435 
and on Astronomical Refractions. 
If 5 be the temperature as indicated by a thermometer, there can 
be little doubt that V is capable of being expressed in a series 
proceeding according to positive powers of so that 
+ + &c. 
a^ b, c, &c., have a certain signification in Taylor’s theorem, but 
without being able to determine their values, d priori, or to obtain 
any relations between them, they may be treated as constants. If 
the latent heat be constant, which is probable, and if the effect 
indicated by the thermometer is proportional to the sensible heat, 
c — h S, V = a b L 
It must, however, be left to experiment to decide how many 
terms are to be taken into account for any given substance, within 
any given range of the thermometric scale, and in order to satisfy 
the results of observation within any given quantity. The other 
suppositions upon which my theory is founded are those of Laplace, 
viz. that the quantity called y by M. Poisson is constant for the 
same substance at different temperatures, and that the equation 
V=: A + B 
rp y 
is the solution of a certain differential equation. See Mec. Cel., 
vol. V. p. 108. Poisson, Mec., vol. ii. p. 640. 
The theorems which are given by M. Poisson in the second vo- 
lume of the Mecanique, and which are also to be found in the 
works of Pouillet and Navier, rest upon the condition that the ab- 
solute heat is constant, v/hile the sensible heat varies. This is the 
most restricted hypothesis which can be made upon the nature of 
heat, and it does not satisfy the observations. In this Treatise I 
have gone a step further, by supposing the absolute heat to vary 
with the sensible heat, or to be represented by an expression 
of the form « + 5 0, (or what is the same, F=C+Z)(l+a0). 
See p. 2.) 0 being the temperature reckoned from some fixed point, 
a and b constants. This includes implicitly the other hypothesis, 
which if true, in determining a and b by means of observations, 
the constant b should come out zero. This in the case of steam 
is certainly not the case, nor is it so in any case which I have 
examined. 
The experiments of Dulong and Arago upon steam at high 
temperatures, those of Southern and Dalton, and those of Dr. Ure, 
furnish data by which the supposition I have adopted and the for- 
mulae which flow from it can be scrutinized ; and if the expres- 
sions which result from it fail to represent those observations, we 
have at least arrived at this conclusion, that the condition of the 
invariability of the quantity called y by M. Poisson does not ob- 
