﻿1875.] 
  

  

  Eos 
  act 
  Rectilinear 
  Motion 
  by 
  Linkwork. 
  

  

  577 
  

  

  describes 
  a 
  straight 
  line 
  3 
  B 
  through 
  B, 
  the 
  angle 
  3 
  B 
  O 
  l 
  being 
  one 
  

   half 
  of 
  the 
  angle 
  3 
  P 
  O 
  r 
  This 
  greatly 
  adds 
  to 
  the 
  usefulness 
  of 
  the 
  

   linkworks. 
  

  

  Fig. 
  16. 
  

  

  It 
  is 
  not 
  suggested 
  that 
  the 
  linkworks 
  here 
  given 
  exhaust 
  7-bar 
  

   line 
  linkworks 
  ; 
  indeed 
  it 
  is 
  obvious 
  that 
  many 
  of 
  them 
  are 
  suscep- 
  

   tible 
  of 
  variations. 
  Enough, 
  however, 
  has 
  been 
  shown 
  to 
  demon- 
  

   strate 
  the 
  important 
  part 
  which 
  the 
  property 
  of 
  a 
  quadrilateral 
  combined 
  

   with 
  the 
  principle 
  of 
  the 
  conjugate 
  image 
  stated 
  at 
  the 
  outset 
  plays 
  in 
  the 
  

   question. 
  

  

  I 
  have 
  strictly 
  confined 
  myself 
  in 
  this 
  paper 
  to 
  the 
  consideration 
  of 
  the 
  

   rectilinear 
  motion 
  of 
  a 
  point. 
  The 
  principles 
  involved, 
  however, 
  are 
  appli- 
  

   cable 
  to 
  many 
  other 
  problems, 
  as, 
  for 
  example, 
  the 
  motion 
  of 
  bars 
  every 
  

   point 
  in 
  which 
  moves 
  in 
  one 
  of 
  a 
  series 
  of 
  parallel 
  straight 
  lines 
  or 
  in 
  the 
  

   same 
  straight 
  line. 
  By 
  means 
  of 
  the 
  peculiar 
  form 
  of 
  the 
  fundamental 
  

   linkage 
  given 
  in 
  figs. 
  6, 
  13, 
  14, 
  valuable 
  results 
  in 
  the 
  reversal 
  or 
  multi- 
  

   plication 
  of 
  angular 
  motion 
  maybe 
  obtained, 
  and 
  a 
  linkage 
  of 
  2n-\-2 
  bars 
  

   may 
  be 
  constructed 
  which 
  will 
  divide 
  any 
  angle 
  into 
  n 
  equal 
  parts. 
  Some 
  

   of 
  these 
  questions 
  have 
  been 
  treated 
  of 
  by 
  me 
  in 
  my 
  paper 
  in 
  the 
  

   4 
  Messenger 
  of 
  Mathematics,' 
  already 
  referred 
  to, 
  which 
  was, 
  however, 
  

   written 
  before 
  I 
  obtained 
  the 
  general 
  results 
  here 
  given. 
  The 
  exten- 
  

   sion 
  of 
  these 
  results 
  to 
  other 
  problems 
  is 
  reserved 
  for 
  future 
  inves- 
  

   tigation. 
  

  

  2x2 
  

  

  