a  Fluid  passing  through  a  Porous  Plug.  561 
which  can  only  be  when    -rTi  =0,  excluding  infinite  values  of 
BF  Bi 
By  differentiation  we  get 
BF       B  /„.  B  AAX     mB2' 
T  ~BA     BTAl7J~±BT'-' 
Hence   the    maximum   inversion-pressure    corresponds    to 
— —  =0  for  the  corresponding  constant-pressure  line  on  a 
v-T  diagram,  that  is  to  say,  it  corresponds  to  a  point  of 
inflexion  on  such  a  diagram. 
(d)  Discussion  of  Olszewski' s  Observation. 
In  Olszewski's  determination  of  his  inversion-point  for 
hydrogen  a  large  fall  of  pressure  was  used  ;  and  consequently 
his  point  does  not  correspond  in  definition  with  those  referred 
to  in  this  paper.  The  criterion  of  all  points  such  as  his  is 
that  the  temperature  does  not  fall  on  the  whole  in  the  actual 
flow,  even  though  the  difference  of  pressure  is  large,  and  this 
corresponds  to  the  condition 
U  +  pv  =  constant, 
where  U  is  the  intrinsic  energy  of  the  fluid.  If  then  it  is 
possible  to  obtain  the  values  of  TJ+pv  for  various  tempera- 
tures and  plot  constant-pressure  values  against  these 
temperatures,  the  resulting  curves  will  necessarily  intersect 
one  another,  the  point  of  intersection  of  any  two  constant- 
pressures  lines  representing  the  inversion-point  in  Olszewski's 
sense.  The  value  of  pv  can  be  determined  for  some  fluids 
from  Ama gat's  determinations  ;  but  the  value  of  U  involves 
calori metric  data  as  well,  and  these  are  very  imperfectly 
known. 
For  a  substance  obeying  van  der  Waals's  equation 
dU  =  d.Q  -pdv  =  WT  +  (t  |P  -  P  \ 
CvdT+^dv, 
and  B(V    _TB"/>      n 
Br  BI-' 
