408  Prof.  Challis  on  the  Hydrodynamical 
overcoming  in  any  sensible  degree  the  inertia  of  the  circumja- 
cent fluid;  while  the  impulses  in  the  direction  of  the  increase  of 
density  have  the  effect  of  causing  a  stream  to  flow  out  of  the  parts 
near  the  denser  end  in  courses  which ,  by  reason  of  the  inertia  of 
the  fluid  beyond,  are  at  first  made  divergent,  and  eventually  are 
turned  completely  backward  :  these  return-currents  are  then  op- 
posed by  the  inertia  of  the  fluid  beyond  the  other  end  of  the 
magnet,  and  are  made  to  converge  towards  that  end  in  such 
manner  as  to  fulfil  by  the  easiest  courses  the  necessary  condition 
of  motion  in  circuits.  According  to  this  view  the  courses  are 
determined  by  a  law  of  least  action.  (See  a  mathematical  theory 
of  this  kind  of  motion  in  the  Philosophical  Magazine  for  July 
1869.) 
12.  Like  considerations  are  applicable  if  the  magnet  has  a 
form  different  from  that  of  a  straight  bar ;  for  instance,  if  it  has 
the  form  of  a  horseshoe.  In  this  case,  as  the  two  ends  are 
brought  near  each  other,  the  mean  course  of  least  resistance  is 
along  the  axis  of  the  magnet,  and  the  stream  passes  out  of  one 
end  immediately  into  the  other.  Also  the  tendency  of  the 
stream  to  escape  from  the  curved  part  of  the  magnet  by  reason 
of  centrifugal  force  is  still  opposed  by  the  inertia  of  the  external 
fluid.  In  order  to  make  the  insulation  of  the  current  more 
complete,  that  part  is  usually  covered  with  sealing-wax,  this 
substance  not  having  the  property  of  easily  conducting  setherial 
streams. 
The  same  hydrodynamical  principles  account  for  the  flow  of  a 
galvanic  current  through  conducting  substances  of  very  irregular 
forms.  In  consequence  of  the  resistance  to  emergence  arising 
from  the  inertia  of  the  surrounding  sether,  the  currents  are  con- 
fined within  the  boundaries  of  the  conductors  just  as  a  stream 
of  water  is  confined  within  channels,  such  as  rigid  pipes,  or  ves- 
sels of  any  form  through  which  it  is  compelled  to  flow.  Only, 
in  the  case  of  the  galvanic  current,  the  condition  of  a  complete 
circuit  is  required  to  be  fulfilled  in  order  that  the  flowing  may 
take  place. 
13.  It  might  be  urged  as  an  objection  to  the  foregoing  rea- 
soning, that  if  an  unlimited  mass  of  elastic  fluid,  such  as  the 
aether  is  conceived  to  be,  were  to  receive,  within  certain  limits  of 
distance  from  a  centre,  impulses  directed  from  the  centre  and 
equal  in  all  directions,  the  effect  of  these  impulses  would  not  be 
neutralized  by  reaction  from  the  inertia  of  the  surrounding  fluid. 
This  objection  admits  of  being  answered  by  an  appeal  to  hydro- 
dynamical principles  which  1  proposed  long  since,  and  have  re- 
peatedly insisted  upon,  although  they  have  not  hitherto  received 
general  recognition.  I  have  pointed  out  that  when  an  elastic 
fluid  receives  impulses  equally  in  all  directions  from  a  centre, 
