1829.] 
On the Scale of Temperature. 
273 
forerejectliquids altogether, as forming, by their expansion, a just and true measureof 
temperature. This they seek in the expansion of gaseous bodies — a class, the mem - 
hers of which have one property in common that seems to give them a claim to he 
singled out. It is this 7 every known gas, has the same rate of expansion for the same 
difference of temperature. Now it cannot he denied, that this fact does appear to 
promise a greater simplicity in the laws of heat when deduced from the affections of 
these bodies, than if they were referred to solids or liquids, the expansion of which 
are so extremely discordant, that probably no two bodies in either of those states have 
the same rate of expansion. 
The theorem already referred to, which gives the arithmetical mean, 83 the true 
temperature of a mixture, is then adopted as the basis of the system. .Equal weights of 
gas, at different temperatures, being supposed to be mixed, the temperature of the 
mixture is considered the middle point. Thus air at 32° lias a volume = to 1, at 392 
it has a volume = 1,75. These two being mixed, the volume is evidently 2,75, and 
that of each portion 2,75-r2 = 1,375. The temperature is 212°, as measured by the 
common thermometer. It is on this principle that the graduation of the air ther- 
mometer is founded. Equal differences of temperature are not supposed to be ac- 
companied by proportional changes of volume, but the increments of temperature 
and volume, it is concluded, both form an arithmetical series. 
It appears to me to be a question to which there is no very decisive reply, which 
is the more just method of estimating the temperature ; by proportional changes of 
volume, or by equal differences. The latter leads to an absurd result, when we in- 
quire, what is "the volume at 448°; for it would appear to be 0, and at any temperature 
under that the volume ought to be leu than 0. By the method of proportional vo- 
lumes, we avoid this absurdity ; for, however low the temperature he taken, there 
would still be volume. There is another objection to this method of estimating the 
temperatures, which as I have never seen noticed, I will say a few words about. It is 
assumed, that the temperature of a mixture is the mean of the original temperatures. 
Now, however this be with regard toliquids, I think it quite clear that it cannot hold 
with regard to gases : and the following considerations will probably he sufficient to 
establish tlie truth of the opinion. 
I suppose we have mixed two equal portions of gases, having temperatures of 32® 
and 392°, their volumes being 1, and 1,75, and that their resultingvolume and temper- 
ature are 1,375 and 212°, the arithmetical means. Now in thigease, I say, that the gas 
at 32* has received more heat than the one at 392° has lost ; and consequently, that 
180” between 32° and 212* indicates more heating power than 180* between 212* 
and 392°. 
The gas which originally had a volume of 1, has expanded to 1,375. Its density 
has then been diminished in the ratio of 1,375 to 1- But we know, that when the 
density of air is diminished in the proportion of 30 to 29,7, heat is absorbed, which 
would have raised the temperature 1°. In other words, two portions of a gas having 
these densities will have their temperatures in equilibrium, though differing by 1*. 
The gas originally at 32° had, then, in expanding to 2,3/5, absorbed 32 . But that 
which was at 392° has only given out 24°. So that heat which would have raised the 
temperature of one of the gases 8° has disappeared ; and the arithmetical mean is 
evidently half this quantity lower than the true mean temperature, the latter being 
on Fahrenheit's scale 216°. This unequal partition of the latent heat of expansion, 
as it has been called, renders elastic fluids much less proper for the application of 
this theorem than liqnids. The latter being incompressible, or nearly so, must have 
always the same temperature when in communication. 
But it has been said, that their specific heat varies. This, as I before noticed, is 
merely to say, that in mixtures the arithmetical mean of Fahrenheit’s temperatures 
is not the resulting one. If they all agree in this respect, as the writer I have re- 
ferred to asserts, it must be admitted, that it is the thermometer and not the fluid 
which departs from the general law. His experiments certainly bear him out in his 
opinion, as far as mercury is concerned. With regard to other fluids, we have none 
to refer to. Nothing is more extraordinary than the fact, that though the thermo- 
meter has been invented so many years, it should be still it dispute whether two por- 
tions of mercury when mixed together give the arithmetical mean of their temper- 
atures. In other words, whether equal expansions arepndicativeof equal increments 
of heat. The usual argument that it does so, because it corresponds pari passu with 
an air thermometer, will not hold, as I have already shown. For air in doubling it 
volume from heat absorbs at the same time 50°. So that in being cooled down to it 
original temperature it would give out, not 448* as usually supposed, but 498°. 
