314 
Prof. Thomson, On the theory of the rotation 
ever, matter is present whose molecules are made up of charged 
parts, then the motion of these parts under the electric field in 
the light wave may give rise to convection currents which have to 
be included in u, v, w, and which will modify the equations. 
From equations (2) and (1), we have 
dy \dx 
or since 
dX\ 
d 
fdX 
dy) 
dz 
V dz 
dX 
dY 
dZ 
dx 
+ dy 
^ dz 
drX 
d 2 X 
d?X 
dx 2 
dy 3 dz- 
dZ\ . du 
dx) = - iw »M’ 
= 0. 
du 
•( 3 ), 
with similar equations for T and Z. 
If the nature of the body through which the light passes is 
such that ~ contains a term ff)’ et l ua ^ on (3) will 
take the form 
d?X <PX d?X = 
dx 2 dy- dz 2 
with equations of a similar type for Y and Z, we can easily show 
that equations of this type represent a rotation of the plane of 
polarization equal to 27 rr/n per unit path. 
Let us now calculate the expression convection current pro- 
duced by the light waves acting on the atoms of the substance. 
Let us suppose that each atom consists of a number of electrified 
bodies rigidly connected together. To find how these move when 
the light wave falls upon them, take as the origin the centre of 
gravity of an atom and for axes x, y' , z fixed in the atom, such 
that if e x , e 2> ... are the charges on the parts of the atom whose 
co-ordinates are respectively (ocf yf zf), (xf yf zf), ..., then 
2 {e^x-ly-i) = 2 (ftXiZi) = 2 (e^i V) = 0. 
Let «!, &)o, &> 3 be the angular velocity of the atom round the 
axes of x, y, z respectively, D, E, F, L, M, N the moments and 
products of inertia of the atom about these axes, then, neglecting 
powers of the co’s higher than the first, we have 
dt 
(— P(l ) 1 — Ncti.j — il/tOy) — P, 
~ <_ iY & ) 1 - Ea>, - Lco 3 ) - Q, 
d 
dt 
(— Mmi — Lco 2 — Fa>s) = R, 
