Prof.  M.  B.  Pell  on  the  Constitution  of  Matter.         183 
with  \a,  when  n  is  large;  so  that  the  system  is  incapable  of  ab- 
sorbing or  transmitting  any  heat  for  which  fju  is  greater  than  2m. 
Equation  (8)  gives 
£cos(:2/i  —  1)^ 
#.= x_ — - — J-Z_  (I  — cos  at). 
sin  yjr  x  n  ' 
So  long  as  this  coefficient  is  greater  than  a,  the  first  of  the  n 
atoms  continues  to  be  accelerated  by  the  aether.  When  steady 
motion  is  established  and  the  acceleration  ceases,  we  have 
£cos  (2n  —  l)ijr  _ 
sini/r  "  ' 
acos(2n-2r+l)1r 
*'~       cos(2»-l)f       [i  ^ 
acos(2r—l)yjr 
as i — U-  (1  —  cos  at) . 
cosy         v 
The  principle  which  I  have  stated,  if  established,  would  afford 
some  hope  of  our  being  able  to  understand  the  facts  of"  spectrum 
analysis."  The  fixed  character  of  the  bright  lines  makes  it  im- 
possible to  conceive  that  the  energy  due  to  the  translation  or 
rotation  of  the  vapour  molecules  can  have  any  thing  to  do  with 
their  production.  They  must  be  caused  by  the  internal  vibra- 
tions of  something  of  which  the  molecule  is  composed.  A  com- 
plete knowledge  of  the  arrangement  and  mode  of  vibration  of 
the  atoms  of  a  molecule  would  involve  a  complete  knowledge  of 
the  corresponding  bright  lines.  We  may  imagine  that  the  mo- 
lecule of  the  very  simple  structure  which  we  have  been  consider- 
ing would  give  one  bright  line,  corresponding  to  its  fundamental 
note  ;  and  fainter  lines  would  correspond  to  some  of  the  terms 
of  the  second  and  higher  approximations. 
It  can  hardly,  I  think,  have  escaped  notice,  that  if  the  mean 
translation  velocity  of  the  molecules  of  an  incandescent  vapour 
become  so  great  as  to  bear  a  sensible  ratio  to  that  of  wave-pro- 
pagation, the  wave-length  of  the  light  corresponding  to  any 
bright  line  will  be  affected  in  a  manner  and  degree  depending 
upon  the  direction  of  motion  relative  to  that  of  the  light  ob- 
served. As  the  temperature  is  gradually  increased,  this  will 
have  the  effect  of  thickening  the  bright  lines,  and  finally  of  con- 
verting them  into  a  continuous  spectrum.  If,  as  the  tempera- 
ture is  increased,  a  rupture  or  change  of  constitution  should  take 
place  in  the  molecules,  we  may  expect  a  sudden  change  in  the 
appearance  of  the  spectrum.  In  reference  to  this  subject,  I  may 
remark,  although  I  express  an  opinion  with  much  hesitation, 
knowing  how  much  there  is  which  has  been  written  upon  this 
subject  which  I  have  not  had  an  opportunity  of  studying,  that 
