DYNAMICAL THEORY OF HEAT. 167 



isotropic rotatory property. The axis of thermo-electric rotation, since the agency 

 distinguishing it as a line, also distinguishes between the two directions in it, may 

 be called a dipolar axis; so may the axis of rotation of a rotating rigid body,* or 

 the direction of magnetization of a magnetized element of matter ; and its general 

 type is obviously different from that of a principal axis of inertia of a rigid body, 

 or a principal axis of magnetic inductive capacity in a crystal, or a line of mecha- 

 nical tension in a solid ; any of which may be called an isotropic axis. 



169. The general directional properties expressed by the first terms of the second 

 members of (40) are perfectly symmetrical regarding the three rectangular lines 

 of reference, and are of a type so familiar that they require no explanation here. 

 We conclude that every substance has three principal isotropic axes of maximum 

 and minimum properties regarding thermo-electric power, which are at right 

 angles to one another ; but that it is only for a particular class of conceivable sub- 

 stances that the thermo-electric properties are entirely symmetrical with reference 

 to these axes ; all substances from which the rotatory power, £>, does not vanish, 

 having besides a dipolar axis of thermo-electric rotation which may be inclined in 

 any way to them. 



170. These principal isotropic axes lose distinction from all other directions in 

 the solid, when the thermo-electric powers along them (the values of the coeffi- 

 cients 6, 0, •\j/) are equal; but a rotatory property, distinguishing a certain line 

 as a dipolar axis, may still exist. By § 159, we see how metallic structures pos- 

 sessing any of these properties (for instance having equal thermo-electric power 

 in all directions, and possessing a given rotatory power, g, in a given direction 

 about a given system of parallel lines), may be actually made. 



171. [Added, Jidy 1854.] It is far from improbable that a piece of iron in a 

 state of magnetization, which I have, since § 147 was written, ascertained to 

 possess different thermo-electric properties in different directions, may also possess 

 rotatory thermo-electric power, f distinguishing its axis of magnetization, which is 

 essentially, in its magnetic character, dipolar, as thermo-electrically dipolar also. 



§§ 172-181. — On the general equations of Thermo-Electric Action in any homo- 

 geneous or heterogeneous crystallized or non-crystallized solid. 



172. Let t denote the absolute temperature at any point, x, y, z, of a solid. Let 

 6, cp, 4, 6', <p', ■4/, 6", </>", i", be the values of the nine thermo-electric coefficients, 



* [Added, Liverpool, Sept., 27, 1854.] — As is perfectly illustrated by M. Foucault's beautiful 

 experiment of a rotating solid, placing its axis parallel to that of the earth's, and so turned that it 

 may itself he rotating in the same direction as the earth ; which the meeting of the British Associa- 

 tion just concluded has given me an opportunity of witnessing. 



■}• [Added, Sept. 13, 1854.] — By an experiment made to test its existence, which has given only 

 negative results, I have ascertained that this " rotatory power" if it exists in inductively magnetized 

 iron at all, must he very small in comparison with the amount by which the thermo-electric power, 

 in the direction of magnetization, differs from the thermo-electric power of the same metal not mag- 

 netized. 



VOL. XXI. PART I. 2 Y 



