766 
where m represents the effective mass of the electron, n 0 the fre¬ 
quency of the free or natural vibration, k a constant coefficient 
connected with the intensity of the damping action which is known 
to take place on the electron and k a structural constant which 
may conveniently be taken as the measure of the intrinsic rotatory 
power of the molecule. 
For the sake of simplicity, terms involving P*, P y and spacial 
differential coefficients of P x and P y and P z have been omitted from 
the expression of the extraneous force acting on the electron. It is 
easy to see that no very great error in our results can arise from 
the neglect of these terms. 
We assume as a solution of (2) 
(3) 
r=to 
n being the freqviency of vibrations in the incident beam of light. 
Writing for brevity 
(4) 
(5) 
1 _ 
n 0 2 — n 2 -j- 2 kni 
h 
n 0 2 n 2 2km 
we obtain 
(6.) *>,= **-y(Mi-B) 
(6b) = 
It must not be forgotten that we have limited the discussion to the 
case of the forced vibration maintained by the continued operation 
of the impressed electric force and that we are ignoring altogether 
the natural vibration of the electron. 
§ 2. The Maxwell-Lorentz fundamental electromagnetic 
equations are in our case, the conduction current being left out of 
account, 
(i) 
4 71 f$P 
curl #= — ( — + 
C \9t 
1 9E\ 
4 n 9t ) 
(ii) 
curl E = — 
1 9H 9 2 2helN ' 
c 9t ' c 2 9t 2 ’ 
H stands here for the magnetic vector at the point considered; and 
