﻿1875.] 
  

  

  Prof. 
  0. 
  Reynolds 
  on 
  Rolling 
  -Friction. 
  

  

  507 
  

  

  lateral 
  extension 
  in 
  the 
  latter, 
  so 
  that 
  in 
  passing 
  from, 
  one 
  point 
  to 
  

   another 
  the 
  roller 
  does 
  in 
  truth 
  pass 
  over 
  a 
  greater 
  extent 
  of 
  surface 
  than 
  

   the 
  distance 
  between 
  these 
  points. 
  A 
  simple 
  experiment 
  was 
  sufficient 
  

   to 
  verify 
  the 
  truth 
  of 
  this 
  conclusion. 
  An 
  iron 
  roller 
  18 
  inches 
  in 
  circum- 
  

   ference 
  was 
  found 
  to 
  roll 
  through 
  something 
  like 
  | 
  inch 
  less 
  than 
  a 
  yard 
  

   in 
  two 
  complete 
  revolutions 
  when 
  rolling 
  on 
  a 
  plate 
  of 
  india-rubber. 
  The 
  

   softness 
  of 
  the 
  india-rubber 
  suffered 
  the 
  roller 
  to 
  indent 
  it 
  considerably 
  ; 
  

   and 
  hence 
  it 
  might 
  be 
  expected 
  that 
  the 
  effect 
  would 
  be 
  much 
  more 
  

   apparent 
  than 
  when 
  the 
  roller 
  was 
  rolling 
  on 
  iron 
  or 
  any 
  hard 
  material. 
  

   At 
  the 
  same 
  time 
  there 
  is 
  doubtless 
  a 
  certain 
  amount 
  of 
  indentation 
  in 
  this 
  

   latter 
  case 
  ; 
  and 
  this 
  will 
  probably 
  cause 
  a 
  similar 
  alteration 
  in 
  the 
  distance 
  

   rolled 
  through, 
  although 
  too 
  small 
  to 
  allow 
  its 
  being 
  measured. 
  

  

  This 
  falling 
  off 
  from 
  what 
  may 
  be 
  called 
  the 
  geometrical 
  distance, 
  sug- 
  

   gested 
  an 
  explanation 
  of 
  the 
  resistance 
  to 
  rolling, 
  namely, 
  that 
  the 
  exten- 
  

   sion 
  of 
  the 
  surface 
  or 
  surfaces 
  at 
  the 
  point 
  of 
  contact 
  causes 
  the 
  one 
  

   surface 
  to 
  slide 
  over 
  the 
  other 
  ; 
  and 
  this 
  sliding 
  is 
  accomplished 
  against 
  

   friction. 
  In 
  this 
  way 
  we 
  should 
  expect 
  to 
  find 
  the 
  resistance 
  to 
  rolling 
  

   greatest 
  under 
  those 
  circumstances 
  in 
  which 
  the 
  sliding 
  is 
  greatest, 
  i. 
  e. 
  

   where 
  the 
  indentation 
  is 
  greatest 
  ; 
  and 
  so 
  far 
  it 
  is 
  in 
  accordance 
  with 
  

   Coulomb's 
  laws. 
  In 
  the 
  case 
  of 
  india-rubber, 
  we 
  find 
  the 
  slipping 
  

   is 
  very 
  large 
  ; 
  and 
  hence 
  we 
  should 
  expect 
  the 
  resistance 
  to 
  rolling 
  to 
  

   be 
  large 
  also 
  ; 
  and 
  accordingly 
  we 
  find 
  it 
  so, 
  for 
  it 
  is 
  more 
  than 
  

   ten 
  times 
  as 
  great 
  as 
  when 
  the 
  roller 
  is 
  on 
  an 
  iron 
  plane. 
  This 
  very 
  

   great 
  resistance 
  which 
  india-rubber 
  causes 
  to 
  rolling 
  appears 
  not 
  to 
  have 
  

   previously 
  caught 
  attention 
  ; 
  and 
  yet 
  it 
  is 
  the 
  natural 
  explanation 
  of 
  the 
  

   invariable 
  failure 
  which 
  has 
  attended 
  the 
  numerous 
  endeavours 
  which 
  

   have 
  been 
  made 
  to 
  use 
  this 
  material 
  for 
  the 
  tires 
  of 
  wheels. 
  

  

  This 
  idea, 
  that 
  the 
  resistance 
  to 
  rolling 
  is 
  due 
  to 
  the 
  friction 
  between 
  

   the 
  surfaces 
  sliding 
  at 
  the 
  point 
  of 
  contact, 
  naturally 
  leads 
  to 
  the 
  conclu- 
  

   sion 
  that 
  it 
  must 
  depend 
  on 
  the 
  coefficient 
  of 
  friction 
  between 
  these 
  sur- 
  

   faces, 
  and 
  that 
  we 
  might 
  expect 
  to 
  diminish 
  the 
  resistance 
  by 
  using 
  oil 
  

   or 
  any 
  other 
  means 
  of 
  reducing 
  the 
  coefficient 
  of 
  friction. 
  This 
  was 
  the 
  

   author's 
  first 
  impression. 
  Experiments, 
  however, 
  showed 
  that 
  the 
  effect 
  

   of 
  oiling 
  the 
  surface, 
  although 
  it 
  did 
  generally 
  reduce 
  the 
  resistance, 
  was 
  

   very 
  small 
  ; 
  and 
  sometimes 
  it 
  appeared 
  to 
  act 
  in 
  the 
  reverse 
  manner, 
  and 
  

   increase 
  the 
  resistance. 
  This 
  conclusion 
  or 
  surmise 
  was 
  therefore 
  wrong 
  ; 
  

   and 
  the 
  cause 
  of 
  the 
  error 
  was 
  not 
  far 
  to 
  seek. 
  It 
  consisted 
  in 
  having 
  

   overlooked 
  the 
  fact 
  that 
  friction 
  not 
  only 
  opposes 
  the 
  sliding 
  of 
  the 
  one 
  

   surface 
  over 
  the 
  other, 
  but 
  also 
  prevents 
  it 
  to 
  a 
  considerable 
  extent, 
  and 
  

   thus 
  modifies 
  the 
  deformation 
  which 
  would 
  otherwise 
  take 
  place 
  ; 
  so 
  that 
  

   any 
  diminution 
  in 
  the 
  coefficient 
  of 
  friction 
  is 
  attended 
  with 
  an 
  increase 
  

   in 
  the 
  extent 
  of 
  slipping, 
  which 
  tends 
  to 
  balance 
  the 
  advantage 
  gained 
  

   by 
  the 
  reduced 
  coefficient. 
  

  

  The 
  truth 
  of 
  this 
  view 
  derives 
  independent 
  support 
  from 
  a 
  circum- 
  

   stance 
  remotely 
  connected 
  with 
  rolling-friction, 
  of 
  which 
  it 
  furnishes 
  an 
  

  

  