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



274°'6 Cent, below that of melting ice, but which is now considered to 

 be more nearly at 274° Cent., or 493°-2 Fahr. below that temperature. 



K, A constant, expressing the height on the thermometric scale of the tem- 

 perature of total privation of heat above the zero of gaseous tension. 

 This constant was then only known to be very small ; according to later 

 experiments, it is either null or insensible. 



wM, The ideal or theoretical weight, in the perfectly gaseous state, of an unit 

 of volume of the substance, under unity of pressure, at the temperature 

 of melting ice. 



C, The absolute temperature of melting ice, measured from zero of gaseous 

 tension (that is to say, according to the best existing data, C = 274' Cent, 

 or 493°-2 Fahr.) 



V, The actual volume of unity of weight of the substance. 



^V, An indefinitely small increment of that volume. 



Bt, An indefinitely small increment of temperature. 



U, A certain function of the molecular forces acting in the substance. 



+ 3Q', The quantity of heat which apj^ears, or -^Q', the quantity of heat 

 which disappears during the changes denoted by ^V and ^t, through the 

 actions of molecular forces, independently of heat employed in producing 

 changes of temperature ; such quantity of heat being expressed in equiva- 

 lent units of mechanical energy. 

 The equation having been given in the above form, it is next shown (in the 

 same volume, p. 1G3), that the differential co-eflQcients of the function U have 

 the following values : — 



'5?4-°'<^ w 





'tfi'^-f^ w 



4. The physical law of which the general equation just cited is the symbolical 

 expression, may be thus stated in words: — The mutual transformation of heat 

 and mechanical energy during any indefinitely small change in the density and tem- 

 perature of an elastic substance, is equal to the temperature, reckoned from the zero 

 of absolute cold, multiplied by the complete differential of a certain function of the 

 pressure, density, and temperature; which function is either nearly or exactly equal 

 to the rate of variation with temperature of the work performed by indefinite expan- 

 sion at a constant temperature. 



5. It may be remarked, that the quantity, — 



9 = Ji hyp. log. ^ + Q^ (byp. log. V-U) = ft hyp. log. r +J-^^ dY . . (4.) 



(ft being the real specific heat of the substance in units of mechanical 

 energy), is what, in later investigations, I have called the " thermody- 



