
DYNAMIUVAL THEORY OF HEAT. 477 
Bee ae ee se sem). 
Lastly, if we denote, as formerly, Carnot’s function of the temperature ¢, by 4, we 
have ( § 21) 
Bogen Doeeh 4d hinor einlaae seins) oc) tear 
86. The use that may be made of these formule in investigations of the physical 
properties of any particular fluid must depend on the extent and accuracy of the 
general data belonging to the theory of the mechanical action of heat, that are 
available. Thus, if nothing be known by experiment regarding the values of J 
and /, we may, in the first place, use equations (4) and (5), or the following de- 
duced from them ( § 20) by eliminating e, 
dp_ qdM dN : 
i J (G- =) : : : : , é ¢ (7); 

and equation (6), as tests of the accuracy of experimental researches on the pres- 
sure and thermal capacities of a fluid, on account of the knowledge we have from 
theory, that J is certainly an absolute constant, and that, in all probability if not 
with absolute certainty, we may regard jas independent of v, and as the same for all 
fluids at the same temperature; and, with experimental data of sufficient extent, 
we may use these equations as means of actually determining the values of J and 
#. No other way than this has yet been attempted for determining » ; and, if we 
except a conceivable but certainly not at present practicable mode of determining 
this element by experiments on thermo-electric currents, no other way is yet 
known. Carnor’s original determination of 4, was effected by means of an expres- 
sion equivalent to that of equation (6) applied to the case of a mass of air; and 
the determinations by CLarryron, and those shewn in Table I. of my Account of 
Carnot’s Theory, were calculated by the formula which is obtained when the 
same equation is applied to the case of a fluid mass, partly liquid and partly in 
the state of saturated vapour (§ 55). 
87. As yet experiments have not been made on the pressure and thermal ca- 
pacities of fluids to a sufficient extent to supply data for the evaluation, even in 
the roughest manner, of the expression given for J by equation (7); and it may be 
doubted whether such data can even be had with accuracy enough to give as exact 
a determination of this important element as may be effected by direct experi- 
ments on the generation of heat by means of friction. At present we may regard 
J as known, probably within ,1, of its own amount, by experiments of this kind. 
88. The value of J being known, equations (4) and (5) may be used for deter- 
mining the mechanical energy of a particular fluid mass in different states, from 
special experimental data regarding its pressure and thermal capacities, but not 
necessarily comprehending the values of each of these elements for all states of 
the fluid. The theory of the integration of functions of two independent variables 
