with van der Waals' and Clausius* Characteristics. 413 

 We thus get for the points where inversion of £' occurs 



N. 



v'. 



7T. 



r. 



v' . 



7T. 



r. 



5 



2-9855 



•52627 



•85816 



23-706 



•05875 



•56175 



6 



2-1289 



•699-16 



•91668 



77759 



•015:33 



•45950 



7 



1-8064 



•78806 



•94319 



21200 



•00495 



•39785 



8 



1-63 



•840 



•958 



543-88 



•00172 



•35353 



9 



1-52 



•873 



•967 



1362-8 



•00062;; 



•31918 



10 



1-45 



•899 



•974 



3389-4 



•000229 



•29136 



II 



1-40 



•918 



•979 



8430-1 



•0000848 



•26818 



12 



1-34 



•933 



•983 



21036- 



•0000315 



•24849 



I have lately been interested to examine by this method 

 the values of the heat-capacities, &c. of a saturated fluid 

 in the neighbourhood of the critical point. For though 

 v. d. Waals' equation is not a correct representation of the 

 behaviour of gases, yet it represents so near an approxima- 

 tion that its indications are of value. 



If we put x~ 1 — v, then in the neighbourhood of the 

 critical point /x and # are very small so that we may expand 

 the terms in the equation of the connode in ascending powers 

 of (jl and x ; we then obtain 



0=log 



4-3<a? + //, 



3(l-g)(3g+/f)(8— 9x+p) 



(2-3#)(2-3#-/0 (2-3*)(4-3ar-/A)( 4 — 3 *+A*) 

 1 ^(3^+/*)M^-/*+i(17^-17^-2 / £ 2 )+K31^-3UV~7V-^ 



+ ^ (837^-837^- 275ay-79*/*3--6 / * 4 )+ ...{ 



whence 



or 



16 



^ = M +,^+-^+ r7 - k ^H 



221) 

 175 



fi — x— - .r — — 7 x* — 



25 



61 

 175 



and thence we deduce 



T=l 



20 



129 

 200' 



',.« 



5967 

 7000 



x° — 



