a  Fluid  passing  through  a  Porous  Plug.  565 
temperature.  For  temperatures  higher  than  this  value  it  is 
easy  to  show  that  there  would  be  a  heating  effect.  Hence  we 
have  in  this  case  a  curve  of  inversion-points  whose  upper 
portion  rises  with  increasing  pressure  instead  o£  diminishing 
as  it  would  do  according  to  the  other  equations,  and  is  at  the 
same  time  much  lower  if  we  take  the  evidence  afforded  by 
observations  on  isopentane. 
The  fact  that  the  slope  of  the  inversion-point  curve  cor- 
responding to  Rose-Innes'  equation  is  for  large  volumes  of 
opposite  sign  to  that  of  the  other  equations,  suggested  the 
idea  that  possibly  the  equation  rigorously  valid  for  an  actual 
gas  might  lead  to  a  curve  parallel  to  the  pressure  axis  ;  this 
would  imply  a  single  inversion-point  for  all  pressures.  It  is 
easy  to  obtain  an  equation  for  which  such  would  be  the  case. 
For,  provided  that  the  fluid  satisfies  Ramsay  and  Young?s 
linear  law,  the  condition  that  there  shall  be  one  inversion- 
point  only  is  that 
v  —;-    —  ( Bv)  =  constant  =  T. ; 
dv  J  dv  v      y  l 
or  d(Bv)  _    dA 
dv  dv 
For  the   sake  of  illustration  we  will  follow  Rose-Innes  in 
taking'  A=  — -,  and  adapt  his  value  of  B  to  satisfv  the 
above  condition  ;  then 
Td{Bv)  _       (2v  ±k)1 
dv  v(v  +  k)2' 
Integrating  this  equation  we  obtain 
TiBv=  ~k{  1oS  y~loS  (V  +  K)~  ^~K  -const,  j  : 
and  the  equation  of  state  becomes 
I    Tr  v  +  K         k    "I  i 
p=  *7fi —   const. -flog +  —         —      -      — ,. 
KU  VL  v  v-i-Kj      v(v  +  k) 
The  value  of  I  x  const.  //cT»  is  R,  the  ordinary  gas  constant. 
How  nearly  such  an  equation,  having  one  inversion-point 
only,  is  capable  of  representing  the  behaviour  of  isopentane 
is  evident  from  fig.  5,  where  pv  for  the  critical  isotherm  is 
plotted  against  the  cube  root  of  the  reciprocal  of  the  volume. 
The  circles  represent  experimental  values,  while  the  dotted 
line  represents  the  above  equation  with  values  of  the  constants 
chosen  so  as  nearly  to  satisfy  four  of  the  experimental  values. 
