Theory  of  Magnetism.  409 
either  at  a  given  distance  during  a  limited  interval  of  time,  or  at 
a  given  instant  through  a  limited  space,  the  subsequent  motion 
cannot  be  a  solitary  wave  of  condensation  or  of  rarefaction ;  for 
in  such  case  the  condensation  would  vary  inversely  as  the  square 
of  the  distance  from  the  centre,  whereas  the  mathematical  solu- 
tion of  the  problem  shows  that  it  varies  simply  as  the  inverse  of 
the  distance.  To  meet  this  difficulty  I  now  adhere  to  the  argu- 
ments I  adduced  in  an  article  in  the  Philosophical  Magazine  for 
January  1859,  and  in  paragraph  10  of  an  article  in  the  Philoso- 
phical Magazine  for  June  186.2,  although  subsequently  I  adopted 
a  different  view.  According  to  those  arguments  the  law  of  the 
simple  inverse  of  the  distance  holds  good  only  in  case  the  dis- 
turbance gives  rise  both  to  condensation  and  rarefaction  and  the 
resulting  motion  is  consequently  vibratory.  It  must  therefore 
be  admitted  that,  whether  the  original  impulses  are.  vibratory  or 
not,  alternations  of  condensation  and  rarefaction  are  actually 
produced ;  and  it  seems  evident  that  this  effect  must  be  attri- 
buted to  the  obstacle  opposed  to  the  impulsive  action  by  the 
iuertia  of  the  surrounding  mass  of  fluid.  This  explanation  is, 
I  think,  complete  when  it  is  supplemented  by  the  consideration 
that,  according  to  the  hydrodynamical  principles  above  referred 
to,  vibratory  motion,  accompanied  by  alternate  condensation  and 
rarefaction,  may  be  shown  to  be  proper  to  an  elastic  fluid  ante- 
cedently to  any  suppositions  respecting  particular  modes  of  dis- 
turbance. (See  the  demonstration  of  Prop.  X.  in  the  Philoso- 
phical Magazine  for  December  1854,  and  that  of  Prop.  XI.  in 
the  '  Principles  of  Mathematics/  pp.  201-205.) 
14.  Again,  when  the  motion  of  an  elastic  fluid  is  supposed  to 
be  in  directions  perpendicular  to  a  given  plane,  the  usual  pro- 
cess for  determining  the  velocity  and  condensation  at  any  point 
conducts,  as  I  long  since  remarked,  to  a  contradictory  result,  in- 
dicative of  faulty  reasoning.  (See  '  Principles  of  Mathematics/ 
pp.  193-195.)  As  in  the  foregoing  case  of  central  motion, 
the  contradiction  is  significant  of  an  effect  of  the  inertia  of  the 
fluid  not  taken  into  account  by  that  process.  By  first  proving, 
antecedently  to  the  consideration  of  arbitrary  modes  of  disturb- 
ance, that  the  fluid  is  susceptible,  by  reason  of  its  inertia,  of 
spontaneous  vibratory  motions  partly  parallel  and  partly  trans- 
verse to  an  axis,  and  thence  arguing  that  arbitrarily  impressed 
motions  must  be  regarded  as  actually  composed  of  such  primary 
motions,  I  have  shown  that  the  above-mentioned  contradiction 
disappears.  (See  Prop.  XI.  above  cited.)  The  conclusions 
arrived  at  in  this  and  the  preceding  paragraph  respecting  the 
generation  of  vibratory  motions  by  impulses  that  are  not  vibra- 
tory, are  of  essential  importance  in  accounting  for  a  large  class 
of  phenomena  of  light  on  the  hypothesis  of  undulations.     Also 
