THERMAL EFFECTS OF FLUIDS IN MOTION. 
347 
with the following equations for calculating p and the terms involving (3 and <y ; 
logio P~ a ~ t + 274-6~(274‘6 + t) 2 ’ 
a=4-950433+log 10 21 14 = 8-27 5 5 38 
log 10 ^ = 3-1851091, 
log 10 7=5-0827176. 
The densities of saturated steam calculated for any temperatures, either by means 
of this formula, or by the expression given above, with the assistance of the Table of 
values of [W], are the same as those which, in corresponding on the subject in 1848, 
we found would be required to reconcile Regnault’s actual observations on steam 
with the results of air-experiments which we then contemplated undertaking, should 
they turn out, as we now find they do, to confirm the relation which the air- 
experiments of 1844 had approximately established. They should agree with results 
which Clausius* gave as a consequence of his extension of Carnot’s principle to the 
dynamical theory of heat, and his assumption of Mayer’s hypothesis. 
Section III. Evaluation of Carnot’s Function. 
The importance of this object, not only for calculating the efficiency of steam- 
engines and air-engines, but for advancing the theory of heat and thermo-electricity, 
was a principal reason inducing us to undertake the present investigation. Our pre- 
liminary experiments, demonstrating that the cooling effect which we discovered in 
all of them was very slight for a considerable variety of temperatures (from about 
0° to 77° Cent.), were sufficient to show, as we have seen in §§ I. and II., that 
must be very nearly equal to the mechanical equivalent of the thermal unit; and 
therefore we have 
— approximately, 
H t 
E 
or, taking for E the standard coefficient of expansion of atmospheric air, ‘003665, 
J 
^ 272-85 + / 
At the commencement of our first communication to the Royal Society on the 
subject, we proposed to deduce more precise values for this function by means of the 
equation 
J JK8— (FV'— PV)+tg . 
(M. dw 
dt 
r*v’ 
where w=z j P^ v ’ 
* Poggendorff’s Annalen, April and May 1850. 
2 y 2 
