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XVI. On the Heat of Vapours. 

 By Sir J. Lubbock, Bart.^ F.R.S.* 



T ET V be the quantity of absolute heat, considered as a 

 -■-' function of the sensible heat or temperature 9, 



p being the density, p the pressure, k and u constants, 

 dp _ «p dp _ up 



dQ~~ l+uQ dS "" l+«fl* 



If c is the specific heat of a gas, the pressure being con- 

 stant, and Cf its specific heat when the volume is constant, so 

 that 



_dFdp _dfd^ _£ 



"""dpdfl ""''dpdQ '^^ c, 



dV dV ^ 



^d7+y^d^=^- 



Laplace evidently considered 7 constant, and he integrated 

 this equation upon that hypothesis, " En supposant cette quan- 

 tite rigoreusement constante, &c.," Mec. Cel. vol. v. p. 127. 

 Again, Poisson, in repeating the same theory, Traite de M^c, 

 vol. ii. p. 6^Q, "En regardant y comme une quantite constante, 

 &c." If y is constant, 



2. 

 V=A + B^^=A + B-(-+^p^-\ 



p a \u / 



(see vol. xviii. p. 507) which is identical with the equation 

 given in the Comptes Rendus, Seance de 31 Mai 184'7, p. 920, 



q=m-\-n{a-\-t)p-'^, 



m — A, n= — , a= —, t=9. 2;=! , A: = y; 



a. a. y 



but if, as Professor Holtzmann maintains (see Taylor's Sci- 

 entific Memoirs, vol. iv. part 14), z is variable, the integral 

 of Laplace does not necessarily obtain, nor does the equation 

 {Comptes Rendus, p. 920) 



obtain ; because if s is a function of t, 



-^^^7ip-^-n{a-\-t)p-<'\ogp-^, 

 * Cuiumunicated by the Author. 



