a  Fluid  passing  through  a  Porous  Plug.  567 
Thus,  from  the  last  two  columns,  it  is  seen  that  this  equation, 
which  only  indicates  one  inversion-point,  actually  fits  the 
experimental  values  better  than  Dieterici's  second  equation 
throughout  a  range  from  large  values  of  v  to  values  below 
the  critical  volume  which  is  4*266.  Below  this,  however,  it 
is  hopelessly  out  of  competition.  At  the  critical  volume, 
however,  it  is  far  superior  to  van  der  Waals's  equation,  as  is 
shown  by  the  cross  on  the  diagram,  which  gives  the  value  of 
pv  for  the  critical  point  as  calculated  from  van  der  Waals's. 
The  constant  inversion-point  comes  out  as  1 J  X  critical  tem- 
perature for  isopentane  ;  bat  it  should  be  noted  that  the 
equation  does  not  satisfy  the  law  of  corresponding  states. 
(f)    General  Condition  for  the  uniqueness  of  the 
Inversion-Point. 
We  have  worked  out  the  special  case  of  a  Ramsay  and  Young 
fluid.  In  the  general  case  where  no  restriction  is  introduced 
it  must  be  possible  to  write 
^(j)=(T-*)/(p,T)> 
where  f(j>,  T)  is  a  function  of  p  and  T  which  never  vanishes 
unless   when  T  =  /c,  and  which  is  not   infinite   when  T  =  k. 
The  constant  inversion-point  is  of  course  T  =  ic. 
Integrating  this  equation,  we  obtain 
as  the  most  general  equation  of  state  which  gives  a  unique 
inversion-point.  In  this  expression  y  is  restricted  to  be  a 
function  of  p  and  T,  whose  first  two  differential  coefficients 
have  no  zero  unless  when  T=  k,  and  no  infinity  when  T  =  k. 
Further,  ^r{p)  is  any  function  of  p  alone. 
Conclusion. 
The  chief  points  brought  out  in  this  paper  are  the 
following  : — 
(1)  The  value  of  the  inversion  temperature  of  the  Joule- 
Kelvin  effect  is  probably  a  function  of  the  pressure  ; 
and  even  for  the  same  pressure  two  inversion-points,  in 
general,  may  exist. 
