a  Fluid  j)as sing  through  a  Porous  Plug.  563 
pressure  lines  do  not  intersect  at  one  point ;  all  within  a 
certain  range  must  therefore  have  a  caustic  curve  as  envelope, 
and  it  should  be  noted  that  each  one  of  these  meets  the 
caustic  twice.  The  actual  calculation  of  the  caustic  is  cum- 
brous, and  as  no  particular  importance  attaches  to  it  the  - 
calculation  has  not  been  made.  In  Olszewski's  experiment 
with  hydrogen  the  initial  pressure  was  eight  times  the  critical 
pressure,  and  the  final  was  atmospheric,  i.  e.  roughly  ■£$  the 
critical  value.  These  constant-pressure  lines  are  shown, 
amongst  others,  on  the  diagram ;  their  intersection  can  be  ' 
calculated  more  accurately  by  successive  approximations  from 
the  equation.  When  this  calculation  is  made  the  point  is 
found  to  be  at  about  5*8  times  the  critical  temperature. 
Now  Olszewski's  experimental  value  is  nearly  six  times  the 
critical  temperature.    There  is  thus  very  good  agreement  be-    fS 
tween  these  two  results.      Inspection  of  the  diagram  (fig.  1) 
shows  that  while  the  gas  decreased  in  pressure  as  it  flowed  from 
one  side  to  the  other  of  the  throttle,  it  must  (if  van  der  Waals's    — 
equation  were  valid)  at  first  have  heated  until  the  pressure 
had  fallen  to  about  three  times  the  critical  ;  in  the  subsequent  *2 
part  of  the  expansion  it  must  have  cooled  by  an  equal  amount, 
thus  bringing  about  zero  change  on  the  whole. 
On  the  other  hand,  inspection  of  the  curve  of  inversion* 
points  corresponding  to  Dieterici's  equation  shows  no  possi- 
bility of  this  compensation  occurring;  for  Olszewski's 
observed  point  lies  within  the  cooling  region.  Thus  the 
evidence  afforded  by  this  single  experimental  value  is  much 
more  in  favour  of  the  validity  of  van  der  Waals's  equation  in 
the  region  involved  than  of  that  of  either  of  the  two  other 
equations. 
(e)  Ramsay  and  Young  Fluids. 
For  any  fluid  obeying  Ramsay  and  Young's  linear  law 
we  have 
p  =  BT-A, 
where  B  and  A  are  functions  of  the  volume  alone.  All  the 
three  equations  which  we  have  considered  satisfy  this  law  ;  it 
is  therefore  of  interest  to  rind  the  general  equation  for  the 
inversion-points  of  such  a  fluid.     We  at  once  obtain 
<*     -T(B+-£)+ 
dT      V~  T</B__</A 
dv        dr 
Iv 
