666 SCIENCE PROGRESS 



represented by points along a third dotted line 78. The tem- 

 peratures at which the pressures are equal are known, and thus 

 the line can be drawn. 



A remarkable feature of these three dotted lines is that they 

 are all in the same direction, a fact which indicates that the 

 volumes represented by points of intersection of the dotted and 

 the full lines are all similar functions of the molecular magni- 

 tudes or the complexities. Moreover, if the molecular critical 

 volumes of the different compounds are equimultiples of the 

 molecular volumes at absolute zero, the molecular volumes at 

 the boiling point, and the reduced pressure P/P* = o , oii796 are 

 also equimultiples of the real molecular volumes : 



Thus V K = xV = 4V approx. 

 V B . P . = yV = |V „ 

 V P/P = zV 2 = 1 '46V approx. 



x, y, and z are constants under the different conditions for the 

 most various substances. 



It is owing to this fact — one which involves the Law of 

 Coincident States — that an investigation of Molecular Volumes 

 from the point of view of Kopp is justified, independently of the 

 fact of the existence or non-existence of a molecular vibration 

 space or co-volume. 



The Law of Coincident States is fatal to Traube's hypo- 

 thesis. 



(ii) Co-volume Proportional to M.V!s under Conditions of Equal 

 Pressure. — Prideaux, who also favours the conception of a co- 

 volume or molecular vibration space {Trans. Chem. Soc. 1910, 

 Nov. 577, 2032), concludes that it is proportional to the real 

 molecular volumes under the conditions laid down by Young, 

 at equal fractions of the critical pressures, or below the normal 

 boiling point equal pressures. He connects the vibration 

 volume with the existence of a vapour pressure above the sur- 

 face. The co-volume and vapour pressures are zero at a certain 

 point (not — 273) ; and as the vapour pressure increases, the 

 co-volume also increases. They are both functions of the 

 temperature, and thus the increase in co-volume may be 

 expressed as a function of the pressure. 



If V p and V represent the volumes of liquid at " p " and 

 " o " pressure 



V p = V [1 + <£(p)] = Vol. at o press. + co-vol. at zero pressure. 



