( 641 ) 



buch" l ), and in Bakhuis RoozebooM 3 ); Landolt's an 



tables do not give anything on this subject, The values indicated at 

 the places mentioned confirm that the percentage of these expansions 

 is not very considerable, which was a priori to be expected ; they amount 

 for the highest cases to little more than 10% and for most substances 

 they are considerably lower. So if we take 10° / e as basis, we 

 shall find for by far the majority of the cases a too great, so for 

 our proof a too unfavourable value. If we introduce this value, we 

 get as condition (neglecting vi by the side of v„) : 



X Vi 



— -=10. 

 «Ï v„ 



So we must now try and get a rough estimation of the relation 



between liquid and vapour volume in the triple point. If at the 



triple point the vapour tension was of the order of an atmosphere, 



this ratio would be about of the order of magnitude 1000. Now, 



however, the vapour tension is always very considerably lower ; 



almost for every substance the melting point lies very considerably 



below the boiling point. If we now assume that the triple point 



lies at about 7, Tk, we find the order of the vapour tension from 



the well known formula : 



, Pc J Tu 

 — I. nat — = / 1 



Pk ' V T 



With ƒ= 7 and T= l / a T h this gives loq V - = - 7 or p e t=-£L. 



* Pk 1000' 



If we put pk at 100 atms. 3 ), p c becomes of the order of 0.1 atm. 



So we may safely say that in general vt/v will be smaller than 



0.0001. For a temperature maximum it is, therefore, necessary, that 



at least : 



— = 10 6 or /. nat — z= 11.5. 



Now according to a formula which has been repeatedly derived 

 by van vm Waals 4 ), for low temperatures (a condition which in 

 this. case is certainly fulfilled) the equation: 



1 — xi x \ra )l\dx b dr 



i) II p. 012 2nd p. 775. 



2) I.e. I p. 89. 



8 ) In the table of Landolt and Börnstein only two substances occur, ammoniac 

 and water which have a higher pr, Hie majority by far is considerably lower, 

 particularly that of the little volatile substances which we have in view. 



*) See e.g. These Proc. VII, p. 159. 



