684  On  the  Plug  Experiment. 
some  degree  of  uncertainty  must  always  attach  to  the 
substitution  of  experimental  values  of  //-,  p,  and  X  for  differ- 
ential coefficients  :  we  can  only  hope  that  the  extrapolation 
from  finite  to  infinitesimal  differences  of  pressure  is  allowable. 
The  quantity  X,  or  (def^v)e,  is  useful  for  expressing  the 
deviations  of  the  behaviour  of  any  real  gas  from  the  simple 
Boyle-Gay Lussac  law,  and  it  would  be  convenient  to  have 
values  of  X  tabulated  for  the  various  gases.  Such  a  tabulation 
has  been  given  by  Amagaf*  for  carbonic  acid  and  ethylene 
up  to  1000  atmospheres,  for  several  temperatures  between  0° 
and  200°  C. ;  also  for  oxygen,  nitrogen,  air,  and  hydrogen  for 
the  mean  temperature  of  50°  up  to  1000  atmospheres,  and 
for  the  mean  temperature  of  25°  from  1000  to  4000  atmo- 
spheres. The  computations  were  made  by  means  of  equation 
(Gr)  from  Amagat's  measurements  of  p  and  (~dp/~d0)v,  on  the 
assumption  that  6  and  T  are  identical.  These  tables  are 
interesting  and  valuable,  but  for  the  particular  purpose  of 
finding  the  relation  of  6  and  T,  we  need  similar  but  more 
detailed  and  exact  values  for  such  pressures  as  are  used  in 
gas-thermometers. 
Equations  (A),  (B),  and  (C)  show  the  relation  of  X  to  fu, 
and  p  ;  i.e.,  how  X  might  be  computed  from  the  results  of 
either  form  of  the  plug  experiment.  I  have  not  made  any 
such  computations,  but  it  seems  not  beyond  the  bounds  of 
possibility  that  with  our  present  experimental  refinements  the 
quantity  X  might  be  measured  directly. 
§  7.  The  two  most  interesting  problems  of  thermodynamics 
at  the  present  day  are  both  concerned  with  the  scale  of 
temperature.  The  first  is  the  performance  of  the  plug 
experiment  at  very  low  temperatures.  For  it  is  a  highly 
interesting  question  whether  such  temperatures  as  1°*7 
absolute,  as  given  in  a  recent  paper  by  Olszewski  f,  would 
really  be  anything  like  that  if  we  could  measure  them  on  the 
thermodynamic  scale.  At  present  we  cannot  say  whether 
they  would  or  not. 
The  other  problem  is  the  purely  theoretical  one  of  inventing 
a  radiation  scale  which  shall  be  based  on  the  two  laws  of 
thermodynamics  in  their  accepted  form,  and  on  nothing  else 
except  experimental  facts  that  we  are  sure  of  and  familiar 
with.  The  Stefan-Boltzmann  law  conies  nearest  to  this. 
Boltzmann's  deduction  depended  ultimately  on  the  assumption 
that  Maxwell's  distribution  of  stress  in  the  electromagnetic 
field  was  the  real  one.  As  Maxwell's  reasoning  on  this  point 
does  not  pretend  to  be  conclusive,  Boltzmann's  deduction  of 
*  Jour,  de  Phys.  (3)  iii.  p.  307  (1894). 
t  Annalen  der  Physik,  1905,  no.  10. 
