238 Intelligence and Miscellaneous Articles. 



bodies exercises an influence on the elastic force of the vapours 

 emitted by them in vacuo at the same temperature." The conclu- 

 sion deduced from M. Regnault's experiments is the following : — 

 " that the molecular forces which determine the solidification of a 

 substance do not exercise any sensible influence on the tension of 

 its vapour in vacuo ; or, more exactly, if an influence of this kind 

 exists, the variations it produces are so slight that they could not 

 be certainly established in our experiments." It must, however, 

 be added that monohydrated acetic acid forms an exception; 

 Regnault attributes this anomaly to impurity of the acid. 



Let us see what the preceding theory indicates in this case ; we 

 have to do with very small differences. We will take the exact 

 formula*. Suppose the vapour-tensions equal in the two condi- 

 tions, p=p K , then v=v', q — 0, and, taking into consideration equa- 

 tions (4), 



q=(*'-iOa(t|L+*-p). 



Take as an example the melting of ice at zero under the pressure 

 of the atmosphere. The substance M represents the ice at zero ; 

 M', the liquid water at zero. The ice in melting absorbs heat ; Q 

 is positive, u'—u negative, the parenthesis positive ; therefore the 

 hypothesis p=p' conducts to an inadmissible conclusion. 



Thus ice and liquid water, both at zero, have different vapour-ten- 

 sions. The difference is very small ; the approximate formula (5) 

 shows it readily. The term KTvp is very considerable in compa- 

 rison with Q, so that^> andp' differ very little. This result is en- 

 tirely conformable to the latter part of M. Eegnault's conclusion. 



Allotropy. — According to the experiments of MM. Troost and 

 Hautefeuille f , ordinary phosphorus at the temperature of 360° has 

 a vapour-tension =3*2 atmospheres. This vapour, under the pro- 

 longed action of heat, deposits red phosphorus ; and the trans- 

 formation ceases when the tension of the vapour takes the minimum 

 value 0*6 atm., which MM. Troost and Hautefeuille have named 

 tension of transformation. This minimum tension may be regarded 

 as the maximum tension of the vapour of red phosphorus at the 

 temperature of the experiment. Supposing, then, white phosphorus 

 to correspond to the first state, M, red phosphorus to the second, 

 M', we have 



T=273 + 360, ^ = 3-2 atm., _p' = 0-6 atm.; 



according to MM. Troost and Hautefeuille, at 440°, or 



T=2734-440, p = 7*5 atm., p' — 1-75 atm. 



The weight of the litre of phosphorus-vapour which remained in the 

 state of vapour at 360° after 240 hours of heating was 1*4 gramme ; 

 therefore the specific volume of the vapour of red phosphorus at 



* Comptes Rendus, vol. lxxvi. p. 7G. t Ibid. 



