( 452) 
1 Vv Vv te m 1 1 
Pa ap = ye Pe Q e \ Ap ha 
Q 
ee lee 
| a de EE 
Ze h dea 
P 
a formula which may now be applied to some particular cases. 
a. Let all parts of the circuit be kept at the same temperature. 
Then, h is a constant, and 
1 m 
va =~ (Ye— Va) tale Ap — Ay) . (33) 
The potential-difference will now have a positive or negative value, 
if the ends of the circuit are made of different metals. It appears 
in this way that the differences that have been observed in this case 
may be attributed either to an inequality of Vp and Vg, i.e. to 
“molecular” forces acting at the places of junction (HELMHOLTZ), or 
to an inequality of Ap and Ag, i.e. to a difference in the “con- 
centrations” proper to the metals (Drupr). 
It need hardly be added that (83) becomes 0 whenever the ends 
are made of the same metal and that the law expressed in Vouta’s 
tension-series is implied by the equation. 
b. Let the metal be the same everywhere. Then A is a function 
of h and (32) will always be 0, if the ends P and Q are kept at 
the same temperature, whatever be the distribution of temperature 
in the intermediate parts. 
c. Let us next examine the potential-difference between the ends 
of an open thermo-electric circuit, a difference that may be regarded 
as the measure for the electromotive force F existing in it. Starting 
from P and proceeding towards Q, the state of things I shall 
consider is as follows: 1s" Between P and a section F’', the metal / 
maintained at a temperature varying from 7'p to 7" in R'. 2"d Between 
R' and S', a gradual transition ($ 6) from the metal / to the metal //, 
at the uniform temperature 7”. 3rd From S' to S”, the metal ZZ with 
temperatures varying from 7” to 7”. 4 Between S" and R", a 
gradual transition from the metal // to the metal /, the temperature 
being 7” in every point of this part of the circuit. 5 Finally, between 
R" and Q, the metal / with a temperature changing from 7” to 
Tq= Tp. It being here implied that the ends of the circuit consist 
of the same metal and have the same temperature, the equation (32) 
reduces to the last term, and we find, after integration by parts, 
e 
