554       Prof.  A.  ~W.  Porter  on  the  Inversion-Points  for 
settle  definitely  whether  this  critical  velocity  of  the  a.  particle 
is  only  apparent  or  has  a  real  existence. 
As  these  experiments  will  take  some  time  to  complete,  I  have 
taken  this  opportunity  of  stating  briefly  the  results  so  far 
obtained. 
I  am,  Gentlemen, 
McGiU  University,  Montreal,  Yours  faithfully, 
February  27,  1906.  E.  RUTHERFORD. 
XL VII.  On  the  Inversion-Points  for  a  Fluid  passing  through 
a  Porous  Plug  and  their  use  in  Testing  Proposed  Equations 
of  State.  By  Alfred  W.  Porter,  B.Sc,  Fellow  of  and 
Assistant- Professor  of  Physics  in,  University  College,, 
London  *. 
IN  a  paper  in  the  Phil.  Mag.  vol.  xlv.  p.  227  (1898),  Rose- 
Innes  showed  that  the  results  obtained  by  Joule  and 
Kelvin  for  the  change  in  temperature  of  a  gas  in  passing 
irreversibly  through  a  porous  plug  could  be  represented  as 
well  by  the  formula  A—  ™  as  by  the  formula  adopted  by 
Joule  and  Kelvin,  viz.  :  7^. 
Eose-Innes'  formula,  if  a  valid  empirical  formula,  would 
indicate  that  a  point  of  inversion  must  exist  ;  that  is  to  say, 
that  there  must  exist  a  temperature  below  which  cooling  will 
occur,  while  heating  takes  place  if  the  gas  is  above  this 
temperature. 
The  fact  proved  later  that  by  sufficient  cooling  hydrogen, 
which  heats  at  ordinary  temperatures,  cools  at  lower  tem- 
peratures, demonstrates  that  for  it  an  inversion-point  exists ; 
and  still  later  {Krakauer  Protocolle,  1901  ;  Drude's  Annalen, 
1902)  Olszewski  has  experimentally  shown  that  hydrogen 
suffers  neither  heating  nor  cooling  when  the  temperature  is 
—  80o,5  C.  and  the  pressures  on  the  two  sides  of  the  plug 
are  about  113  atmospheres  and  that  of  the  atmosphere. 
The  object  of  the  present  paper  is  to  examine  the  subject 
more  minutely  ;  and  the  outcome  of  it  is  that  it  is  shown 
that  any  of  the  usually  adopted  equations  of  state  of  a  gas 
require  that  there  shall  be  not  one  inversion-point  only,  but 
a  whole  series  of  such  points  corresponding  to  all  possible 
pressures. 
Instead  of  dealing  with  finite  changes  of  pressure  we  shall 
*  Communicated  by  Prof.  F.  T.  Trouton,  D.Sc,  F.K.S. 
