514 On the Steam and Hoar-frost Lines of Water-substance. 



P"o( w/ o~- ?/ o) is (lone on tlie mass# Hence 

 (^o-^ / o)(^o<-/o) = (^o-^(^o^o)+J ? o+/ / oO / o-- w o)- 



But, by the above assumption, V f =v a.n&p' =p Q =*2?"o > aiso 

 z/ and u Q may both be neglected in comparison with v , of 

 which they are less than the 200,000th part. The equation 

 in its simplified form therefore becomes 



"UT — -arrr— — — • 



A numerical value for this difference is thus found : if the 

 pressure of 1 millim. of mercury be taken as unit pressure, 



then J = f||§ = 31-153; also l =80, * =273°*7, t< = 209*9 



(calculated by theory) ; whence ^=0'043. M. KirchhofF 



remarks : — " This difference is too small to be safely inferred 

 from Regnault's experiments. It is interesting, however, to 

 remark that a difference of the same sign and order of mag- 

 nitude as the theory requires is furnished by the numbers 

 which Regnault gives as the results of his experiments." For 

 M. Regnault's empirical formula for the pressure of steam 

 over ice gives < bt / = 0*361 ; and that for the pressure of 

 steam over water gives nr = 0*329; whence 's/q— «r = 0*032. 

 The lines therefore cut each other ; and the angle of intersec- 

 tion is re-entrant downwards as vr < vrj. M. Kirchhoff's 

 numbers do not agree so well as the above, since he assumed 

 that both the above empirical formula? give the same value for 

 p at 0° C, whereas the one gives 4*610 and the other 4*600. 



M. Moutier has lately taken up the same line of reasoning, 

 in a paper, " Recherches sur les vapeurs emises a la meme 

 temperature par un meme corps sous deux etats diffe rents," 

 published in Annales de Chiraie et de Physique, [5] i. (1874) 

 p. 343. He has, however, assumed that -sr^-cr; whence it 

 would follow that at no temperature could water and ice have 

 the same vapour-tension. This mistake has been corrected in 

 the 'Proceedings' of the Royal Society, 1874, xxii. p. 461, by 

 Prof. Riicker, who reasons from Prof. James Thomson's con- 

 clusions, but without exactly reproducing M. KirchbofTs 

 result. 



May 15th, 1877. 



