V' V 



( 659 ) 



daldx a ( MRT 



— '— = 1.8- = 1 



daldx 

 and so (v — ?; s ) becomes of the order of magnitude 1.8 \MRT — 



— p(u — v s )\. With this volume and the low temperature holding 

 here the latter term is certainly a small fraction of MRT, also 



MRT db 



— — , so that the expression becomes negative. 



v — o dx 



fdp\ 

 Nor does the case that r- may become zero in the examined 



\dxj 



region, call for a further discussion, for it does not present any new 



fdp\ da 



points of view. If t- becomes zero in consequence of — first being 

 \dxj v dx 



negative then positive (minimum critical temperature), we shall have 



on either side what in the first case took place on the left side 



(fig. 6 — 12); if da/dx is first positive then negative (minimum of 



vapour pressure) we have on either side what happens on the right 



side in figs. 13 —16. 



Nor does, in view of the foregoing, the occurrence of cases in which 

 the plaitpoint curve meets the three phase line, offer any difficulty. 

 It is only clear, that the two points where this meeting takes place, 

 must lie below the point of detachment (double point of the binodal 

 curve solid-fluid) both in pressure and in temperature. For when detach- 

 ment has taken place, and so the binodal curve has split up into two 

 branches, it seems no longer possible, when the rvr-tigure constantly 

 contracts and hence (ssf) has a negative value, that the three phase 

 pressure coincides with a plaitpoint pressure l ). But nothing indeed 

 pleads against this conclusion. Only when we cling to the supposition 

 that the point of detachment must always lie at the rim we are 

 confronted by unsurmountable difficulties. For then the temperature 

 and pressure of the point of detachment coincide with those of 

 B (fig. J), and this point, lying considerably below the triple point, 

 lies certainly, at least in pressure, far below any plaitpoint. 



In conclusion we may remark that the cases where x s lies between 

 1 and 0, i.e. where the solid substance is a compound entirely or 

 partially dissociated in the Huid state, may be derived in all their details 

 from the v, ^-figure (fig. 2) without any further difficulty. We gel 

 then at low temperatures Smits' diagrams in the figures 4 — 7 in his 



] ) Compare the figures referring to tins in van der Waals, (These Proc. VI, 

 p. 237, VIII, p. 194 fig. (2) and Smits (These Proc. VI, p. 491 and i!>:> and VIII, 

 p. 200 (fig. !0). 



