In  the  equation,  pv=-|-mnC2,  p,  v,  and  C  depend


MOLECULES

on  temperature,  and  p,  v,  m,  n,  and  C  on  the
nature  of  the  gas.  And  as  pv=£mnC2,  3pv/2n=
mC2/2  ;  and  substituting,


or  more  simply,

PiVi/pav8=p'iv'i/p',v'a  ;

that  is,  for  equal  changes  of  temperature,  the
change  of  the  numerical  value  of  the  product  pv
alters  for  all  gases  in  the  same  ratio.  This  is  Gay-
Lussac's  Law  in  its  most  general  form.  If  we  keep
p  constant,  we  get  the  usual  statement,  that  all
gases  undergo  equal  change  of  volume  on  equal
change  of  temperature.
If  two  gases  are  at  the  same  temperature  and
under  the  same  pressure,  the  average  momentum
of  the  molecules  of  each  must  be  equal  ;  or,

mC2/2=m'C/2/2.
If  the  volumes  of  the  gases  are  also  equal,
2/3nm/2C2=2/3n/m//2C2  ;

hence  n=n';  that  is,  under  equal  conditions  of
temperature  and  pressure,  equal  volumes  of  gases
contain  equal  numbers  of  molecules.  Now,  the
molecules  consist  of  small  whole  numbers  of
atoms  ;  and  as  the  above  law  holds  for  new
gaseous  molecules  formed  during  any  chemical
reaction,  the  proportions  in  which  any  two  gases
89


ELEMENTS  AND   ELECTRONS

act  on  each  other  must  be  simple.  This  was  proved
by  Gay-Lussac,  long  before  the  kinetic  theory
was  imagined  ;  and  the  theory,  embracing  all  the
facts,  lends  additional  probability  to  the  view.
But  the  kinetic  theory  leads  us  farther.  It  is
possible  by  its  help  to  calculate  the  average
velocity  of  molecules  of  all  gases  at  definite
temperatures  ;  and,  furthermore,  the  prediction
can  be  controlled  by  experiment.
