 
element of a dielectric, it puts it into such a state that it produces the 
same effect as if there were electricity of surface-density x on the face 
dy dz of the element, and art equal quantity of electricity of the opposite 
sign on the parallel face, x being given by the equation 
X= eX, 
the variations in the electromotive forces acting on the dielectric are 
supposed to produce the same effect as ordinary conduction currents 
whose components are %, , 3, where x, p, 3 are the components of a 
vector quantity which in isotropic media is parallel to the electromotive 
force and equal to the product of « and the intensity of the force. This 
agrees with Maxwell’s assumption, provided 
e= K/4r, 
where K is the specific inductive capacity of the dielectric. If ¢ be the 
electrostatic potential of the free electricity, ) the potential due to the 
polarisation of the dielectric, then Helmholtz shows that 
2 fats t otwhs t fats t + y } 
+4 { (144m) £ (0-49) b= — ey, 
where E is the volume-density of the free electricity. The corresponding 
equation in Maxwell’s theory is of the same form, provided 
1 + 4re = K.. 
1 Ueber die Theorie der Elektrodynamik ; die celektrodynamische Krifte in 
bemegten Leitern, Crelle, Ixxviii. p. 309; Gesammelte Werke, ii. p. 745. 
2 Ueber die Theorte der Elektrodynamik, Crelle, lxxii. p. 57; Gesammelte 
Werke, i. p. 544. 
