Atomic  Hypothesis  and  Dissected  (Structural)  Formula.     247 
ent  formulae  of  this  kind  exists  similar  to  that  which  exists  in  the 
case  of  the  formulae  of  volatile  compounds,  and  to  which  the  term 
"law  of  multiple  proportions"  is  given j  this  law  is  therefore 
extended  so  as  to  include  such  cases  of  non-volatile  substances. 
11.  From  the  specific  heats  of  sodium,  magnesium,  iron,  and 
platinum  the  combining  numbers  of  these  elements  are  respect- 
ively fixed  as  23,  24,  56,  and  198.  The  composition  of  some 
of  the  compounds  of  these  elements  with  chlorine  are  then  ex- 
pressible by  the  formulae  NaCl,  MgCl2,  FeCl2,  PtCl2,  FeCl3, 
PtCl4,  in  which  instances  the  law  of  multiple  proportions  is 
noticeable  as  holding.  It  is  manifest  that  any  of  the  formulae 
Na2Cl2,  Mg8Cl4,  F2C14,  Pt2  CI4,  Fe2  CI6,  Pt2Cl8,  or  Na3Cl3, 
Mg3  CI6,  Fe3  CI6,  Pt3  CI6,  Fe3CF,  Pt3  CI1'2,  &c.  would  equally  well 
express  the  composition  by  weight  of  these  compounds.  Vapour- 
density  being  the  sole  means  of  deciding  on  the  formula  of  a 
body  (apart  from  reasons  based  on  analogy),  and  being  inappli- 
cable in  such  cases,  the  simplest  integral  formula  is  chosen,  not 
because  there  is  any  evidence  in  its  favour,  but  solely  for  the 
sake  of  simplicity.  This  amounts,  therefore,  to  making  the  sup- 
position that  two  volumes  of  vapour  of  the  body,  if  obtainable, 
would  contain  weights  of  the  constituents  indicated  by  the  simplest 
i  n  tegra  I  form  ula . 
In  some  cases,  however,  the  progress  of  discovery  has  shown 
that  the  formula  deduced  from  this  supposition  is  lower  than  the 
correct  one :  thus  the  composition  of  ferric  chloride  is  expres- 
sible by  the  simplest  integral  formula  FeCl3,  which  was  accord- 
ingly attributed  to  it  until  the  vapour-density  of  the  compound 
was  taken,  when  the  formula  was  found  to  be  really  Fe2  CI6. 
Similarly,  arguments  from  analogy  and  other  considerations 
sometimes  lead  to  the  adoption  of  a  formula  higher  than  that  de- 
duced from  the  above  convention.  Thus  two  carbon  chlorides 
whose  simplest  integral  formulae  are  CC12  and  CC13  exist ;  vapour- 
density  shows  that  the  true  formulae  are  C2  CI4  and  C2  CI6;  hence 
it  is  inferred  that,  as  ferric  chloride  has  the  formula  F2  CI6,  fer- 
rous chloride  is  F2  CI4  and  not  FeCl2.  Again  the  simplest  inte- 
gral formulae  for  the  two  copper  chlorides  are  CuCl  and  CuCl2; 
but  the  generalization  that  variation  in  valency  proceeds  by  even 
differences  (§  22)  leads  to  the  higher  formula  Cu2  CI2  for  the 
first  compound.  Again,  the  simplest  integral  formula  for  codeine 
is  C18  H21  NO8;  but  the  first  product  obtainable  from  this  sub- 
stance by  the  action  of  hydrogen  chloride  is  C36  H43  C1N2  O6; 
hence  it  is  inferred  that  the  true  formula  for  codeine  is  double 
the  simplest  integral  one,  t.  e.  is  C36  H42  N2  O6. 
12.  The  formulae  of  bodies  are  thus  fixed  from  consideration 
of  the  following  points  : — Quantitative  volumetric  composition  in 
the  case  of  volatile  compounds  (i,  e.  the  weights  of  the  compo- 
