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 £, n , s for 

 these lines of reference are as follows: — 



£ = COS A , r) — Q COS \l , 5 = COS V. 



(11 1) zv\ 

 - , - , - J , in which the temperature 



varies most rapidly, to the axis of thermo-electric rotation, and if a, £, 7 de- 

 note the angles at which a line perpendicular to the plane of this angle i is in- 

 clined to the axes of reference, we have 



rj w — ^ v = q sin i cos a \ 



S u — £w = q sin i cos (3 \ • • • • (42). 



Z,v — r)U = <? sin i cos y J 



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 to a 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, q, 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 q cos X, 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 Faraday 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 



