( 159 ) 



ttie nonrial siiltslaiicos in uciici'jil and fVoiii llial for isopcMilaiic in 

 partic'uUii'. ') 



Oui' previous diaui-am') retei-red to a niiicli smaller region of 

 temperature than that embraced bv the present one, for it extended 

 only from /(>ƒ/ t =: to -|- ^-^^^ '^'^'^ i'nnn /o(/^.V'=z — 'J. 8 to — 3.2. 

 For the constrnetion in the region above the critical temperature 

 and in the region of unsaturated vapour of the diagram now given 

 we may refer to §2 of our previous paper. In these regions percen- 

 tage "*) deviations of />r from the values of pr obtained from VTI. 1 

 are again plotted as functions of Io</ ^.v> and arranged according to 

 /(>;/ t. In the liquid region deviations in r at any tern ])eratiire occasion 

 very much laruor deviations in pr, so much so thai it would be 

 im[)0ssible to show at the same time in a single diagram percentage 

 deviations of pr in both the liquid and gaseous states. This difficulty 

 has been avoi<led by taking A?' ^\ in percent of r ') calculated from 

 VII. 1 in the region of small volumes") as the deviations and plotting 



1) With reference to the list of values of f published on page 1019 of our 

 previous paper (IX of this series, Proc. March 1911, Gomm. N". I20f/) we may 

 remark that these values were obtained by substituting the vapour pressures and 

 the corresponding temperatures along with Tk and 2)k of Proc. May 19J0, Gomm. 

 N". H5 in the van dkr Waals vapour pressure formula, and that in these values 

 of f 'm the neighbourhood of the critical temperature errors of observation are 

 magnified. To diminish the influence of observation errors upon the deduction of 

 tlie course of f in the neighbourhood of the critical temperature the observations 

 can be adjusted by means of a vapour pressure formula which is in good agree- 

 ment with tlie real values, and from these smoothed values the value of /" 

 for every temperature may be calculated. This was the treatment adopted in 

 Gomm. N'. 115, Proc. May 1910, and for the critical point was then deduced 



f ^= — VTr/ ^=^•''^12, which by using common logarithms in the vapour pressure 



formula as wa? done in Gonnn. N^. 1:20a becomes 2.481 ; it must therefore he 

 concluded lliat f between — 140° G. and the critic^al point gradually increases in 

 value from 2.415 to 2.481 or in natural logarithms from ö.-j(jl to 5.712. 



In this connection compare J. D. vak der Waals, Proc. April 1911. 



^) Proc. March 1911 Gomm. N'\ 120a. 



=^) 1 % corresponds to 2 mm. on the diagram. 



^) Proc. June 19(J1, Gomm. N". 71 § G and Arch. Néerl. (2) <5. 874. 1901. 

 Gomm. N". 74 § 4. 



^) The symbol A will always be used to represent the ditlerence between tin- 

 observed value of a magnitude and the corresponding value deduced from Vll. 1, 

 e.g. Lv = v^^ — v^^ . 



Ar 



^) The evaluation ot , A/>ü having ahead v been calculated, is made in the 



r ' 



d {lo,l r) _ 



tollowuig iiractical lashion: the quantify — — r^ is evalualrd alontt' the isotherms 



• d{pv) 



11* 



