Te ewe) eee oe « &- Cea et eee = 
me ‘s sh 7”; ; + aa 2 Bn ee 
122 
THERMO-ELECTRICITY * 
Il. 
Sb Eote by considerations of Dissipation of Energy, I 
was led some years ago to the hypothesis that specitic 
heat of electricity must be, like thermal and electiic 
resistance, directly proportional to the absolute tempe- 
rature. If this were the case, the lines in the diagram 
would be straight for all metals; and parabolas would be 
the graphic representation not only of electromotive force, 
but of the Peltier effect,in terms of the temperature of a 
junction. And I found by actual measurement of curves 
plotted from experiment, that, within the range of mercury 
thermometers, the curves of electromotive force for junc- 
tions of any two of iron, cadmium, zinc, copper, silver, 
gold, lead, and some other metals, are pirabolas with 
their axes vertical; the differences from parabolas being 
in no case greater than the inevitable errors of experi- 
ment and the deviation of mercury thermometers 
from absolute temperature. If, then, the line for 
any one of these metals be straight within these limits of 
temperature, so are those of all the others. This makes 
the tracing of the diagram within these limits a very 
simple matter indeed. And an easy verification is fur- 
nished by the fact that from the parabolas for metals 
A and B, and A and C, we can draw the lines for Band C, 
assuming any line for A; and we can then compare the 
temperature of the intersection of these lines with that of 
the neutral point of B and C as found directly. Another 
verification is supplied by the tangents of the angles at 
which these parabolas cut the axis of abscissze, for the 
sum of two of them ought in every case to be equal to 
the third. 
In fact, if we assume, in accordance with what has been 
said above, 
o, = kt, og = he, 
where /, and #, are constants, Thomson’s formule give 
at once 
T= — |e — baat, 
or 
TT = (4, — Ay)(Ty,2 — 2)¢ 
where T,,. (the constant of integration) is obviously the 
temperature of the neutral point. 
Also 
E=J [Fat = 3-4) [Tye - Dat 
JA 42) — 2,)(Tie 
where /, is the temperature of the cold junction. This is 
the parabolic formula already mentioned. 
Comparing with the parabola as given by observation 
we get the values of #, — #, and Ty». Similarly we obtain 
ky — Ag and Ty,; Hence we may calculate #, — #,, and 
(by the second equation above) the value of T,,, from the 
relation 
(4 - hy) Ty + (4, — ,)T 235 + (43 — Ay)T 4,3 =0. 
Thus we have the means of verification above alluded 
to—for the equation just written expresses the relation 
between the tangents of the angles at Which the three 
parabolas cut the axis of absciss@. . 
[It is to be remarked that if the circuit consist of one 
and the same metal, we have 
ky = ky, T = &, (4, — &y)T = 7 suppose, 
whence I = r/, 
which shows that the electric convection of heat may be 
regarded as an infinitesimal case of Peltier effect between 
adjacent portions of thé same metal at infinitesimally 
different temperatures. : 
Also, on the same hypothesis, we have 
i) eee Be Fee ee 
which seems to accord with the result of some experiments | 
* Abstract of the Rede Lecture, concluded from p. 88. 
NATURE 
| come there will be a maximum of capital, then a poi 
| Sune x2, 1873 4 
made for me by Mr. Durham, in which the deflection due 
to the contact of the hot and cold ends of the same wire 
was shown to be proportional to the difference of ternpe- 
ratures and independent of the actual temperature of 
either. ] 
Endeavouring to extend the investigation to tempera- 
tures beyond the reach of mercury thermometers, I 
worked for a long time with a smull air-thermometer, of 
which the principle was suggested to me by Dr. Joule. 
Butthis involved very great experimental difficulties, due 
mainly to chemical action at high temperatures ; and, after 
much unsatisfactory work, | reselved to make one thermo- 
electric junction play the part of thermometer in observing 
the indications of another. In fact, an exceedin ly ele-. 
gant result follows at once from the preceding formula, if 
we suppose the specific h at of electricity to be propor- 
tional to the absolute temperature in each of four metals, 
and then draw a curve whose ordinate ani abscissa are 
the simultaneous galvanometric indications of pairs of — 
these metals, with their hot and cold junctions respec- 
tively at the same temperatures. For if r be the diffe- 
rence of absolute temperature of the junctions, we have 
x= Ar-+ Br 
y = Cr+ Dr 
where the four constants depend upon the nature of the 
metals and upon the absolute temperature of the cold 
junction, These equations give 
(Da — By)? = (CB — AD) (Ca — Ay) 
which is the equation of another parabola, also passing 
through the origin, but with its axis no longer vertical, 
A simple proof of this theorem is turnished by the 
motion of projectiles in vacuo, Supposea particle to move 
under gravity, and subject, besides, to another constant 
force parallel to a given horizontal line—its path 
would have both ordinate and abscissa parabolic functions 
of the time. But its path might also be found by com- 
pounding into one the two accelerations, and as each of 
these is constant in direction and magnitude, their 
resultant will have the same property, and thus the 
resultant path is a parabola. Tried in this way through 
ranges of temperature up to a red heat, I found that 
while some pairs of circuits gave excellent parabolas, 
others were far from doing so, sometimes in fact giving 
curves with points of contrary flexure. I was on the 
point of recurring to the air-thermometer, when I noticed: 
that in nearly every case in which the curve was not a. 
parabola, tron was one of the metals employed ; and, b 
the help of some alloys of platinum, I was enabled to get 
an idea of the true cause of the anomaly, and afterwards 
to verify it by an independent method. The cause is 
this, that while, as Thomson discovered, the specific heat 
of electricity in iron is zega¢ive at ordinary temperatures, 
it becomes Positive at some temperature neat low ted 
heat ; and remains positive till near the melting point of 
iron, where it appears possible, from some of my experi- 
ments, that it may again change sign. Thus the line for 
iron, straight at ordinary temperatures, passes downwards 
from the first quadrant to the fourth, and thence rises into 
the first again. yA 4 
To recur to our analogy, an income represented by the 
iron line is one which for a number of yeats steadily 
diminishes, reaches a minimum, and then steadily in- 
creases. If this be associated with a steady expenditure, 
the fluctuations of capital will depend upon the compara- 
tive values of the expenditure and the minimum income, 
If the expenditure be less than the minimum income, the 
capital will go on increasing slower and slower to a certain. 
point, then faster and faster; there will be no stationary 
point, but there will be a point of contrary flexure. If 
the expenditure be just equal to the minimum income, 
the point of contrary flexure will be also a stationary, 
point. If the expenditure be greater than the minimu 
