416  Prof.  ChalhVs  on  the  Hydrodynamical 
motion  for  which  udoc  +  vdy  +  wdz  is  integrable  by  a  factor. 
When  that  differential  is  exact,  the  general  equation  (e)  conducts 
to  a  unique  result  belonging  to  a  different  class  of  motions,  as  I 
have  elsewhere  shown:  Principles  of  Mathematics,  pp.  186-188. 
The  equation  is  in  that  case  satisfied  by  rectilinear  motion,  which, 
by  reason  of  the  other  general  equations,  is  restricted  to  motion 
along  an  axis  of  longitudinal  and  transverse  vibrations.  Mo- 
tions of  the  vibratory  class  are  inapplicable  to  galvanic  and  mag- 
netic phenomena.) 
26.  The  mathematical  investigation  concluded  above  gives 
the  means  of  explaining  in  what  manner  a  galvanic  current  flows 
to  any  distance  along  a  fine  cylindrical  wire  of  copper.  Together 
with  the  movement  of  a  stream  along  the  wire,  both  within  it 
and  outside,  and  symmetrical  with  respect  to  its  axis,  there  must 
be  transverse  circular  motion  about  the  axis ;  for  otherwise,  since 
by  the  contraction  of  channel  the  velocity  is  greater,  and  the 
pressure  less,  within  the  wire  than,  in  the  circumjacent  space, 
the  fluid  would  flow  from  all  sides  towards  the  axis,  and  thus  a 
stop  would  be  put  to  the  current.  The  spiral  motion  which  re- 
sults from  the  composition  of  the  longitudinal  and  transverse 
motions,  being  accompanied  by  centrifugal  force  due  to  the  cir- 
cular motion,  has  the  effect  of  maintaining  the  current.  When 
the  continuity  of  the  wire,  or  of  any  other  substance  by  which  a 
current  is  conducted,  is  abruptly  broken,  at  the  first  instant  the 
stream  issues  from  the  terminal,  and  impinges  on  the  surround- 
ing fluid ;  but  since  it  ceases  at  the  same  instant  to  be  main- 
tained by  means  of  circular  motion  about  an  axis,  the  compound 
motion  is  immediately  converted  into  the  kind  for  which 
udx  +  vdy  -f  wdz  is  an  exact  differential,  and  is  consequently 
turned  back  by  having  to  encounter  the  inertia  of  an  unlimited 
mass  of  the  fluid.  The  return  course  will  be  along  the  original 
conductor  if  this  be  the  only,  or  the  readiest,  channel.  If,  how- 
ever, another  wire  conductor  should  be  in  the  neighbourhood  of 
the  first,  there  would  seem  to  be  no  reason  why  the  revulsion 
due  to  the  fluid's  inertia  should  not  cause  a  partial  return  of  the 
fluid  along  this  wire  also.  In  fact  it  has  been  proved  experi- 
mentally by  Faraday  that  such  motion  actually  takes  place.  I 
venture  here  to  express  the  opinion  that  no  explanation  of  this 
induction  of  a  galvanic  current,  other  than  one  resting  on  hydro- 
dynamical  principles,  is  likely  ever  to  be  discovered. 
27.  The  inquiry  as  to  the  origination  of  the  rectilinear  and 
circular  motions  which  combine  to  produce  a  galvanic  current  is 
distinct  from  the  preceding  investigation,  inasmuch  as  it  involves, 
together  with  deductions  from  hydrodynamical  principles,  con- 
siderations respecting  the  chemical  action  between  dissimilar 
bodies,  as  also  respecting  the  effect  of  the  particular  arrange- 
