428 Prof. Thomson on the Dynamical Theory of Heat. 

 the equations 



(^+^)m 



1 



• w 



r i-_J__ i+Exioo p^ 



'-°'-' ~ 1693-5 ■ i+E^ "nj 



where \jjC\ denotes the quantity tabulated for the temperatures 

 0°, 1°, 2°, ... 230° in Table I. of my Accomit of Cavnot's Theoiy ; 

 and [(j] denotes the density of satm-ated steam which was 



assumed in the calculation of that table, the values of ^ in the 



expression for it being obtained by dividing the numbers tabu- 

 lated at the end of Eegnault's eighth IMemoii-e by 760. The 

 considerableness of the deviations from the gaseous laws which 

 equation (11) indicates, is seen at once by comparing the num- 

 bers in column 2 with those in column 3 of the preceding table, 

 and observing that the coefficient of [a] in (II) is, for each tem- 

 peratm-e shown in that table, obtained by dividing the corre- 

 sponding number in column 2 by that in column 3. Column 4 

 shows what the values of fi would be if the density of saturated 

 steam at 100° were -—^ instead of jgijrj, and, for other tempe- 

 ratures, varied according to the gaseous laws. 



68. This subject has been very carefully examined by Clausius, 

 who has indicated the great deviations from the gaseous laws of 

 density that Mayei-'s h's^othesis requires in saturated steam, and 

 has given an empirical formula for the density of saturated steam 

 founded on that h}q5othesis, and on Eegnault's observations on 

 the pressure and latent heat. In this direction theory can go 

 no further, for want of experimental data ; although, from what 

 we know of gases and saturated vapoiu'S, it may be doubted 

 whether such excessive delations, in the case of steam, from the 

 laws of a " perfect gas " are rendered probable by a hj^othesia 

 resting on no experimental evidence whatever*. 



69. To Joule v>t are indebted for a most important series of 

 experimental researches on the relation between the thermal 

 eflFects, the external mechanical effects, and the internal mecha- 

 nical effects {vis viva destroyed by fluid friction) due to com- 

 pressions and expansions of air in various circumstancesf. These 



* Joule's experimental verification of Mayer's law for temperatures of 

 from 50° to 60 Falu*. shows, if rigorously exact, that the density of satu- 

 rated steam at about 10° Centisrade must be ' ^^ ', of what was assumed for 



it in the calculations of my former paper, but docs not go towards indica- 

 ting any deviation from tlie gaseous laws of variation in the density of satu- 

 rated steam at different temperatures, 

 t Philosophical Magazine, May 1845. 



