402  Prof.  Challis  on  the  Hydrodynamical 
sity ;  and  it  is,  further,  supposed  that  the  atoms  are  so  small 
that  even  in  dense  bodies  the  space  which  they  occupy  is  very 
small  compared  with  the  intervening  spaces. 
2.  In  general,  when  the  atoms  of  any  substance  are  in  posi- 
tions of  stable  equilibrium,  the  attractive  forces  acting  on  any 
atom  in  the  direction  of  any  straight  line  drawn  through  its 
centre  will  just  counteract  each  other ;  and  the  same  will  be  the 
case  with  respect  to  the  repulsive  forces.  But  it  is  also  con- 
ceivable that  the  equilibrium  of  the  atom  may  be  maintained  by 
the  mutual  counteraction  of  attractive  and  repulsive  forces.  For 
instance,  let  the  substance  be  a  long  rectangular  bar  of  steel, 
slightly  increasing  in  density  by  regular  gradations  from  one 
end  to  the  other,  and  of  uniform  density  in  any  transverse  sec- 
tion. Then  the  direction  of  the  resultant  of  the  molecular 
attractive  forces  will  be  parallel  to  the  length  of  the  bar,  as  well 
as  that  of  the  resultant  of  the  atomic  repulsive  forces ;  and  it  is 
therefore  supposable  that  by  the  former  any  atom  may  be  as 
much  attracted  towards  the  denser  end  as  by  the  latter  it  is  re- 
pelled towards  the  rarer  end.  This,  in  fact,  is  assumed  in  the 
present  theory  to  be  the  case  in  a  permanently  magnetized  bar 
of  steel,  the  gradation  of  density  being  conceived  to  be  originally 
generated  by  the  usual  processes  of  magnetization,  and  to  be 
maintained  exclusively  by  the  proper  atomic  and  molecular 
forces  of  the  steel.  In  soft  iron  a  like  gradation  of  density, 
produced  by  the  action  of  an  extraneous  magnet,  or  that  of  a 
galvanic  current,  continues  only  so  long  as  the  action  lasts.  In 
diamagnetic  substances,  such  as  bismuth,  gradation  of  density 
is  similarly  produced  and  maintained  by  the  action  of  a  magnet, 
but  the  direction  in  which  the  density  increases  is  opposite  to 
that  in  soft  iron  under  analogous  circumstances.  Also  the  ap- 
plication of  heat  under  certain  conditions  gives  rise  to  magnetic 
or  galvanic  phenomena,  which,  according  to  this  theory,  are  re- 
ferable to  the  production  of  gradations  of  atomic  density  by  the 
dynamical  action  of  the  heat. 
3.  In  all  cases  of  the  existence  of  such  gradation  of  density, 
it  can  be  shown  on  the  above-stated  hypotheses,  by  reasoning 
which  will  be  presently  indicated,  that  motions  either  of  the 
aether  within  the  body,  or  of  the  body  relative  to  the  sether,  have 
the  effect  of  producing  accelerations  of  the  sether.  The  secondary 
currents  thus  generated  are  considered  to  be  the  immediate  cause 
of  magnetic  or  galvanic  attractions  and  repulsions.  Also,  in  the 
Theory  of  Frictional  Electricity  which  I  proposed  in  the  Philo- 
sophical Magazine  for  October  1860,  electrical  attractions  and 
repulsions  are  accounted  for  in  the  same  manner.  Hence  as  the 
generation  of  secondary  streams  under  the  above-stated  condi- 
tions is  a  fundamental  proposition  in  the  hydrodynamical  theories 
