556         Prof.  A,  W.  Porter  on  the  Inversion-Points  for 
From  this  and  the  previous  equation  7  can  be  eliminated, 
with  the  result 
«.=  ^(2, 
T). 
This  formula  connects  the  reduced  pressure  and  volume 
which  correspond  to  an  inversion-point.  The  simplest  mode 
of  calculation  is  to  obtain  7  for  a  series  of  assumed  values  of 
ft,  and  then  to  calculate  a.  by  means  of  the  last  equation. 
The  curve  obtained  by  plotting  7  against  a  is  shown  in 
the  following  diagram  (fig.  1). 
Fig.  1. 
Eeduced  Inversion-points  according  to  van  der  Waals's  Equation. 
.\iyA, 
w 
Jimr 
§      R 
icior 
[>}<, 
'otsgp 
~>ik  1 
,-i" 
Coo\ 
-mg    f 
Hio 
> 
\ 
J 
1 
~     , .  f  Ordinates— Reduced  Temperature. 
Continuous  curve  j    Absciss£e  _Reducea  Pressure. 
Dotted  curve 
Ordinates — Reduced  Teiu  perature. 
Abscissas — Reduced  Volume. 
The  form  of  this  curve  involves  the  following  consequences: 
(1)  For  all  pressures  from  zero  to  nine  times  the  critical 
pressure  there  are  two  inversion  temperatures 
which  range  from  a  little  below  the  critical  tem- 
perature to  about  6*7  times  the  critical  value. 
(2)  At  pressures  higher  than  nine  times  the  critical  value 
there  is  no  inversion-point. 
The   curve  separates  the  regions   for  which  cooling  and 
warming  occur  from  one  another.     The  cooling  region  is  of 
