438 Prof. Thomson on the Drjnamical Theory of Heat, 



motive force ; and the resultant intrinsic electromotive force of 

 the bar is therefore 



Similarly, if there were only the lateral variation ive of tempera- 

 ture in the bar, we should find a resultant longitudinal electro- 

 motive force equal to 



If all the three variations of temperature are maintained simul- 

 taneously, each will produce its own electromotive force as if the 

 others did not exist, and the resultant electromotive force due to 

 them all will therefore be 



i-{(r^, + Br/ + zjr/' + V)«+(^i-0^+K'-W")«^}- 



This being the electromotive force of each bar of the first 

 system in any of the cubes composing the actual solid, must be 

 the component electromotive force of each cube in the direction 

 to which they are parallel, and therefore 



must be the component electromotive force of the entire paral- 

 lelopiped in the same direction. Similar expressions give the 

 component electromotive forces parallel to the edges h and c of 

 the solid, which are similarly produced by the bars of the second 

 and third systems, and we infer the proposition which was to be 

 proved. 



161. Cor. By choosing metals of which the thermo-electric 

 relations, both to the standard metal and to one another, vary, 

 we may not only make the nine coefficients have any arbitrarily 

 given values for a particular temperature, but we may make 

 them each vary to any extent with a given change of tempe- 

 rature. 



162. For the sake of convenience in comparing the actual 

 phsenomena of thermo-electric force in different directions pre- 

 sented by an unequally heated crystalline solid, let us now, 

 instead of a parallelopiped imbedded in the standard metal, con- 

 sider an insulated sphere of the crystalline substance, with sources 

 of heat and cold applied at its surface, so as to maintain a uni- 

 form variation of temperature in all lines perpendicular to the 

 parallel isothermal planes. Let the rate of variation of tempera- 

 ture per unit of length, perpendicular to the isothermal surfaces, 

 be q, and let the cosines of the inclinations of this direction to 

 the three rectangular directions in the substance to which the 

 edges of the parallelopiped first considered were parallel, and 

 which we shall now call the lines of reference, be I, m, n respect- 



