350 
MR. J. P. JOULE AND PROFESSOR THOMSON ON THE 
when substituted in the general expression for gives 
From this we find, with the data of the eight experiments just quoted, the following 
values for - at the temperature 16° Cent., 
289-044, 289-008, 288-849, 289-112, 28878 7, 288*722, 288*505, 288*559, the 
mean of which is 288"82, 
giving a correction of only -03 to be subtracted from the previous approximate 
estimate E+*‘ 
It should be observed that Carnot’s function varies only with the temperature ; and 
therefore if such an expression as the preceding, derived from Mr. Rankine’s formula, 
be correct, the cooling effect, h, must vary with the pressure and temperature in such 
a way as to reduce the complex fraction, constituting the second term, to either a con- 
stant or a function of t. Now at the temperature of our experiments, c) is very approxi- 
mately proportional simply to P— P', and therefore all the terms involving the pressure 
in the numerator ought to be either linear or logarithmic ; and the linear terms should 
P 
balance one another so as to leave only terms which, when divided by log p, become 
independent of the pressures. This condition is not fulfilled by the actual expression, 
but the calculated results agree with one another as closely as could be expected from 
a formula obtained with such insufficient experimental data as Mr. Rankine had 
for investigating the empirical forms which his theory left undetermined. We shall 
see in Section V. below, that simpler forms represent Regnault’s data within their 
limits of error of observation, and at the same time may be reduced to consistency 
in the present application. 
As yet we have no data regarding the cooling effect, of sufficient accuracy for 
attempting an independent evaluation of Carnot’s function for other temperatures. 
In the following section, however, we propose a new system of thermometry, the 
adoption of which will quite alter the form in which such a problem as that of 
evaluating Carnot’s function for any temperature presents itself. 
Section IV. On an absolute Thermometric Scale founded on the Mechanical Action 
of Heat. 
In a communication to the Cambridge Philosophical Society* six years ago, it 
* “ On an Absolute Thermometric Scale founded on Carnot’s Theory of the Motive Power of Heat, and 
calculated from Regnault’s observations on Steam,” by Prof. W. Thomson, Proceedings Camb. Phil. Soc. 
June 5, 1848, or Philosophical Magazine, Oct. 1848. 
