386 
ON  SOME  POINTS  OF  CHEMICAL  THEORY,  ETC. 
divisor ;  and,  accordingly,  in  the  cases  of  the  elements  just  named, 
he  represented  their  combining  weights  by  the  average  numbers, 
deduced  from  his  best  analyses ;  even  though  the  numbers  ob- 
tained varied  from  a  whole  number  by  an  amount  so  small  as 
not  to  exceed  the  inevitable  error  of  the  best  conducted  analysis. 
At  a  comparatively  recent  period,  Dumas  undertook  a  research 
for  the  express  purpose  of  determining  whether  the  law  of  Prout 
was  well-founded,  at  least  so  far  as  those  elements  are  concerned 
which  have  a  small  combining  weight ;  and  the  result  of  his  ex- 
amination has  been,  that,  setting  out  with  the  hydrogen  standard 
unit,  carbon  may  be  represented  by  6,  oxygen  by  8,  and  nitro- 
gen by  14,  without  any  appreciable  error.    The  proof  of  the 
accuracy  of  these  numbers  is  so  convincing,  that,  at  the  present 
day,  the  whole  chemical  world  adopts  them.    The  next  import- 
ant step  in  this  investigation  relates  to  the  combining  weight 
of  chlorine.    A  number  of  skilful  chemists  have  labored  to 
determine  its  combining  weight  ;  as  it  is  the  hinge  on  which  a 
great  many  analyses  turn.    It  was  found  to  be  between  35 
and  36,  and  for  many  years,  3542  was  adopted  as  a  close  ap- 
proximation to  the  truth.    These  investigations,  therefore,  mili- 
tated against  Prout's  law,  as  he  enunciated  it ;  for  35  and  a 
fraction  is  not  an  exact  multiple  of  1.     The  investigation  of  the 
number  for  chlorine  has  been  lately  resumed  by  Dumas  and 
other  distinguished  chemists,  who  have  settled  down  in  the  belief 
that  35-5  is  its  correct  combining  weight.    Prout's  law,  as  laid 
down  by  him,  constituted  one  case  only  under  the  general  law, 
that  all  the  combining  numbers  are  divisible  by  the  same  number 
without  a  remainder.    The  case,  adopted  by  Prout  under  the 
general  law,  was  to  make  the  divisor  equal  to  the  hydrogen 
combining  weight,  which,  consequently,  contained  the  divisor 
once.    But  the  verity  of  the  general  law  did  not  depend  upon 
its  being  true  in  this  particular  case ;  but  its  truth  depended 
upon  this ;  namely,  whether  there  could  be  found  any  number 
which  would  be  contained  in  all  the  combining  numbers,  an 
exact  number  of  times  without  a  remainder.    Let  us  see,  then, 
whether  the  adoption  of  the  number,  35-5  for  chlorine,  militates 
against  the  general  law,  as  we  have  given  it.    To  decide  this 
question,  let  us  select  five-tenths  as  the  common  divisor.  Thus, 
five-tenths  are  contained  in  1,  the  hydrogen  number,  twice ;  in 
