160 PROFESSOR W. THOMSON ON THE 



planes through the substance, if it be non-crystalline ; we may assume the fol- 

 lowing expression for the reversible thermal effects of the current : — 



0(6 c)=&«j (h 6 + i 0" +j -vj/) 



Qcc«)= c a j (k & + i (p +j -vj/') 



(81). 



where Q (ftc) , Q (co) , Q (o6) , denote quantities of heat absorbed per second at the 

 sides by which positive current components enter, and quantities evolved in the 

 same time at the opposite sides. Hence, if the opposite sides be kept at different 

 temperatures, currents will pass, unless prevented by the resistance of surround- 

 ing matter; and the electro-motive forces by which these currents are urged, in 

 directions parallel to the three edges of the parallelepiped, have the following ex- 

 pressions, in which ua, vb, and we denote the difference of temperature between 

 corresponding points in the pairs of sides be, ca, and a b, respectively reckoned 

 positive, when the temperature increases in the direction of positive components 

 of current ; 



E = —a(ud + v6' + vj 6") \ 



F =-b (u4>" + v(f) + w<t>') I ... (32 . 



G = — c (u 4-' + v 4" + w -v}/) j 



The negative signs are prefixed, in order that positive values of the electro- mo- 

 tive components may correspond to forces in the direction assumed for positive 

 components of current. 



158. The most general conceivable elementary type of crystalline thermo-elec- 

 tric properties is expressed in the last equations, along with the equations (31) 

 by which we arrived at them, and we shall see that every possible case of thermo- 

 electric action in solids of whatever kind maybe investigated by using them with 

 values, and variations it may be, of the coefficients cp, 6, &c, suitable to the cir- 

 cumstances. It might be doubted, indeed, whether these nine coefficients can be 

 perfectly independent of one another ; and indeed it might appear very probable 

 that they are essentially reducible to six independent coefficients, from the extra- 

 ordinary nature of certain conclusions which we shall show can only be obviated 



by supposing 



& = (p", 6" = 4', and <p' = 4". 



Before going on to investigate any consequences from the unrestricted funda- 

 mental equations, I shall prove that it is worth while to do so, by demonstrat- 

 ing that a metallic structure may be actually made, which, when treated on 

 a large scale as a continuous solid, according to the electric and thermal condi- 



