MR W. J. MACQUORN RANKINE ON THE DENSITY OF STEAM. 149 



namic function f and that by its use, and by making k=0, equation 1 is 

 reduced to the simplified form, 



-5Q' = r5?)-|i5r; (5.) 



but the following notation is more convenient : Let ^h denote the whole 

 heat absorbed by the substance^ not in units of mechanical energy, but in 

 ordinary thermal units, and J the value of an ordinary thermal unit in 

 units of mechanical energy, commonly called " Joule's Equivalent," so 

 that 



then the general equation of thermodynamics takes the form 



Jdh=Td<p (6.) 



6. For the purposes of the present paper, the most convenient form of the 

 thermodynamic function is that given in the second line of Equation 4 ; but it 

 may nevertheless be stated, that in a paper read to this Society in 1855, and 

 which now lies unpublished in their archives, it was shown that another form of 

 that function, viz. 



p=:(fe + ^«)hyp.logr-/^P, .... (7.) 



P V 1 



was useful in solving certain questions ; ° ° denoting the same thing with ^-^ 



in Equation 1. 



Application of the General Equation of Thermodynamics to the Latent Heat and Density 



of Steam. 



7. At the time when the general equation (1.) was first published, suflQcient 

 experimental data did not exist to warrant its application to the computation of 

 the density of a vapour from its latent heat. But very soon afterwards, various 

 points, which had previously been doubtful, were settled by the experiments of 

 Mr Joule and Professor William Thomson ; and in particular Mr Joule, by his 

 experiments published in the " Philosophical Transactions" for 1850, finally de- 

 termined the exact value of the mechanical equivalent of a British unit of Heat, 

 to which he had been gradually approximating since 1843 — viz., 



J = 772 foot-pounds ; 



and Messrs Joule and Thomson in 1851, 1852, and 1853, made experiments on the 

 free expansion of gases, especially dry air, and carbonic acid, which established 

 the very near, if not exact, coincidence of the true scale of absolute temperature 

 with that of the perfect gas-thermometer ; that is to say, those experiments 

 proved that k in the equation (1.) is sensibly =0. When, with a knowledge of these 

 facts, equation (1.) is applied to the phenomenon of the evaporation of a liquid 



