564       Prof.  A.  W.  Porter  on  the  Inversion-Points  for 
This  is  zero  whenever 
dk  dA 
v  i  VJ~ 
dv  dv 
dv        dv 
unless  T  is  the  critical  point  at  which 
TdB  _dA_  Q 
dv        dv  ~ 
Another  example  of  a  characteristic  equation  following 
Ramsay  and  Young's  law  is  the  five-constant  equation  of 
Rose-Innes.     In  this  equation 
B-l(l-  +'   .Aa.-^ 
v  \        v  +  K—gjv1  J  v[v-\-k) 
where  e,  k,  g,  /are  constants,  and  R  is  the  ordinary  gas  constant. 
From  these  we  obtain 
dk.  _  _  vl(2v  +  /c) 
dv  {v -\- k)2v2 
and 
d(Bv)  _  Rg(l  +  2r/fa) 
dv       ~         (y  +  K-glvy- 
The  inversion-points  are  therefore  given  by 
T__2Z_   1  +  k/'2v  J g V 
l'~  Re'l  +  2glv*\        r2(r  +  *)J  ' 
Hence  when  v  is  very  large  the  inversion-point  approaches 
the  value  21 /Re ;  while  as  v  diminishes  T*  at  first  increases 
since  k/2v  is  the  dominant  small  term. 
For  isopentane  the  values  of  the  constants  as  given  by 
Rose-Innes  (Phil.  Mag.  vol.  xliv.  p.  81)  are 
I  =  5420800,     k  =  3-636, 
e  =  7-473,  g  =  6-2318, 
R  =  1/-001158. 
The  critical  constants  as  calculated  from  these  data  and  as 
observed  by  Young  are 
Critical  temperature     .     .     191°"7  C.,  187-8  C. 
„       pressure      .     .     .     26250  mm. 
„       volume        .     .     .     4*5,    4*266  cm3,  per  gr. 
The  value  o£  Tj  for  infinite  volume  is  therefore  1666 
absolute,    that    is    about    3'6    times  the    calculated   critical 
