Prof. Thomson on the Dynamical Theory of Heat. 525 



Lastly, if we denote by fjt,, as formerly, Carnot's function of the 

 temperature t, we have (§ 21) 



t=« M <«)• 



86. The use that may be made of these formulae in investiga- 

 tions regarding 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 /J,, we may, in the first place, use equations (4) and (5), 

 or the following deduced from them (§ 20), by eliminating e, 



dp (dm d^\ 



lt- d \~dt~lh) (7) ' 



and equation (6), as tests of the accuracy of experimental re- 

 searches on the pressure 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 /x as independent of v, and as 

 the same for all fluids at the same temperature ; and with expe- 

 rimental data of sufficient extent, we may use these equations as 

 means of actually determining the values of J and/u,. No other 

 way than this has yet been attempted for determining /jl ; 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. Carnot's original 

 determination of /j, was effected by means of an expression equi- 

 valent to that of equation (6) applied to the case of a mass of 

 air ; and the determinations by Clapeyron, and those shown 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 capacities 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 he 

 effected by direct experiments on the generation of heat by means 

 of friction. At present we may regard J as known, probably 

 within 7 ^ n of its own amount, by experiments of this kind. 



88. The value of J being known, equations ( 1) and (5) may 

 be used for determining the mechanical energy of a particular 

 fluid mass in different states, from special experimental data 



