THEORY OF ELECTROMAGNETISM. 
761 
The following- results may be noted :— 
No series of experiments confined to determinations of the electromotive forces 
resulting from differences of temperature at the junctions of thermoelectric circuits can 
distinguish between the two theories. 
On the theory of reversibility the following statement is true; on the theory of 
irreversibility the contrary is true. In a thermoelectric circuit of two metals, if a 
galvanic current be passed across the junction in the same direction as that of the 
current that would be produced' by heating the junction, the effect is absorption, and 
vice versd [Tait’s ‘ Heat,' 1st ed., § 192]. In many cases this statement has been 
verified experimentally, and no one, I think, has ever asserted that he has obtained 
the contrary. Hence the main thermoelectric effects cannot be explained on the 
theory of irreversibility. 
On the theory of reversibility cr — 6 P 0 takes the place of a in the ordinary theory. 
91. This last statement is of importance in connection with a difficulty purposely 
passed over till now. By equation (23) § 82 it appears that D enters into the 
expression for the stress unless P be independent of the strain. Thus the stress 
depends on the electric history of the substance. This involves difficulties of two 
kinds. First it shows that in all bodies for which P is not thus independent the 
stress would probably be widely different from what it is ordinarily assumed to be. 
This, however, would not affect the apparent mechanical effect on a conductor as a 
whole since, as already noticed, that effect depends upon the stress just outside the 
conductor, i.e., the stress in the surrounding dielectric in -which D does not increase 
indefinitely. Bat one would think that its effects on the mutual behaviour of 
different parts of a conductor would have been observed. The second difficulty is 
connected with equation (24). It might be thought a truism that should remain 
constant in a steady field. But as with B j (§ 84) this is not the case. We saw' in § 75 
that so long as any term which contributes to ff contributes zero to ffA' and [</>'UV] a+6 , 
it produces no effect on the motion and strains of bodies, that is, no mechanical effect 
whatever. The conditions for a steady field, so far as stress is concerned, are, 
therefore, that f A' = 0 and [j'OJv''] a+b = 0. If then g is the only term in l con¬ 
taining D, equation (24) gives for a steady field 
m^SCnq© . = °> [m^SCraqQ . = 0 . . . (25). 
To see what may be the approximate effect of this, let us assume ar to be a scalar 
(P) wffiatever be the strain, and let the scalar be a function of the temperature and 
the density of the body only. Then 
<*>/ = 2m- 1 SC© . X CID.Y. 0P/0D,/ 
= 2D* m^SC© . x a (m" 1 ) x '. 0P/0D*' [§ 49] 
= - D W /SC'©'. 0P/3D* [(10) § 54 and II. § 8]. 
5 E 
MDCCCXCII.—i\. 
