ON ELECTRICAL THEORIES. 137 
If X, #, v are the intensities of magnetisation, $ the coefficient of 
induced magnetisation, the equations satisfied by the components of the 
dielectric and magnetic polarisation are of the type 
v3x= Are (1+ 479) Awex 12 pe (14473) (1+4:) \ a 
~ (1+4rreg) (1447S) di? k dz 
. dx , dp <3 | 
gaia ee ’ 
ik Are (14479) 24*r 
zz (1+ 4:re9) (144735) dt’ 
where €) and 3, are the values of « and $ for air. 
These equations show that the dielectric and magnetic polarisations 
are propagated by waves. For the dielectric polarisation longitudinal 
waves are propagated with the velocity 
1 { (1+47e) (1+4 9) (14473 ) 3. 
A Amel 
‘Transverse waves are propagated with the velocity 
1 (1+4e9) (1 +4235) 
A 4re (14+473) : 
Longitudinal waves of magnetic disturbances are propagated with 
an infinite velocity, and traverse ones with the same velocity as the 
transverse waves of dielectric polarisation. The electrostatic potential is 
propagated with the velocity 1/A/%. In Maxwell’s theory the corre- 
sponding equations are 
dx 
V?a=uK 7? 
d?X 
ae Nn cee 
be 
where p is the magnetic permeability and K the specific inductive capacity, 
so that for both dielectric and magnetic polarisation the velocity of the 
longitudinal wave is infinite, while the velocity of the transverse wave is 
1//uK. The velocity of propagation of the electrostatic potential is 
infinite. If in Helmholtz’s theory we put k=0, 3,=0, ¢/e9 =K, while 
both « and ¢ are infinite, we see that the results of his theory will in this 
respect agree with Maxwell’s. 
Though in Maxwell’s theory the velocity of propagation of the electro- 
. static potential is infinite, and in Helmholtz’s theory 1/A./k, the electro- 
motive force at a point, and consequently the dielectric polarisation, does 
not travel with an infinite velocity in Maxwell’s theory, or with the 
velocity 1/A./% in Helmholtz’s. We can see the reason of this more 
easily from Maxwell’s theory, as the equations are simpler. 
Using the notation of that theory, viz., f, g, h, for the components of 
the electric displacement, F, G, H for the components of the vector 
potential, and ¢ for the electrostatic potential, then in a dielectric the 
equations are 
