Atomic  Hypothesis  and  Dissected  (Structural)  Formulce.     263 
actions ;  but  whenever  he  is  led  by  any  of  these  considerations 
to  a  formula  which  contains  a  fraction  of  any  atomic  weight,  he 
takes  a  multiple  of  the  formula  sufficiently  high  to  be  entirely 
free  from  such  fractions.  In  no  case  does  he  reason  on  a  basis 
independent  of  the  atomic  theory." 
From  the  exposition  given  above,  and  employing  the  term 
atom  in  the  sense  ascribed  to  it  by  Dalton,  it  is  evident  that  the  law 
of  multiple  proportion  is  simply  the  statement  of  a  generaliza- 
tion first  made  gravimetrically  by  Dalton,  and  subsequently  ex- 
tended volumetrically  by'Laurent  and  Gerhardt,  viz.  that,  if  cer- 
tain numbers  be  attributed  to  each  element  respectively,  the 
quantitative  compositions  of  compounds  are  expressible  by  taking 
simple  multiples  of  these  numbers  and  comparing  the  products 
thus  obtained  :  these  numbers  being  in  the  ratios  of  simple  mul- 
tiples or  submultiples  of  the  vapour-densities  of  the  elements, 
the  volumetric  composition  of  compound  vapours  must  necessa- 
rily be  expressed  by  simple  integral  numbers — i.  e.  1  volume  of 
one  constituent  to  1  of  another,  1  to  2,  2  to  3,  &c.  This  ge- 
neralization is  not  identical  with  the  hypothesis  of  the  existence 
of  material  atoms,  advanced  to  account  for  the  facts  summed 
up  in  the  generalization;  and  to  say  that  the  law  has  no  exist- 
ence apart  from  the  atomic  hypothesis  is  to  give  a  meaning  to 
the  term  atom  different  from  that  attributed  to  it  by  Dalton*. 
Similarly  the  method  of  finding  the  formula  of  a  body  from 
its  percentage  composition  is  a  simple  deduction  from  Dalton' s 
generalization,  but  has  no  necessary  connexion  with  his  hypo- 
thesis. 
The  conclusions  to  be  drawn  from  the  foregoing  train  of 
thought  appear  to  be  as  follows  : — The  salient  facts  of  chemistry 
may  be  expressed  in  words,  and  more  or  less  completely  repre- 
sented and  referred  to  by  the  ordinary  symbols,  the  notion  of 
material  atoms  possessed  of  dimensions  in  space,  mass,  and  time 
being  in  no  way  involved  in  such  expressions  or  representations. 
This  notion  of  material  atoms  does  not  afford  an  adequate  expla- 
nation of  several  facts,  more  particularly  of  those  where  force  of 
some  kind  is  involved  as  a  necessary  element  of  the  point  in 
question ;  and,  moreover,  the  phraseology  of  the  hypothesis  of 
the  existence  of  such  atoms  is  employed  by  chemists  in  different 
senses,  in  some  cases  in  senses  involving  notions  the  contrary  of 
*  That  the  term  atom  is  not  used  by  Dr.  "Williamson  in  the  same  sense 
as  that  in  which  Dalton  employed  it,  is  evident  from  his  statement  (loc.  cit.) 
that  "  whether  elementary  atoms  are  in  their  nature  indivisible  or  whether 
they  are  built  up  of  smaller  particles  is  a  question  upon  which  I,  as  a  chemist, 
have  no  hold  whatever ;  and  I  may  say  that  in  chemistry  the  question  is 
not  raised  by  any  evidence  whatever.  They  may  be  vortices  such  as  Thom- 
son has  spoken  of "  , 
