166 PROFESSOR W. THOMSON ON THE 
tain axis fixed in the substance, which I shall call its axis of thermo-electric ro- 
tation to any three rectangular lines of reference, then the values of ¢, », 9 for 
these lines of reference are as follows :— 
=e cosA, »=E cosp, =O Cos V. 
If ¢ denote the inclination of the direction (<. 3° ANE in which the temperature 
varies most rapidly, to the axis of thermo-electric rotation, and if a, 6, y de- 
note the angles at which a line perpendicular to the plane of this angle 7 is in- 
clined to the axes of reference, we have 
yw —Sv=Eqsin? cos a 
3u—fw=eqsinicos B ae os Seater 2 rr (20). 
Cu—nu =e qsinicos 
Hence we see that the last terms of the general formula for the component elec- 
tro-motive forces along the lines of reference express the components of an electro- 
motive force acting along a line perpendicular both to the axis of thermo-electric 
rotation, and to the direct line from hot to cold in the substance, and equal in 
magnitude to the greatest rate of variation of temperature perpendicular to that 
axis, multiplied by the coefficient 0. 
167. Or again, if we consider a uniform circular ring, of rectangular section, 
, cut from any plane of the substance inclined at an angle A toa plane perpendicular 
to the axis of thermo-electric rotation, and if the temperature of the outer and 
inner cylindrical surfaces of this ring be kept each uniform, but different from 
one another, so that there may be a constant rate of variation, g, of temperature 
in the radial direction, but no variation cither tangentially or in the transverse 
direction perpendicular to the plane of the ring, we find immediately, from (42), 
that the last terms of the general expressions indicate a tangential electro-motive 
force, equal in value to gq cos A, acting uniformly all round the ring. This 
tangential force vanishes if the plane of the ring contain the axis of thermo- 
electric rotation, and is greatest when the ring is in a plane perpendicular to the 
same axis. 
168. The peculiar quality of a solid expressed by these terms would be destroyed 
by cutting it into an infinite number of plates of equal infinitely small thickness, 
inverting every second plate, and putting them all together again into a continu- 
ous solid ; a process which would clearly not in any way affect the thermo-electric 
relations expressed by the first term of the general expressions for the compo- 
nents of electro-motive force; and it is therefore of a type, to which also belongs 
the rotatory property with reference to light discovered by Farapay as induced 
by magnetization in transparent solids, which I shall call dipolar, to distinguish 
it from such a rotatory property with reference to light as that which is naturally 
possessed by many transparent liquids and solids, and which may be called an 
