Prof.  M.  B,  Pell  on  the  Constitution  of  Matter.         165 
dinate  representing  attraction.  Supposing  one  atom  fixed  at  O, 
A  is  a  position  of  stable  equilibrium  for  the  other,  and  corre- 
sponds to  the  solid  state  at  the  absolute  zero  of  temperature ; 
B  is  a  position  of  unstable  equilibrium,  and  corresponds  to  the 
liquid  state.  Distances  greater  than  0  B  correspond  to  the  con- 
dition of  gas  or  vapour.     It  is  necessary  to  suppose  that  in  all 
cases  A  B  is  small  compared  with  0  A,  and  that  -~-  is  large  at 
the  point  A,  but  generally  small  at  the  point  B.  I  do  not  know 
that  we  have  any  means  of  forming  an  opinion  as  to  the  relative 
magnitude  of  0  C  ;  but  such  a  point  as  C  must  exist  if  we  assume 
the  transition  from  Newton's  law  to  that  of  gaseous  repulsion 
to  be  gradual.  This  necessitates  the  existence  of  a  maximum 
negative  ordinate  D  Q.  It  may  be  remarked  that  the  distance 
0  J)  would  correspond  to  the  saturation-point  at  the  absolute 
zero  of  temperature;  for  supposing  a  number  of  equidistant 
atoms  in  a  confined  space,  if  the  distances  be  intermediate  in 
magnitude  between  0  B  and  0  D,  the  equilibrium  is  unstable, 
but  for  distances  greater  than  O  D  it  is  stable.  For  refractory 
solids  E  P  must  be  large,  and  D  Q  comparatively  very  small. 
For  gases,  A  B  or  E  P  or  both  are  probably  very  small,  and  D  Q 
must  be  very  large  compared  with  its  magnitude  for  non-volatile 
substances. 
If  a  small  velocity  be  impressed  upon  the  moveable  atom  in 
the  direction  0  x,  it  will  oscillate  about  A.  If  the  initial  velo- 
city be  increased  to  a  certain  value  (that  is,  under  the  action  of 
a  certain  amount  of  heat),  the  atom  will  just  reach  B  and  there 
remain.  With  a  greater  velocity  it  will  pass  beyond  B,  and  the 
solid  connexion  between  the  atoms  will  be  destroyed.  It  may 
be  seen  without  any  mathematical  investigation  that  the  vibra- 
tory motion  about  A  produces  two  effects. 
(1)  It  increases  the  mean  distance  between  the  atoms ;  that 
is,  it  produces  expansion. 
(2)  It  diminishes  the  cohesive  force  between  the  atoms ;  that 
is,  it  produces  softening. 
If  the  initial  velocity  be  sufficient  to  carry  the  atom  to  B,  the 
cohesive  force  is  entirely  destroyed,  and  the  condition  is  that  of 
perfect  liquidity,  the  mean  distance  between  the  atoms  being- 
then  0  B.  It  may  be  observed  that  the  greater  the  initial  velo- 
city, and  the  more  nearly  in  consequence  the  atom  approaches  B 
(the  position  of  unstable  equilibrium),  the  greater  is  the  propor- 
tion of  energy  in  the  potential  or  latent  state.  If  the  atom  just 
reaches  B,  the  whole  energy  becomes  latent. 
With  reference  to  the  obvious  objections  that  the  liquid  state, 
as  thus  represented,  is  one  of  absolute  instability,  and  that  the 
whole  of  the  heat  appears  to  become  latent,  1  must  remark,  in 
