70 



3. Those which would be true for every fluid subject to those 

 laws of density, if " Mayer's hypothesis," that the heat evolved by 

 compression, when the temperature is kept constant, is the exact 

 equivalent of the work spent in the compression, were true for any 

 one such fluid. 



The principal formulas of the first class are two which express re- 

 spectively the quantity of heat evolved by the compression, by uni- 

 form pressure in all directions, of any substance whatever, kept at 

 a constant temperature ; and the total quantity of heat evolved by 

 a given quantity of fluid forced through a small orifice, before it 

 attains to precisely its primitive temperature. 



The former of these formulae reduces itself to 



E 



H= ~7T— tt-nW 



where W is the mechanical work spent in the compression, and H 

 the quantity of heat emitted, for any fluid subject to Boyle's and 

 Dalton's laws. This formula was first given in the Appendix to the 

 author's Account of Carnot's Theory, — where it was shown to fol- 

 low from Regnault's observations on the pressure and latent heat of 



saturated steam, that t=; cannot be nearly constant for all 



temperatures, if the density of saturated steam fulfils Boyle's and 

 Dalton's laws ; but that the value of this expression is very nearly 

 J, the mechanical equivalent of a thermal unit, for ordinary atmo- 

 spheric temperatures. Hence this theory, and the assumed density 

 of saturated steam, are in full agreement with Joule's experiments 

 which establish as approximately true for atmospheric temperatures 

 the hypothesis which was assumed irrespectively of experimental 

 verification, by Mayer. 



The other formula mentioned above becomes, for a fluid subject to 

 the "gaseous" laws, — 



H= < — ^^— } p u log — 



where p is the uniform pressure in one portion of a long tube ; 

 p' the uniform pressure in another portion, separated from the 

 former by a piece of tube containing a partition with a very small 

 orifice ; t the temperature of the entering fluid up to the locality 



