368 C. Barns — Expression in Thenno-electrtcs. 



5. Now to show that equation (3) contains Tait's equation as 

 one of its approximate forms, suppose that in an expansion of 

 the exponentials in (3), terms involving higher powers than 

 the second can be rejected. Then (3) leads to 



(5) E= («-9 ) (A' ± A")e. | - (J±^r + «.) + ^ } 



But for dE/dd = 0, = m , and 6 m may therefore be found 

 either by differentiating (5) or by expanding (4). Its value is 



*-=*- + :ot < 6 > 



Substituting (6) in (5), 



(7) . . . . ^=(fl_^(4-±4'")^|_fl m + ?+4l 



Since (A 2 ± A /2 )e n is constant for the given couple, and since 

 m for reasons already given, § 4, may be either positive or 

 negative, equation (7) is identical with Tait's equation. 



6. Now it is desirable to look somewhat more in detail at 

 the physical meaning of the elementary equation (1). In my 

 work* on the thermal variation of the viscosity, rj, of a very 

 viscous body like marine glue I found that the elementary 

 equation dvj/dd = — Br), where 6 denotes temperature, very 

 fully reproduced the results. But since by Maxwell's theory 

 of viscosity ; rj is immediately dependent on the contigurational 

 stability of a body, the same is true of the rate d'/j/dd at which 

 viscosity varies with temperature. Again the result, men- 

 tioned in §3, put in the form dr/dd = —br shows that like the 

 resistance r, so also the rate dr/dd at which resistance de- 

 creases with temperature is immediately dependent on the 

 molecular stability of the electrolyte. An interesting research 

 of Auerbach'sf on the resistance and bulk density of a given 

 metallic powder (silver) is particularly suggestive here. He 

 finds dr/dd =—nr, where d is the bulk density and n constant. 

 Comparing this with the preceding equation, it is clear at once 

 that the internal contacts are similarly increased in the two 

 cases. 1 therefore infer finally that equation (1) is open to an 

 analogous interpretation, viz : that the thermoelectric condi- 

 tion e of an element of length of the thermocouple is directly 

 related to the molecular stability of the element. In other 

 words two metals are thermoelectrically identical, when the 

 sign and the number of available molecular paths which the 

 current (or better the elementary charge) is free to take, is the 



* Proceedings Am. Acad., xxvii, p. 13, 1892; this Journal, xlv, p. 87, 1893. 

 \ Auerbach : Wied. Ann., xxviii, p. 609, 1886. 



