Prof. Thomson on the Dynamical Theory of Heat. 441 



of reference, then the values of f, 77, ^ for these Hues of reference 

 are as follows : — 



f^/3C0S\j r) =s p cos fjb, ■Jsspcosv. 



If i denote the inclination of the direction (—,—, — ), in which 



\q q qJ 



the temperature varies most rapidly, to the axis of thermo-elec- 

 tric rotation, and if ct, j3, y denote the angles at which a line 

 perpendicular to the plane of this angle i is inclined to the axes 

 of reference, we have 



T)iv — ^v = pq sin i cos a^ 



iu — ^w = pq sin i cos /3 > ... (42). 



^v — '}]u = pq sin i cosy J 



Hence we see that the last terms of the general formula for the 

 component electromotive forces along the lines of reference ex- 

 press the components of an electromotive force actuig 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 tempera- 

 ture perpendicular to that axis, multiplied by the coefficient p. 



167. Or again, if we consider a uniform circular ring of rect- 

 angular section, cut from any plane of the substance inclined at 

 an angle X 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 either tan- 

 gentially 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 electromotive 

 force, equal in value to pq cos \, 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 continuous solid, 

 in planes perpendicular to the axis of thermo-electric rotation ; 

 a process which would clearly not in any way affect the thermo- 

 electric relations expressed by the first term of the general expres- 

 sions for the components of electi'omotive force ; and it is there- 

 fore of a type, to which also belongs the rotatory property with 

 reference to light discovered by Faraday as induced by magnet- 

 ization iu transparent solids, which 1 shall call dipolar, to distin- 



Phil. May. S. 4. Vol. 11. No. 74. June 1856. 2 G 



