( 87 ) 



Finally /?-{-"A-- tloes not change in tlie denominator either, as a 

 and V' become both «^/'-times greater and /; remains unclianged, of 

 course. So it follows from this that the constant c must necessarily 

 be independent of the quantity of the considered substance, and 

 consequently must not contain Unearly the quantities v or R. In 

 how far is this in harmony with what {e) gives for c ? 



Apart from terms which apparently do not change wlien the 

 quantity of substance becomes /?i-times as great, the terms: 



■ ^ h {n—\) log R, 



are left, in which particularly at first sight, the term with log R 

 looks strange. 



On closer consideration of the so-called entropy constants 7^„, 

 however, we see that it is not strange at all. For when calculating 

 the entropy of a perfect gas, we arrived at the expression: 



T V 



s — ^„ = k log -— -\- R log — , 



by integration between the limits i\ and v, 1\ and 7" {i\ and T^ 

 arbitrary initial states). Hence 



s zzz (sg — k log 1\ — R log v^) -\- k log 'T -\- R log v, 



and in this t^o> the entropy constant was written for s^ — k log 1\ 

 — Rlogt\; i.e. 1^0 is properly speaking = i/o — R log v^, and so: 



\- (w— 1) log R = 



— {71 — 1) R log Vg -j- (n — ^) log R, 



in which now in the fraction of the second member both the 

 numerator — (?/i)o + H^i-2)o ^^^^ tl^e denominator R become //^-times 

 larger, so that we may write : 



R 



log c z=: loq L\ -\- (n — 1) log — , 



which entirely solves the apparent contradiction. In consequence of 

 R and i\ the quantity c now remains really unchanged, when the 

 quantity of substance is increased or decreased. 



32. Let us now examine in the second place what takes place 

 with the formula for the pressure of coexistence liquid-solid, as we 

 derived it in V (These Proc, Oct. 1910) p. 454—458. In this we 

 shall assume that both in the liquid phase and in the solid phase 

 only /i-fold molecules are present — in the liquid phase only to a 



