ON ELECTRICAL THEORIES. 131 
as, however, he subsequently puts J=0, we may at once simplify the 
equation by making this assumption. 
Since the kinetic energy equals 
3{{{(Fu +Gv+Hw)dz dy dz, 
we see by Lagrange’s equations that the electromotive force tending to 
increase u 
— dF. 
dt ’ 
in addition to this there is the force arising from the electrostatic poten- 
tial ¢, so that the total electromotive force parallel to the axis of « 
me a 
Ty db ode 
so that if o be the specific resistance of the substance, K its specific induc- 
tive capacity, then 
F. Ene ana 
PGR TN ae. dn 
. 
? 
_ df__1fdF, do] _KJ@F, a \ 
prt hin OS aits Pole ‘ie | de dedi 
but we saw before that 
Arpu=— 77°F; 
substituting for wu this value, we see 
An dF d CE, dd 
op_4te f dE aa es mat 
nae o { dt 7 a ao dt? “ae dt J’ 
thus in the dielectric the equation becomes 
@2E 
¥ ere { a ae } ; 
in the conductor 
Aur dE do 7 
= oe RN, 
o dt Tak f 
‘The equation for the dielectric shows that it represents a wave-motion 
propagated with the velocity 1/./ Ku; the numerical value of this velocity 
agrees very approximately with the velocity of light, and this led Max- 
well to the theory that the changes in the structure of the dielectric 
which take place when the dielectric is polarised are of the same nature 
as those which constitute light. This theory, which is called the electro- 
magnetic theory of light, might almost as justly be called the mechanical 
theory of dielectric polarisation. Kirchhoff, in his paper ‘ Ueber die 
Bewegung der Electricitét in Drihten’ (Pogg. Ann., vol. c. 1857 ; 
Gesammelte Werke, p. 131), was the first to point out that some elec- 
trical actions are propagated with the velocity of light. In this paper he 
considers the motion of electricity in wires whose diameters are small 
compared with theirlength. There are three things which have to be con- 
sidered in this problem—(1) the self-induction of the electric current, and 
K2 
