1187 



We should then liave : pf ease /> J ,7 .s- ; 2'"' cuse /< J ,7 .s-> 1,35 .v; 

 3'fi case /< 1,35.9. 



At the (M-itical teinperatiii-e v^ = 3,8 /^„ (at least foi- "ordinary" 

 siibstaiices), hence / = .9V^3,8 = 1,56 .v (the inolecnie thonght to be 

 cubical). Hence the tiUii-e sol'ul state and almost all liquid vuluntes, 

 starting- from the ineUing point (/=l,ü8.v about) to far above the 

 boiling-point, are in the third case, every molecule being continually 

 within the sphei-e of attraction of tiie neigld)ouriug molecules. Only 

 the volumes quite close to I'k, both the liquid and the vapour volumes, 

 belong to the second (transition) case, and almost all the vapour 

 volumes should be reckoned to the tirst case (see fig. 1). 



When (^) is taken still somewhat greater than 1,7.9, e.g. = 2.v, the 

 transition case lies between 2.9 and 1,5 .v, and then comprises only 

 the smallest vapour volumes in the neighbourhood of the critical 

 point, while (practically) all the liquid volumes uj) to 'J\, where 

 /=:1,56.9, belong to the third case. 



We must now make a plausible supposition about the nature and " 

 the way of action of' the attractive and repulsive forces, which 

 supposition should also enable us to iTiake the mathematical calcu- 

 lations easy to cai-ry out. Among all the suppositions which 1 have 

 tried with respect to the attractive forces on different occasions, now 

 and before, the simplest is this that we assume the attraction to 

 increase from the sphere of attraction o linearlii propoi-tionate to 

 the distance to that sphei-e. If e.g. the molecule is in the point P 

 (fig. 2), the attraction that it undergoes from ^1/ would be =/',/■ ^-lJ/^ 

 Instead, therefore, of supposing the attractive action to decrease 

 from the centre of the molecule outwards to the edge of the sphere 

 of atti-action (according to a certain leciprocal power of the distance 

 r to the centi-e, by e.g. putting T r= f -. r\ or T := {/ : r'') \ e—'^", 

 which renders the integrations always unfeasible oi' exceedingly 

 complicated, and iji consequence of which the attracti\e action at 

 the edge of the sphere of attraction never becomes = 0), the reversed 

 course is taken, and the attractive action is made to increase from 

 the edge of the sphei-e of attraction iivrards. The results will not 

 differ much, but a great simplification of the calculations is reached. 

 We shall only see quantitative diffei-ences appear on ditferent suppo- 

 sitions about the attractive forces (in the numerical coefficients etc.), 

 but the found form of the functions of temperature and volume 

 will remain qualitatively unchanged. And it still remains the question 

 whether our supposition, in connection with the assumption thai the 

 molecules and atoms are all electron-systems, is not at least as 

 justifiable as the other above-mentioned su[)positious. 



