﻿576 
  

  

  Mr. 
  A. 
  B. 
  Kempe 
  on 
  the 
  production 
  of 
  [June 
  17, 
  

  

  C 
  D' 
  is 
  produced 
  to 
  any 
  point 
  Q 
  and 
  a 
  point 
  M 
  is 
  taken 
  on 
  B 
  C 
  such 
  

   that 
  B 
  M=D' 
  Q. 
  A 
  B 
  is 
  fixed. 
  The 
  equal 
  bars 
  MO, 
  QO 
  are 
  added. 
  

   Then 
  O 
  clearly 
  moves 
  on 
  the 
  straight 
  L 
  perpendicular 
  to 
  A 
  B, 
  B 
  L 
  

   being 
  equal 
  to 
  L 
  D'. 
  This 
  linkwork 
  was 
  given 
  by 
  me 
  in 
  the 
  ' 
  Mes- 
  

   senger.' 
  

  

  § 
  15. 
  In 
  the 
  linkwork 
  of 
  § 
  11 
  replace 
  the 
  bar 
  ST 
  by 
  the 
  bar 
  TJY. 
  

   Make 
  

  

  a=d, 
  7c= 
  — 
  =1. 
  

   a 
  

  

  Fig. 
  15. 
  

  

  Then 
  it 
  will 
  be 
  seen 
  that 
  

  

  B 
  coincides 
  with 
  D', 
  

   B' 
  „ 
  „ 
  T>, 
  

  

  and 
  the 
  bars 
  AD, 
  AB 
  become 
  superfluous 
  and 
  may 
  be 
  removed. 
  There 
  

   then 
  remains 
  Mr. 
  Hart's 
  5-bar 
  linkwork. 
  This 
  is 
  the 
  only 
  5-bar 
  link- 
  

   work 
  giviug 
  rectilinear 
  motion 
  that 
  has 
  as 
  yet 
  been 
  obtained. 
  

  

  § 
  16. 
  In 
  many 
  of 
  the 
  previous 
  cases 
  the 
  point 
  O, 
  which 
  moves 
  in 
  a 
  

   straight 
  line, 
  will 
  be 
  found 
  to 
  be 
  connected 
  to 
  a 
  fixed 
  point 
  through 
  which 
  

   the 
  straight 
  line 
  passes 
  by 
  two 
  equal 
  bars. 
  "Whenever 
  this 
  occurs 
  the 
  

   motion 
  of 
  the 
  bar 
  containing 
  the 
  moving 
  point 
  is 
  of 
  the 
  sort 
  described 
  by 
  

   Professor 
  Sylvester 
  as 
  " 
  tram 
  motion." 
  That 
  is, 
  its 
  motion 
  is 
  that 
  of 
  a 
  bar 
  

   sliding 
  between 
  two 
  fixed 
  rectilinear 
  trammels, 
  or, 
  to 
  present 
  this 
  motion 
  

   in 
  its 
  fullest 
  generality, 
  the 
  motion 
  of 
  a 
  plane 
  in 
  which 
  a 
  whole 
  series 
  of 
  

   points 
  lying 
  on 
  a 
  circle 
  move 
  each 
  of 
  them 
  in 
  straight 
  lines 
  passing 
  

   through 
  a 
  fixed 
  point. 
  Turning 
  to 
  fig. 
  16, 
  if 
  B 
  P, 
  P 
  1 
  be 
  equal 
  bars 
  

   and 
  O 
  x 
  moves 
  in 
  the 
  straight 
  line 
  O 
  x 
  B 
  passing 
  through 
  B, 
  then 
  if 
  O 
  x 
  P 
  

   be 
  produced 
  to 
  2 
  so 
  that 
  P 
  2 
  =P 
  O 
  x 
  , 
  2 
  obviously 
  moves 
  in 
  the 
  straight 
  

   line 
  B 
  2 
  perpendicular 
  to 
  1 
  B, 
  so 
  that 
  O 
  x 
  2 
  slides 
  between 
  the 
  two 
  

   straight 
  lines 
  B 
  Q 
  v 
  B 
  2 
  . 
  In 
  this 
  case 
  it 
  is 
  clear 
  that 
  any 
  point 
  3 
  

   attached 
  to 
  the 
  bar 
  C^PO,,, 
  and 
  distant 
  a 
  distance 
  P0 
  3 
  =P0 
  1 
  from 
  P, 
  

  

  