a  Fluid  i^assing  through  a  Porous  Plug.  557 
very  limited  extent.     It  corresponds  to  positive  values  of 
On  the  same  figure  is  plotted  the  reduced  temperature 
against  the  reduced  volume  corresponding  to  the  series  or 
inversion-points ;  whence  it  can  be  seen  that  the  inversion- 
point  which  corresponds  to  the  maximum  pressure  occurs  when 
the  volume  is  equal  to  the  critical  volume,  the  temperature 
being  three  times  and  the  pressure  nine  times  their  critical 
values. 
Olszewski's  so-called  inversion-point  is  inserted  in  the 
same  figure  (reduced  pressure  =  8,  reduced  temperature  5*95). 
It  is  obvious  from  the  diagram  that  in  his  experiment  the 
gas  during  its  expansion  must  first  of  all  have  risen  in 
temperature  and  afterwards  cooled  down  to  the  same  value 
as  at  first.  The  point  obtained  is  therefore  only  a  fictitious 
inversion-point.  We  shall  return  to  a  consideration  of  this 
question  later  on  in  this  paper. 
(b)  Dieterici  s  Equation. 
In  Drude's  Annalen  for  1901  (v.  p.  51),  Dieterici  published 
an  equation  of  state,  viz.  : 
T?T      — ^ 
1       v-b         > 
which  fits  remarkably  well  throughout  a  very  wide  range 
both  above  and  below  the  critical  point.  Indeed,  it  is  the 
most  satisfactory  of  all  which  contain  three  constants  only. 
The  law  of  corresponding  states  is  true  for  this  equation, 
and  when  reduced  it  becomes 
_  rye    V        y" 
*        2/3-1     ' 
The  reduced  temperature  of  the  inversion-point  is  given 
in  terms  of  the  reduced  volume  by  the  equation 
_  4(2/3-1). 
7  /3        ' 
and  it  is  given  in  terms  of  the  reduced  pressure  by  the 
equation 
CC  =  (S-ry)e 
-y 
