: 
‘DYNAMICAL THEORY OF HEAT. 159 
blishes Proposition II., enunciated above in § 149, and shows the amount of the 
electro-motive force producing the stated effect, in terms of T and T’, the tempera- 
tures of the two sides of the bar, the obliquity of the bar to the crystalline axis of 
symmetry, and the thermo-electric properties of the substance; since, if @ and 
¢ denote its thermo-electric powers, along the axis of symmetry, and along lines 
perpendicular to this axis, at the temperature ¢, and w the inclination of this axis 
to the length of the bar when the substance is at the temperature ¢, we have 
as ; (p—@)sinweosw . . Bee = (Ze): 
155. By an investigation exactly similar to that of § 115 which had reference to 
non-crystalline linear conductors, we deduce the following expression for the 
electro-motive force, when the ends of the bar are kept at temperatures T, T’, from 
the terminal thermal agency 0, of a current investigated in § 153. 
Weowa 
r=sf" z at j : ; : ; (29), 
n= 5(0 cos’w + @ sin? «) Jee ot ht ete Tie nah 11) 
where 
§§ 156-170. On the Thermal Effects and the Thermo-electric Excitation of Electrical 
Currents in Homogeneous Crystalline Solids. 
156. The Propositions I. and II., investigated above, suggest the kind of assump- 
tions to be made regarding the reversible thermal effects of currents in uniformly 
heated crystalline solids, and the electro-motive forces induced by any thermal 
circumstances which cause inequalities of temperature in different parts. The 
formule expressing these agencies in the particular case which we have now in- 
vestigated, guide us to the precise forms required to express those assumptions 
in the most general possible manner. 
157. Let us first suppose a rectangular parallelepiped (a, }, c) of homogeneous 
crystalline conducting matter, completely surrounded by continuous metal of the 
standard thermo-electric quality touching it on all sides, to be traversed in any 
direction by a uniform electric current, of which the intensity components parallel 
to the three edges of the parallelepiped are /, 7, 7, and to be kept in all points ata 
uniform temperature ¢. Then taking ¢, 6, J, to denote the thermo-electric powers 
of bars of the substance cut from directions parallel to the edges of the parallele- 
piped, quantities which would be equal to one another in whatever directions 
those edges are if the substance were non-crystalline; and 6 6”, 2, 0", VV; 
other elements depending on the nature of the substance with reference to the 
directions of the sides of the parallelepiped, to which the name of thermo-electric 
obliquities may be given, and which must vanish for every system of rectangular 
VOL. XXI. PART I, 2uU 
