Prof. Thomson on the Dynamical Theory of Heat. 383 



thermo-electric properties of copper and iron wires are affected 

 by alternate tension and relaxation in such a manner as to leave 

 no doubt but that a mass of either metal, when compressed or 

 extended in one direction, possesses different thermo-electric rela- 

 tions in different directions. Fragments of different metals may 

 be put together so as to form solids, possessing by structure the 

 thermo-electric characteristic of a crystal, in an infinite variety 

 of ways. Thus, a structure consisting of thin layers alternately 

 of two different metals, possesses obviously the thermo-electric 

 qualities of a ciystal with an axis of symmetry. I have investi- 

 gated the thermo-electric properties in all directions of such a 

 structure in terms of the conducting powers for heat and elec- 

 tricity, and the thermo-electric powers, of the two metals of 

 which it is composed ; and bars made up of alternate layers of 

 copper and iron, one with the layers perpendiculai', another with 

 the layers oblique, and a third with the layers parallel to the 

 length, illustrating the theoretical i-esults which were communi- 

 cated along with this pajjer, were exhibited to the Royal Society. 

 The principal advantage of considering metallic structures with 

 reference to the theory of thermo-electricity is, as will be seen 

 below, that we are so enabled to demonstrate the possibility of cry- 

 stalline thermo-electric qualities of the most general conceivable 

 type, and are shown how to construct solids (whether or not 

 natural crystals may be ever found) actually possessing them. 



149. The following two propositions with reference to thei'mo- 

 electric effects in a particular case of crystalline matter are pre- 

 mised to the unrestricted treatment of the subject, because they 

 will serve to guide us as to the nature of the agencies for which 

 the general mathematical expressions are to be investigated. 



Prop. I. If a bar of crystalline substance, possessing an axis 

 of thermo-electric symmetry, has its length oblique to this axis, 

 a current of electricity sustained in it longitudinally will cause 

 evolution of heat at one side and absorption of heat at the oppo- 

 site side, all along the bar, when the whole substance is kept at 

 one temperature. 



Prop. II. If the two sides of such a bar be kept at different 

 temperatures, and a homogeneous conducting arc be applied to 

 points of the ends which are at the same temperature, a current 

 will be produced along the bar, and through the arc completing 

 the circuit. 



150. For proving these propositions, it will be convenient to 

 investigate fully the thermo-electric agency experienced by a bar 

 cut obliquely from a crystalline substance possessing an axis of 

 symmetry, when placed longitudinally in a circuit of which the 

 remainder is composed of the standard metal, and kept with 

 cither its sides or its ends unequally heated. Let 9 and ^ 



