upon the Freezing of Fluids. 549 



fluid and partly with a vaporiform body ; and then, instead of per- 

 mitting a fresh portion of the fluid to evaporate, to allow a por- 

 tion of it to freeze, &c. 



One of the two principal equations deduced therefrom was— • 



r=A(« + 0(s-<^)|; (Va) 



and this holds good for the freezing also, p and t again denoting 

 the pressure and temperature, and or the volume of a unit of 

 weight of the fluid, whereas s denotes the volume of a unit of 

 weight of a solid body (instead of vapour, as in the former case), 

 and r the latent heat of the freezing (instead of the evaporation). 

 The latter, however, must be here taken as negative, because by 

 freezing, heat will be liber'ated, and not rendered latent. We 

 have therefore — 



dt _ K{a + t)[s-a) 



dp~ r ^ ^ 



Let the value of -r-, given by Joule in his last investigation* as 



the most probable result of all his experiments, that is 423'55 

 (772 English), be here substituted, as also for a the number 

 273; further, with regard to the water, ^=0, r=79, o-«: 0*001, 

 and 5=0'001087 ; and, finally, let jo be expressed in atmospheres 

 pressing upon, a square metre, instead of in kilogrammes, we 

 then obtain — 



^ = -0-00733, 

 dp 



which may be regarded as equal to the value calculated by 

 James Thomson, and corroborated by William Thomson, namely 

 -00075. 



The other principal equation deduced from the maxim on the 

 equivalence of heat and work was — 



| + c-A=A(.-.)|. . . . . (III.) 



To apply this to the case of freezing, besides their former 

 meaning, w^e must regard c and h as two quantities which diffbr 

 from the specific heat of the fluid and solid body only so far as 

 they express, not the heat which must be imparted to a body 

 when it is simply warmed, but that which is necessary when 

 the pressure varies with the temperature in the manner indi- 

 cated by equation (I.). This difi'erence cannot be considerable, 

 as Regnaultf has found that water, by an additional pressure 



* Phil. Trans, of the Royal Society of London for the year 1850, Part L 

 p.61. 



t Mem. de VAcad. de VInst. de France, vol. xxi. Mem. VII. 



