16 Mr. Herapath on True Temperature y and the [Jan. 



Article V. 



Tables of Temperature , and a Malhematical Development oj the 

 Canses and Laivs of the Phcenomena which have been adduced 

 in Support of the Hypotheses of ** Calori/ic Capacity, Latent 

 Heatj' Sfc. By John Herapath, Esq. 



(^Concluded from vol. ii. p. 462.) 



Theory of Evaporation. 



Prop. XXIII. Prob. VIII. 



The weights of two quantities of water and steam in contact 

 being given, and their common temperature, it is required to 

 determine the temperature and quantities of water and steam 

 which will result from the mixture with them, in a given space, of 

 a given weight of any other body whose baromerin and temper- 

 ature are known ; no chemical action being supposed to take 

 place. 



In the solution of this problem, we suppose no foreign 

 cause to influence the results either by " radiation " or other- 

 wise. 



Case 1 . — Let us conceive the matter of the vessel to have no 

 effect. Put W, w, and t, for the primitive weights of water and 

 vapour and their common temperature ; and let Q, q, t, and Q', 

 denote the weight, baromerin, temperature, and volume or mag- 

 nitude of the other body. Let also W denote the weight of 

 water after the mixture, and r its temperature. Then by the 

 principles we have already demonstrated 



T(Qq+ 11 W + Uw^iW) = Qqt' 4-(6W4-ll^)^....A 



Again : suppose v be the volume of unity weight of water at 

 the temperature T, and that it becomes v + -^ {r — T) ot any 

 other temperature t ; then we havejW v + W^^^ (t •— T) for the 

 volume occupied by the water in the mixture. In the same 

 manner, if r u represent the volume of unity weight of vapour 



at the temperature T and elasticity E, we shall have ^— ^ 



r V (W -i- w — WO for the volume of vapour in the mixture by 

 Prop. 15 of the present paper, and the Theorem in the Annals 

 ror July, 1816. Whence putting S for the given space in which, 

 the mixture is made, we have, by thequestion, supposing Q' at 

 the temperature t becomes Q' + % (t— O X (t— /0 + Q' + 



W'-fv -f 4^(t-T)} + ^^rt;(W + w -WO = S B. 



Eliminating from A and B the quantity W"', we shall have an 



