504         Dr.  C.  R.  A.  Wright's  Reply  to  "An  Examination 
From  these  quotations,  together  with  the  statement  (p.  339) 
that  "  the  so-called  law  of  multiple  proportions  has  no  existence 
apart  from  the  atomic  theory/'  and  the  phrase  (pp.  334  and 
336)  "  theory  of  multiple  proportions/'  it  is  evident  that  what 
Dr.  Williamson  accepts  as  the  meaning  of  the  term  atomic 
theory  is  not  the  same  as  that  which  I  have  attributed  to  the 
phrase  atomic  hypothesis ;  which  latter^  as  accepted  by  Dalton 
and  Berzelius,  maybe  thus  enunciated,  the  terms  Generalization, 
Convention,  and  Hypothesis  being  previously  denned.  A  gene- 
ralization is  a  statement  whereby  a  large  number  of  observations 
or  experimental  facts  are  expressed  with  either  absolute  or  ap- 
proximate accuracy;  thus  the  statements  that  mammalia  are 
vertebrated,  that  nitrates  are  soluble  in  water,  that  gases  expand 
Y^y  Pai*t  °f  tneir  bulk  at  0°  for  each  1°  C.  increase  of  tempera- 
ture, are  generalizations :  in  the  first  case  there  is  absolute  ac- 
curacy ;  for  no  mammalia  which  are  not  vertebrated  are  known ; 
in  the  second  and  third  there  is  approximate  accuracy ;  for  ex- 
tremely few  nitrates  are  known  that  are  not  readily  soluble  in 
water ;  and  in  the  third  case,  which  is  perhaps  the  most  to  the 
point  in  the  present  discussion,  no  gas  is  known  the  behaviour 
of  which  is  rigorously  in  accordance  with  the  statement  at  all 
temperatures;  but  no  gas  is  known  which  does  not,  under  cer- 
tain defined  conditions,  exhibit  a  behaviour  which  is  in  close 
proximity  to  that  stated  to  occur. 
The  term  convention  is  applied  to  an  expressed  or  tacit  under- 
standing that  a  given  mark,  symbol,  or  name,  &c.  shall  be  ap- 
plied to  a  given  proposition,  fact,  object,  &c.  Thus  the  state- 
ment that  the  letter  A  represents  in  England  a  particular  sound, 
that  the  sign  x2  represents  unity  taken  x  times,  and  the  resulting 
sum  or  product  taken  x  times  again,  are  referred  to  as  con- 
ventions. 
The  term  Hypothesis  is  applied  to  some  proposition  incapable  of 
direct  proof  (at  least  in  our  present  state  of  knowledge),  but  by 
admitting  which  a  number  of  facts  may  be  coordinated  and 
shown  to  be  correlated,  and  by  means  of  wtiich  one  can  induc- 
tively argue  from  the  known  to  the  unknown. 
Now  the  two  terms  Theory  andZtfw  appear  to  be  employed  by 
different  writers  in  different  acceptations.  The  majority  refer  to 
a  theory  as  being  simply  an  hypothesis  in  a  further  state  of  deve- 
lopment :  when  the  predictions  deducible  from  an  hypothesis 
are  found  to  be  mostly  verified  by  experiment  and  observation, 
the  term  theory  is  applied  to  it ;  and  when  no  exceptional  case 
is  known  with  which  the  theory  cannot  grapple  and  which  it 
does  not  elucidate,  the  term  Law  of  nature  is  then  employed;  so 
that  Hypothesis,  Theory,  and  Law  are  three  terms  of  a  similar 
nature,  differing  only  in  their  range  of  application.     Others, 
