﻿1875.] 
  Production 
  of 
  Exact 
  Rectilinear 
  Motion 
  by 
  IAnkwork. 
  565 
  

  

  sexual 
  difference 
  in 
  the 
  weight 
  of 
  the 
  male 
  brain 
  overrides 
  the 
  influence 
  

   of 
  stature, 
  or 
  subsists 
  in 
  spite 
  of 
  his 
  greater 
  stature, 
  which 
  has 
  a 
  tendency 
  

   to 
  diminish 
  his 
  proportionate 
  amount 
  of 
  brain. 
  

  

  Further 
  comparisons 
  show 
  that 
  the 
  stature 
  ratio, 
  as 
  it 
  may 
  be 
  called, 
  

   diminishes 
  with 
  the 
  height 
  less 
  markedly 
  and 
  less 
  constantly 
  in 
  the 
  

   case 
  of 
  the 
  cerebrum 
  than 
  in 
  the 
  case 
  of 
  the 
  cerebellum, 
  which 
  latter 
  

   organ, 
  therefore, 
  obeys 
  the 
  influence 
  of 
  stature 
  more 
  exactly 
  and 
  impli- 
  

   citly, 
  so 
  far 
  as 
  regards 
  its 
  relative 
  proportion 
  to 
  the 
  body. 
  

  

  3. 
  It 
  becomes 
  evident, 
  and 
  may 
  be 
  shown, 
  that 
  all 
  estimates 
  of 
  other 
  

   influences 
  regulating 
  the 
  brain-weights 
  in 
  Man, 
  whether 
  these 
  be 
  sex, 
  

   age, 
  occupation, 
  education, 
  or 
  disease, 
  are 
  liable 
  to 
  error 
  unless 
  the 
  influ- 
  

   ence 
  of 
  stature 
  be 
  first 
  eliminated. 
  Instances 
  of 
  this 
  statement 
  are 
  easy 
  

   to 
  find. 
  

  

  ; 
  4. 
  It 
  may 
  in 
  this 
  mode 
  be 
  demonstrated 
  what 
  is 
  the 
  true 
  influence 
  of 
  

   sex, 
  age, 
  disease, 
  and 
  other 
  modifying 
  causes. 
  

  

  5. 
  Lastly, 
  in 
  this 
  way 
  alone 
  can 
  we 
  arrive, 
  as 
  it 
  seems 
  to 
  me, 
  at 
  a 
  

   correct 
  appreciation 
  of 
  that 
  residual 
  cause 
  of 
  peculiarity 
  or 
  deviation 
  

   in 
  the 
  weight 
  of 
  the 
  encephalon 
  and 
  its 
  parts, 
  especially 
  of 
  the 
  cerebrum, 
  

   which 
  may 
  be 
  called 
  its 
  proper 
  we'ujlit— 
  variation, 
  as 
  an 
  independent 
  

   or 
  quasi-independent 
  organ. 
  

  

  6. 
  This 
  residual 
  variation, 
  it 
  may 
  be 
  thus 
  shown, 
  is 
  far 
  larger 
  than 
  any 
  

   other, 
  a 
  fact 
  obviously 
  of 
  the 
  highest 
  interest 
  and 
  importance. 
  

  

  In 
  support 
  of 
  these 
  propositions, 
  and 
  others 
  of 
  greater 
  detail, 
  I 
  propose 
  

   to 
  make 
  a 
  lengthened 
  communication 
  hereafter. 
  

  

  XVIII. 
  " 
  On 
  a 
  General 
  Method 
  of 
  producing 
  exact 
  Rectilinear 
  

   Motion 
  by 
  Linkwork/' 
  By 
  A. 
  B. 
  Kempe_, 
  B.A., 
  of 
  the 
  Inner 
  

   Temple, 
  late 
  Scholar 
  of 
  Trinity 
  College, 
  Cambridge. 
  Commu- 
  

   nicated 
  by 
  J. 
  J. 
  Sylvester, 
  F.R.S. 
  Received 
  June 
  4, 
  1875. 
  

  

  Since 
  the 
  invention 
  by 
  James 
  Watt, 
  in 
  178-1, 
  of 
  the 
  3-bar 
  linkwork 
  

   known 
  as 
  " 
  "Watt's 
  Parallel 
  Motion," 
  which 
  gives 
  an 
  approximate 
  recti- 
  

   linear 
  motion, 
  many 
  attempts 
  have 
  been 
  made 
  to 
  obtain 
  a 
  more 
  perfect 
  

   solution 
  of 
  the 
  problem 
  how 
  to 
  obtain 
  accurate 
  rectilinear 
  motion 
  by 
  means 
  

   of 
  linkwork. 
  Professor 
  Tchebicheff 
  succeeded 
  in 
  obtaining 
  a 
  3-bar 
  link- 
  

   work 
  giving 
  a 
  much 
  closer 
  approximation 
  to 
  a 
  true 
  result 
  ; 
  but 
  in 
  his 
  case, 
  

   as 
  in 
  that 
  of 
  others, 
  the 
  solution 
  is 
  only 
  approximate, 
  and 
  it 
  may 
  be, 
  in 
  

   fact, 
  shown 
  that 
  with 
  3 
  bars 
  an 
  accurate 
  result 
  cannot 
  be 
  obtained. 
  It 
  

   was 
  not 
  until 
  1864 
  that 
  the 
  problem 
  was 
  solved 
  ; 
  in 
  that 
  year 
  M. 
  Peau- 
  

   cellier 
  made 
  his 
  memorable 
  discovery 
  of 
  an 
  accurate 
  7-bar 
  solution; 
  and 
  

   in 
  1874, 
  when 
  the 
  subject 
  was 
  brought 
  prominently 
  forward 
  in 
  England 
  

   by 
  Professor 
  Sylvester, 
  Mr. 
  Hart, 
  in 
  a 
  paper 
  read 
  before 
  the 
  British 
  Asso- 
  

   ciation, 
  gave 
  a 
  solution 
  by 
  means 
  of 
  5 
  bars. 
  Both 
  these 
  linkworks, 
  as 
  is 
  

   now 
  well 
  known, 
  depended 
  upon 
  the 
  inversion 
  of 
  a 
  circle 
  with 
  respect 
  to 
  

   a 
  point 
  on 
  its 
  circumference. 
  

  

  