MR. J. LARMOR ON A DYNAMICAL THEORY OF 
38 
})er unit volume of j^olarization of the molecules, the electric force acting on a single 
molecule Avill, as in § 19 but now using electroclynamic units, be = P + Xc”/ ' ; 
this force will maintain vibratory motion in the jAolar molecule, but will not cause 
any oscillation of its centre of mass. The interaction of the electric field with the 
internal coordinates of the molecule will thus introduce an extraneous potential 
energy function of the form 
W' = F {t) — { 0 ^ 9 ^ + c^O.i Pj, 
higher powers of the small internal coordinates 6^, ^ 3 , . . . . 6„ being, as usual in 
])roblems of vibration, omitted ; and here again the coefficients c^, Co,. ... c,, must be 
independent of the time. There Avill also be terms in the kinetic energy involving 
the interaction of the magnetic intensity of the field with the component velocities 
of the molecular vibration : now in a train of waves of type exp. q{t — K'-c“k), the 
magnetic induction h, being derived from the electric force P, both in the plane xy of 
the wave-front, by the relation — dhjdt = dVjdz, is equal to K'-c^^P : hence this 
part of the total kinetic energy will be of the form 
T — J{t) + (c ^01 -}“ c 3^2 c K "C ^P, 
where c\, c' 2 , .... c'„ are coefficients independent of the time. 
The form of W' shows that . . . . + c,fin is equal to the electric 
polarization in the molecule on which the electric force P^ acts. If unit volume of 
the medium contains molecules of one kind, of another and so on, and the 
polarizations in each molecule are respectively f^, fo and so on, then 
f' = ^h/i + '‘hfi +. 
25. To obtain the general equation of propagation in the mther, let JT denote the 
electric force, or the torque acting on the aether; and we have, as in Part II. § 11 , 
the kinematic relation (Itt) ^ curl 13 = djdt{W + -p and also the dynamical 
equation — d^/dt = cwv\ ^ where d?* If is to be observed that this 
dynamical equation leaves out the purely local part of the electric force. The 
propagation of radiation of ordinary wave-length is in fact an action invohdng the 
medium in bulk, and not one of molecular type; thus in accordance with the 
Young-Poisson principle [infra § 47) the local part of the electric force, arising from 
the surrounding molecules, is compensated intermolecularly by an influence on the 
physical jmoperties of the material medium which thereby become functions of the 
density and strain, and this part therefore does not enter into the molar electric 
forcive maintaining the radiation. These equations lead to 
rPV-i® = d^klt^ [m + i3') + dil^/dt. 
Hence, when the current of conduction CT is non-existent, K' = 1 -j- 13' 13 ; v hilst 
liere is J', and 47rc-i3, or P, is 1\ - Xcf '; so that (K' - 1)/(K' - i + 47r X) 
= Xc^./'/Pi, or taking X equal to Itt, we have (K' — l)/(K' -f- 2 ) — l7rC",y'/P]. 
2 G. The value, of y '/P] is to be obtained from the equations of lorced vibration of 
