Prof.  M.  B.  Pell  on  the  Constitution  of  Matter.         179 
received ;  that  is,  it  would  give  back  the  fundamental  note  of  its 
molecules  quite  pure. 
If  it  shall  hereafter  appear  that  we  are  justified  in  inferring 
that  atoms  under  any  natural  arrangement,  under  the  action  of 
heat  of  a  certain  wave-length,  would  behave  in  a  manner  analo- 
gous to  that  which  they  appear  to  adopt  when  constrained  to 
move  in  a  straight  line,  then  I  think  it  will  be  found  that  we 
have  fallen  upon  a  principle  of  great  importance  in  the  economy 
of  nature.  It  may  be  briefly  stated  thus.  The  arrangement  of 
atoms  in  a  molecule  is  caused  by  the  prevalent  heat,  and  depends 
upon  its  wave-length ;  and  every  molecule  generated  under  the 
action  of  heat  of  a  certain  wave-length,  radiates  heat  of  the  same 
or  nearly  the  same  wave-length.  I  do  not  consider,  of  course, 
that  the  existence  of  this  principle  is  proved,  or  that  these  inves- 
tigations afford  us  any  thing  more  perhaps  than  a  hint  of  the 
truth.  In  the  further  remarks  which  I  shall  have  to  make  I 
shall,  however,  assume  the  truth  of  the  principle  which  I  have 
stated;  but  I  hope  that  it  will  be  understood,  if  I  appear  to 
adopt  too  confident  a  tone,  that  I  do  so  merely  to  avoid  the 
awkward  recurrence  of  a  hypothetical  mode  of  expression. 
Before  indulging  in  any  speculations,  I  must  dwell  a  little 
longer  upon  the  dry  formula?.  We  will  endeavour  to  form  some 
general  idea  of  the  value  of  yfr  from  the  equations  p  =  2m  sin  yfr, 
2py\r  =  ir.  fi  we  know  is  very  large;  and  m  for  ordinary  solids 
must  also  be  very  large,  for  the  molecular  forces  are  enormous 
77* 
in  relation  to  the  masses  upon  which  they  act.     If  i/r=  — ,  then 
IT 
»  =  2;  if  -v/r  is  greater  than  —  ,j9  =  l,  or  the  supposed  molecular 
o 
arrangement  would  not  occur.     If  there  be  any  simple  substance 
77" 
for  which  -v/r  is  greater  than  — ,  it  must  exist  in  the  state  of  in- 
dependent atoms  and  be  incapable  of  assuming  the  liquid  state, 
except  perhaps  under  great  pressure  ;  if  heated,  it  would  pass  at 
once  from  the  solid  to  the  vaporous  state.  It  would  show  no 
bright  lines  in  the  spectrum  at  any  temperature.  In  a  state  of 
vapour  no  heat  could  be  consumed  in  internal  vibrations ;  so  that 
Maxwell's  factor  /3  would  in  this  case  be  unity.  I  am  not  aware 
that  there  is  any  substance  possessing  these  properties ;  but  at  all 
events  we  may  presume,  from  the  complicated  constitutions 
which  molecules  appear  to  possess,  thatj?  is  generally  consider- 
able and  -v/r  therefore  small.     The  above  equations  give  us 
8p  Syjr  Sfj, 
p  ij/"  fc^r  cot  ^ 
N  2 
