384 Prof. Thomson on the Dynamical Theory of Heat. 



denote the thermo-electric powers of two bars cut from the given 

 substance in directions parallel and perpendicular to its axis of 

 symmetry respectively. Let us suppose the actual bar to be of 

 rectangular section, with two of its opposite sides perpendicular 

 to the plane of its length and the axis of symmetry of its sub- 

 stance. Let a longitudinal section in this plane be represented 

 by the accompanying diagram ; let OA or any line parallel to it 

 be the direction of the axis of symmetry through any point j and 

 let (o denote the inclination of this line to the length of the bar. 

 Let the breadth of the two opposite sides of the bar perpendicular 

 to the plane of the diagi-am be denoted by a, and in the plane of 

 the diagram b. The area of the transverse section of the bar 

 will be ab ; and therefore if 7 denote the strength, and i the in- 

 tensity, of the current in it, we have (§ 142) 



ab' 



15L We may suppose the current, itself parallel to the length 



of the bar, and in the direction from left to right of the diagram, 



to be resolved (§ 142) at any point P at the side of the bar into 



two components in directions parallel and perpendicular to OA, of 



which the intensities will be i cos a> and i sin a> respectively. The 

 former of these components may be supposed to belong to a 

 system of currents crossing the bar in lines pai'allel to OA, and 

 passing out of it aci'oss the side CD into a conductor of the 

 standard metal ; and the latter, to a system of currents entering 

 the bar across CD from the same conductor of standard metal, 

 and crossing it in lines perpendicular to OA. The resultant 

 current in the supposed standard metal beside the bar will clearly 

 be parallel to the length, and can therefore (this metal being 

 non -crystalline) produce no effect influencing the thermal agency 

 at the side of the bar or within it. The inclinations of the cur- 

 rents to a perpendicular to the separating plane of the two metals 



