On Thermo-electric Circuits. 449 
From these equations the value of the total E.M.F. of the 
simple circuit, with its two junctions at temperature 0, and @,, 
is obviously 
B= (ka—hs)(O1 — 9s) {O—3(9, ay G2) 3 
a well-known formula, first established empirically by Avena- 
rius as far as the variable part is concerned. 
Now although II, the Peltier coefficient, can thus be re- 
garded as a function to be integrated all round the circuit, it 
is possible also to regard it as localized—part of it constituting 
an H.M.F’. residing at the junctions, and part of it having its 
abode wherever a slope of temperature occurs in either metal. 
And, indeed, the generation and destruction of heat at the 
junctions, observable when a current flows round the circuit 
and known as the Peltier effect, together with the apparent 
convection of heat by electricity discovered by Sir William 
Thomson, and which in 1876* I ventured to call the Thomson 
effect, compel us to picture to ourselves an H.M.F. at each 
junction, which may be called specifically Peltier forces and 
be denoted by IT, and II,, and another H.M.F’. in each metal 
wherever the temperature slopes; the total force in the metal A 
between the temperatures 0, and 0, being denoted by @,, 
that in the other metal by ©,, and both being called Thomson 
orces. 
i The Peltier effect and the Thomson effect depend on a cur- 
rent passing ; the existence of the forces is independent of such 
an accident. The Thomson force depends for its existence - 
upon inequality of temperature ; the Peltier force does not, it 
varies only with absolute temperature and nature of metals. 
Equality of temperature throughout the circuit abolishes the 
Thomson forces, but only renders equal the Peltier ones, their 
continued existence being provable by producing the Peltier 
effect. The resultant H.M-F. of the whole simple circuit, 
with junctions at 6, and @., is 
H=11),—H,+ ©,—9, ; 
whence, from the preceding equations, we get 
Th, = ha ko) 01(Oo— 1); 
TI,=(ka— bs )A2( 9 — 92), 
O.=h,(6?—@), 
O=hi( 8-62), 
where the k’s may quite easily be negative in certain metals. 
By these formule the tables of Peltier and Thomson contact 
series, given in section 23 of the paper? above referred to, were 
* Phil. Mag. [5] Dec. Suppl. vol. ii, p. 584. 
+ Phil. Mag. May 1885, pp. 354, 306, 
