88 
NATURE 
| May 29, 1873 
as a real fluid, there are the fatal objections that his 
method makes no provision for the explanation of the 
Peltier, or of the Thomson, effect ; and therefore cannot 
be looked upon as having any useful relation to the 
subject. Similar remarks apply to the attempt of Aven- 
arius to account for thermo-electric currents by the 
variation with temperature of the electrostatic difference 
of potentials at the points of contact of different 
metals. 
By employing the thermo-electric pile instead of the 
thermometers used by. Thomson, Le Roux has lately 
measured the amount of the specific heat of electricity 
in various metals, and has shown that it is very small, or 
altogether absent, in lead. Strangely enough, though he 
has verified Thomson’s results, he does not wholly accept 
the theoretical reasoning which led to their prediction 
and discovery. 
One of Thomson’s happiest suggestions connected with 
this subject is the construction of what he calls a thermo- 
electric diagram. In its earliest form this consisted 
merely of parallel columns, each containing the names of 
a number of metals arranged in their proper thermo-elec- 
tric order for some particular temperature. Lines drawn 
connecting the positions of the name of any one metal in 
these successive columns indicate how it changes its place 
among the other metals as the temperature is raised. 
Thomson points out clearly what should be aimed at in 
perfecting the diagram, but he left it merely as a pre- 
liminary sketch. The importance of the idea, however, 
is very great ; for, as we shall see, the diagram when 
carefully constructed gives us not merely the relative 
positions of the metals at various temperatures, with the 
temperatures of their neutral points, but also gives graphic 
representations of the specific heat of electricity in each 
metal in terms of the temperature, the amount of the 
Peltier effect, and the electromotive force (and its direc- 
tion) fora circuit of any two metals with given tempera- 
tures of the junctions. In short, the study of the whole 
subject may be reduced to the careful drawing by experi- 
ment of the thermo-electric diagram, and the verification 
of Thomson’s thermo-dynamic theory will then be effected 
by a direct determination either of Peltier effects or of 
specific heat of electricity at various temperatures, and 
their comparison with the corresponding indications of 
the diagram. 
The diagram is constructed so that abscissze represent 
absolute temperatures, and the difference of the ordinates 
of the lines for any two metals at a given temperature is 
the electromotive force of a circuit of these metals, one of 
the junctions being half a degree above, the other half a 
degree below, the given temperature. 
It will be seen by what follows that nothing but direct 
measurement of the value of the specific heat of electricity 
at various temperatures can give us the actual form of the 
line representing any particular metal ; but if the line for 
any one metal be assumed, those of all others follow from 
it by the process of differences of ordinates just described. 
So that it is well to begin by assuming the axis of abscissze 
as the line for a particular metal (say lead, in consequence 
of Le Roux’s result) ; and if, at any future time, this 
should be found to require change, a complex shearing 
motion of the diagram parallel to the axis of ordinates 
will put all the lines simultaneously into their proper 
form. 
Thomson’s theoretical investigation may be put in a 
very simple form as follows :—Let us suppose an arrange- 
ment of two metallic wires, one end of each of which is 
heated, their cold ends being united, and in which the 
circuit can be closed by a sliding piece or ring, always so 
placed as to join points of the two metals which are at the 
same temperature 7. Let E be the electromotive force in 
the circuit, II the Peltier effect, and o,, o, the specific 
heats of electricity in the two metals. Then, if the sliding 
piece be moved from points at temperature ¢ to others at 
t+ 64, the first law of thermodynamics gives by inspec- 
tion the equation pes. 
sE=J (81 + o, - oy 82), 
and the second law gives 
o = 8(%) 4 te, 
These equations show at once that, if there were no 
electric convection of heat, or if ituvere of equal amount 
in the two metals, the Peltier effect would always be pro- 
portional to the absolute temperature ; and the electro- 
motive force would be proportional to the difference of 
temperatures of the junctions ; so that there could not be 
a neutral point in any case. In fact, the lines in the 
diagram for all metals would be parallel: and, on the 
former of the two hypotheses, parallel to the axis of 
abscissee. 
Eliminating o,—c, between the equations, we have 
oE=J 8 
Now, by the construction of the diagram, is the 
difference of the ordinates of the lines for the two metalS 
at temperature 7 Hence, whatever be the form of the 
lines for two metals, the Peltier effect at a junction at 
temperature ¢ is always proportional to the area of the 
rectangle whose base is the difference of the ordinates, 
and whose opposite side is part of the axis of ordinates 
corresponding to absolute zero of temperature. This area 
becomes less and less as we approach the neutral point, 
and changes sign (i.e., 7» ¢usned over) after we pass it ; 
the current being supposed to go from the same one of 
the two metals to the other in each case. 
The electromotive force itself, being the integral of 
aE 
at 
to the area intercepted between the lines of the two 
metals, and ordinates drawn to correspond to the tempe- 
ratures of the junctions respectively. 
between the limits of temperature, is proportional 
Again, the second of the preceding equations shows . 
us that the difference of specific heats in the two metals 
is proportional to the absolute temperature and to the 
difference of the tangents of the inclinations of the lines 
for the metals to the axis of abscissz. If we assume 
this axis to be the line of a metal in which the electric 
convection of heat is wholly absent, the measure of this 
convection in any other metal is simply the product of 
the absolute temperature into the tangent of inclination 
of its line to the axis. ‘Thus, if the thermo-electric line 
for a metal be straight, electric convection is in it always 
proportional to the absolute temperature; and it is 
positive or negative according as the line goes off to 
infinity in the first or in the fourth quadrant. If the 
lines for any two metals be straight, and if one junction 
be kept at a constant temperature, the electromotive force 
will be a parabolic function of the temperature of the 
other juncticn—the vertex of the parabola being at the 
temperature of the neutral point of the two metals, and 
its axis beizg parallel to the axis of ordinates, 
For the benefit of such of my audience as are not 
familiar with mathematical terms, I may give an illus- 
tration which is numerically exact. Let time stand for 
temperature, years corresponding say to degrees. Let 
the ordinate of one of the metals represent a man’s in- 
come, that of the other his expenditure. The difference 
of these ordinates represents the rate of increase of his 
capital or accumulated savings, which here stands for 
electromotive force. As long as income exceeds expen- 
diture, the capital increases ; when income and expen- 
diture are equal (¢.c.) at a “neutral point,” capital remains 
stationary, indicating, in this case, a maximum value ; for 
in succeding years expenditure exceeds income, and 
capital is drawn upon, P, G, TaIt 
(Lo be continued.) 
