102 
PHYSICS: E. H. HALL 
proportion of water, the smaller is the mechanical effect per unit mass of the 
mixture. 
In the isothermal alloy 'bridge/ of composition varying from pure a at 
one end to pure 0 at the other end, which is supposed to connect the two 
metals at their hot or at their cold ends, we must have, when it stands de- 
tached, no cyclic movement of the electrons. Accordingly we get, in place 
of equation (1), the two equations 
dP 
and 
dP + dP f = 
dP„ = 0 
dp 
ne 
(5) 
(6) 
FIG. 3 
These lead to the following, as the expression for the virtual e.m.f. due to 
the non-homogeneity of the isothermal bridge: • 
(dP + dP f ) 
(7) 
The first member of (7) is the reversible work that would be done, on the 
free electrons only, during the passage of the unit quantity of electricity 
through the bridge. 
The expression for the work done on the electrons (A) is absent here, for the 
reason that, according to equation (5), no reversible work would be done on 
them. 
For a thermo-electric circuit, made up of a bar of metal a, a bar of metal 
/3, and two isothermal alloy bridges a-(3, we find the net, or total, virtual 
e.m.f. to be represented by (1 -f- Ge) times the area A' B' C D' in figure 3, 
where A B, B C, A D, and D C indicate the pressure- volume relations of one 
gram of free electrons in the four parts of the circuit respectively, and A' B' ', 
B! C", A ' D', D' C ', are found respectively from the corresponding full lines 
by means of the ratio k f -f- (k a + k f ), applied as in figure 2. 
In spite of the conspicuous part which the specific potentials P a and Pj 
