140 PRINCIPLES OF CHEMISTRY 



its gaseous state (that is, its elasticity, or the physical energy of its 

 molecules, or their rapid progressive movement) with comparative ease 



coefficients of expansion of gases with a change of pressure, and according to the 

 methods of determination (Note 26). Besides this, Van der Waals' formula shows that 



at temperatures above 273 ( a 1\ only one actual volume (gaseous) is possible, 



whilst at lower temperatures, by varying the pressure, three different volumes liquid, 

 gaseous, and partly liquid partly saturated-vaporous are possible. It is evident that 



the above temperature is the absolute boiling point that is, (tc) = 273 f ~ 1 J . It is 



found under the condition that all three possible volumes (the three roots of Van der 

 Waals' cubic equation) are then similar and equal (vc = Sb). The pressure in this case 



(we) = a 9. These ratios between the constants a and b and the conditions of critical 

 276 



state i.e. (tc) and (pc) give the possibility of determining the one magnitude from the 

 other. Thus for ether (Note 29), (tc}= 193, (*p) = 40, from whence a = 0'0307, 6 = 0'00533. 

 From whence (t>c) = 0'016. That mass of ether which at a pressure of one atmosphere at 

 occupies one volume for instance, a litre occupies, according to the above- mentioned 

 condition, this critical volume. And as the density of the vapour of ether compared with 

 hydrogen = 37, and a litre of hydrogen at and under the atmospheric pressure weighs 

 0-089(5 grams, then a litre of ether vapour weighs 3'32 grams ; therefore, in a critical 

 state (at 193 and 40 atmospheres), 3'32 grams occupy 0*016 litres, or 16 c.c. ; therefore 1 

 "gram occupies a volume of about 5 c.c., and the weight of 1 c.c. of ether will then be 0'21. 

 According to the investigations of Kamsay and Young (1887), the critical volume of ether 

 was approximately such at about the absolute boiling point, but the compressibility of 

 the liquid is so great that the slightest change of pressure or temperature acts consider- 

 ably on the volume. ^But the investigations of the above savants gave another indirect 

 demonstration of the true composition of Van der Waals' equation. They also found for 

 ether that the isochords, or the lines of equal volumes, are generally straight lines if the 

 temperatures and pressures vary. For instance, the volume of 10 c.c. for 1 gram of ether 

 corresponds with pressures (expressed in metres of mercury) equal to 0'185 8'3 (for 

 instance, at 180 and 21 metres pressure, at 280 and 34'5 metres pressure). The recti- 

 linear form of the isochord (then v & constant quantity) is a direct result of Van der 

 Waals' formula. 



When, in 1883, I demonstrated that the specific gravity of liquids decreases in propor- 

 tion to the rise of temperature [S, = S -K or S,= S (1-Kf)], or that the volumes 

 increase in inverse proportion to the binomial 1 K, that is, V/ = V (1 Ktf)" 1 , where K 

 is the modulus of expansion, which varies with the nature of the liquid (an exactitude of 

 the same kind as that by which for gases the volumes increase proportionately to the 

 binomial l + at), then, in general, not only does a connection arise between gases and 

 liquids with respect to a change of volume, but also it would appear possible, by availing 

 oneself of Van der Waals' formula, to judge, from the phenomena of the expansion of 

 liquids, as to their transition into vapour, and to connect together all the principal pro- 

 perties of liquids, which up to this time had not been considered to be in direct dependence. 

 Thus Thorpe and Riicker found that 2(f c) + 278 = 1/K, where K is the modulus of expan- 

 sion in the above-mentioned formula. For example, the expansion of ether is expressed 

 with sufficient accuracy from to 100 by the equation S< = 0'786 (1-0'00154), or V< 

 = 1 (1 0'00154), where 0'00154 is the modulus of expansion, and therefore (tc) = lS8, or 

 by direct observation 193. For silicon tetrachloride, SiCl 4 , the modulus equals 0'00186, 

 . from whence (c) = 231, and by experiment 280. On the other hand, D. P. Konovoloff, 

 admitting that the external pressure p in liquids is insignificant when compared with the 

 internal (a in Van der Waals' formula), and that the work in the expansion of liquids is 

 proportional to their temperature (as in gases), directly deduced, from Van der Waals' 

 formula, the above-mentioned formula for the expansion of liquids, V t =-l/ (1 Kt), and 



