472  Royal  Society. 
It  need  hardly  be  said  that  this  indeterminateness  is  a  consequence 
of  the  conditions  assumed  for  the  purpose  of  simplifying  the  condi- 
tions of  the  questions ;  it  does  not  exist  in  nature.  Attention  is 
frequently  drawn  to  this  point  in  the  course  of  the  work ;  and  a  short 
chapter  (chap,  vii.)  is  devoted  to  its  elucidation.  A  considerable 
number  of  particular  cases  are  worked  out  in  illustration  of  the  ge- 
neral theorems  ;  and  in  the  last  chapter  the  problems  of  the  top,  of 
friction-wheels,  and  of  the  driving-wheels  of  locomotive  engines  are 
considered  in  detail. 
In  concluding  our  notice  of  this  work  we  must  not  fail  to  add  that 
it  seems  to  us  one  of  conspicuous  originality  and  power  ;  it  is  plainly 
the  product  of  long  and  mature  thought ;  and  it  claims,  and  we  doubt 
not  will  receive,  the  careful  study  of  all  who  are  interested  in  the 
science  of  Theoretical  Mechanics. 
LIX.  Proceedings  of  Learned  Societies. 
ROYAL  SOCIETY. 
[Continued  from  p.  396.] 
February  8,  1872. — George  Biddell  Airy,  C.B.,  President    n  the 
Chair. 
rPHE  following  communications  were  read : — 
•*-      "  Experiments  on  the  directive  power  of  large  Steel  Magnets,  of 
Bars  of  Magnetized  Soft  Iron,  and  of  Galvanic  Coils,  in  their  action 
on  external  small  Magnets."     By  George  Biddell  Airy,  Astronomer 
Royal,  C.B.,  P.R.S. 
The  author,  after  adverting  to  some  imperfect  experiments  made 
by  Coulomb  in  the  last  century,  describes  the  apparatus  which  he  had 
himself  used.  He  employed  a  bar-magnet  14  inches  in  length,  placed 
in  one  series  with  its  edge  towards  the  small  compass  on  which  its 
directive  power  was  estimated,  and  in  another  series  with  its  flat 
side  towards  the  small  compass;  also  a  galvanic  coil  13*4  inches  in 
length,  animated  by  a  battery  of  three  cells,  and  the  same  coil  with 
the  insertion  of  a  soft  iron  coil.  In  the  field  of  experiment  the  earth's 
magnetism  was  sensibly  neutralized  by  external  large  magnets.  The 
direction  of  the  needle  of  the  small  compass  was  estimated  by  eye. 
The  magnitude  of  the  directive  force  was  found  by  observing  the  po- 
sition taken  by  the  needle  when  the  poles  of  a  horseshoe-magnet 
were  placed  in  a  definite  position  above  it :  for  the  measure  of  the 
force  of  the  galvanic  coil  without  core,  a  very  small  magnet  was  used 
in  the  same  manner ;  its  power  was  found  to  be  about  jj^  that 
of  the  horseshoe-magnet.  The  circle  on  which  the  deflections  were 
observed  was  graduated  to  cotangents,  which  gave  immediately  the 
measure  of  the  force  of  the  large  magnet  or  coil,  &c.  In  each  case, 
observations  were  taken  in  30  stations  in  one  oval  ring  surrounding 
the  magnet  &c,  and  in  38  stations  in  another  oval  ring  surrounding 
it  at  a  greater  distance.  Omitting  notice  of  the  measures  in  general, 
the  following  specific  points  are  remarked  : — 
At  a  constant  distance  from  the  steel,  the  greatest  force  exerted 
by  a  magnet  is  not  the  longitudinal  force  at  the  end,  but  the  trans- 
