the  Plug  Experiment.  683 
Equations  (H)  and  (I)  show  how  we  may,  if  the  experi- 
mental data  are  at  hand,  find  the  ratio  of  the  numerical 
values  of  any  two  temperatures  denoted  by  6  and  #0  on  the 
thermodynamic  scale,  at  which  the  specific  volume  of  the  gas 
has  the  values  v  and  r0  at  the  constant  pressure  ir.  Equa- 
tion (J)  gives  us  similar  information  in  terms  of  pressure  at 
the  constant  specific  volume  <f>.  By  using  the  equation 
pv=HT  which  defines  the  absolute  temperature  T  of  the  gas- 
thermometer,  when  either  p  or  v  is  constant,  it  is,  of  course, 
easy  to  replace  v  or  p  by  the  absolute  temperature  measured 
by  a  constant-pressure  or  constant- volume  thermometer  filled 
with  the  gas  in  question. 
These  deductions,  which  make  no  pretence  of  novelty,  are 
all  quite  simple  enough  to  be  put  into  the  most  elementary 
text-book  of  thermodynamics.  In  view  of  the  difficulty 
students  have  in  getting  any  clear  ideas  about  the  thermo- 
dynamic scale  of  temperature  from  Joule  and  Lord  Kelvin's 
papers  on  the  plug  experiment,  I  think  it  would  be  well  if 
some  such  simple  discussion  were  more  commonly  given. 
For  although  this  treatment  is  only  formal,  any  one  can  see 
from  the  equations  what  experimental  data  are  needed  and 
how  we  must  use  them  if  we  wish  to  go  on  to  find  actual 
numerical  relations.  The  main  thing  is  to  have  the  conviction 
that  there  is  a  definite  way  in  which  the  experimental  data 
might  be  used  if  we  had  them,  and  anyone  who  has  not 
attained  that  conviction  by  the  "  seeing-is-believing  "  process 
must  sometimes  feel  rather  at  sea  in  using  thermodynamics. 
§  6.  In  order  actually  to  perform  the  integrations  indicated 
in  equations  (H),  (I),  and  (J),  we  have,  in  the  case  or  the 
adiabatic  plug  experiment,  to  know  the  values  of  /x  and  Cp  as 
functions  of  v  for  the  given  constant  pressure  used  in  our 
constant-pressure  gas-thermometer  ;  and  it  may  be  noted  that 
the  value  of  Joule's  equivalent  is  also  involved,  unless  we 
have  the  values  of  GP  measured  directly  in  ergs.  For  the 
isothermal  plug  experiment,  we  need  merely  the  value  of  p 
as  a  function  of  v  at  the  same  constant  pressure.  By 
supplying  this  energy  p  electrically,  it  may  be  measured  in 
ergs  as  exactly  as  the  absolute  accuracy  of  our  electrical 
standards  permits.  This  method  would  not  serve  us  in  the 
case  of  hydrogen  above  —80°  C,  nor  for  other  gases  above 
their,  as  yet  unknown,  inversion  temperatures,  though  it  is 
conceivable  that  in  such  cases  the  Peltier  effect  might  be 
utilized  for  electric  cooling.  For  the  free  expansion  experi- 
ment the  data  needed  are  the  values  of  X  in  terms  of  p  at 
the  given  specific  volume  used  in  the  constant- volume  gas- 
thermometer.     It  may  be  remarked,  in  this  connexion,  that 
2  Y2 
