178         Prof.  M.  B.  Pell  on  the  Constitution  of  Matter. 
it  be  objected  tbat  I  am  assuming  an  unnaturally  complicated 
and  fantastic  law,  I  can  only  repeat  tbat  it  is  not  assumed  arbi- 
trarily, but  is  little  more  tban  a  reflex  of  plain  facts.  If  all  the 
various  phenomena  relating  to  inorganic  matter  are  to  be  ac- 
counted for  by  the  motions  of  atoms  acting  upon  one  another 
according  to  some  one  law  (and  this  assumption  must  be  the 
foundation  of  every  such  attempt  as  the  present),  it  is  bardly 
reasonable  to  suppose  that  the  law  of  action  whicb  is  to  be  the 
cause  of  such  a  vast  variety  of  complex  relations  will  be  of  a 
very  simple  kind. 
Having  considered  the  motion  of  the  system  whilst  being 
heated  as  it  were,  let  us  now  consider  what  would  occur  if  the 
disturbance  were  to  cease  and  the  system  be  left  to  vibrate  of 
itself.     When  fit  is  any  multiple  of  2tt, 
__    cos  (2n  —  2r+l)-v^    ^V__n 
Xr~a      cos  (2W  +  1W     '  ~dt  "~°' 
At  any  such  instant  let  the  disturbing  atom  be  removed,  and 
we  have  for  the  subsequent  motion  the  initial  conditions 
cos(2?i—  2r+l)^     ,  ,  *     n 
$(r)—a — K— ^ — ,  ,.  ,      ,  ^>1(r)  =  0. 
^  V  '  COS  (2^  +  1)^  r 
We  suppose  that  the  system  is  an  aggregation  of  molecules, 
formed  as  above  described,  under  the  action  of  the  prevailing 
heat;  so  that  n  is  a  multiple  pv  otp-,  and  if  2p^=.ir  exactly, 
we  have 
7T 
cos  (2r  —  1)—              ,0       1N 
„    .               ...                v           '  2p        cos  (2r  —  1U«7 
2n-4r  =  v7r,  d>(r)=a  — — ~  =  a — -• 
r  '    rV   '  IT  C0SV7 
cos  — 
2p 
Referring  to  equation  (6),  2</>(r)  =  0, 
KZni4>ir)  cos(2r- 1)57=  -^-Scos(2r-l)^7cos(2r-l>7, 
a 
cos  try 
which  vanishes  for  all  values  of  s  except  s  =  v,  and  in  that  case 
an 
is 
2  cos  vy 
%r  —  aco$  (2r  —  l)vycos/jLvt, 
fiv  =  2m  sin  vy = 2m  sin  ^  =  p, 
cos  (2r  — l)-v/r 
xr-=-a - — —  cos  lit ; 
cosi/r  ^ 
or  the  motion  continues  in  this  case  to  be  the  same  exactly  as 
that  impressed  upon  the  system  by  the  disturbance.  The  system 
in  cooling  would  radiate  the  same  kind  of  heat  as  that  which  it 
