a  Fluid  passing  through  a  Porous  Plug.  559 
consequences  with  regard  to  the  series  of  inversion-points. 
At  the  same  time  they  exhibit  the  extreme  sensitiveness  of 
phenomena  depending  upon  the  Joule-Kelvin  effect  in  dis- 
criminating between  different  equations  of  state.  On  each 
of  them  are  shown  the  points  representing  hydrogen  (H) 
under  usual  conditions  (i.  e.  about  20°  C.  and  a  few  atmo- 
spheres pressure).  This  point  for  hydrogen  is  calculated 
from  the  values  of  the  critical  temperature  recently  determined 
by  Olszewski,  viz.,  32°'2  absolute  (Drude's  Annalen,  1905, 
x.  p.  986).  It  will  be  seen  that  both  van  der  Waals's  and 
Dieterici's  equations  given  above  indicate  a  heating  of  hydro- 
gen in  expanding  at  ordinary  temperatures.  The  inversion- 
point  corresponding  to  a  few  atmospheres'  pressure  is  about 
6*7  times  the  critical  temperature  according  to  van  der 
Waals's  equation,  i.  e.  at  about  216°  abs.  ;  while  according  to 
Dieterici's  it  is  at  8  times  the  critical  temperature,  i.  e.  at 
about  258°  abs.  Thus  for  moderate  pressures,  if  the  latter 
equation  holds  good,  hydrogen  should  undergo  cooling  at 
temperatures  much  higher  than  has  hitherto  been  thought. 
An  accurate  determination  of  this  temperature  for  various 
pressures  will  discriminate  between  these  two  equations,  even 
at  points  in  the  neighbourhood  of  atmospheric  temperature 
and  pressure,  in  a  way  which  no  direct  measurements  of 
p,  Vj  and  t  can  ever  be  expected  to  do. 
Dieterici  had  previously  published  another  equation  similar 
to  van  der  Waals's,  but  in  which  the  molecular  pressure  term 
is  given  by  a/v*  instead  of  a/v2.  This  equation  holds  good 
near  the  critical  point  only,  at  which  point  it  is  very 
satisfactory. 
The  law  of  corresponding  states  applies  and  the  reduced 
values  for  the  inversion-points  are  easily  shown  to  be 
4(4/3  -l)2 
9/51 
16(5/9-2) 
a  = 
3/3f       • 
The  same  general  conclusions  can  be  derived  from  these 
values.  The  equation  does  not  profess,  however,  to  have  an 
equally  general  validity  as  the  others,  and  consequently  will 
not  be  further  discussed. 
It  is  a  notable  fact  with  regard  to  each  of  these  equations 
that  the  maximum  pressure  which  gives  any  inversion-point 
is  that  for  which  the  volume  is  the  critical  volume.  A  further 
connexion  is  shown  between  any  inversion-curve  and  the 
corresponding  equation  of  state  by  the  following  considerations. 
