﻿508 
  Mr. 
  K. 
  V. 
  Southwell 
  on 
  the 
  

  

  with 
  curves 
  derived 
  by 
  the 
  above 
  theory 
  from 
  the 
  stress- 
  

   strain 
  diagrams 
  of 
  compression 
  tests. 
  The 
  latter, 
  drawn 
  on 
  

   the 
  left-hand 
  sides 
  of 
  the 
  figures, 
  are 
  representative 
  diagrams 
  

   for 
  hard 
  and 
  annealed 
  brass 
  and 
  steel, 
  as 
  given 
  in 
  any 
  text- 
  

   book. 
  In 
  the 
  case 
  of 
  fig. 
  2, 
  the 
  Curve 
  V 
  is 
  first 
  drawn 
  to 
  

   represent 
  the 
  circumferential 
  compressive 
  stress, 
  or 
  u 
  fibre 
  

   stress," 
  from 
  the 
  equation 
  * 
  

  

  p 
  =12,575,000 
  i{ 
  , 
  (9) 
  

  

  and 
  the 
  Curves 
  III 
  and 
  IV 
  are 
  obtained 
  from 
  this. 
  Fig. 
  2 
  

   illustrates 
  clearly 
  a 
  point 
  which 
  the 
  present 
  paper 
  is 
  intended 
  

   especially 
  to 
  emphisize, 
  i. 
  e. 
  the 
  danger 
  of 
  undue 
  reliance 
  in 
  

   design 
  upon 
  experimental 
  estimates 
  of 
  the 
  resistance 
  of 
  

   drawn 
  tubes 
  to 
  collapse, 
  owing 
  to 
  the 
  transitory 
  nature 
  of 
  

   that 
  part 
  of 
  their 
  strength 
  against 
  buckling 
  which 
  they 
  

   possess 
  in 
  virtue 
  of 
  the 
  hardening 
  processes 
  of 
  manufacture. 
  

   Exact 
  analyses 
  and 
  stress-strain 
  diagrams 
  of 
  the 
  brass 
  com- 
  

   posing 
  his 
  tubes 
  were 
  not 
  published 
  by 
  Professor 
  Carman, 
  

   but 
  it 
  is 
  clear 
  that 
  the 
  process 
  of 
  drawing 
  would 
  tend 
  to 
  

   harden 
  the 
  material 
  at 
  points 
  close 
  to 
  the 
  surface, 
  so 
  that 
  

   the 
  experimental 
  results 
  may 
  be 
  expected 
  to 
  agree 
  more 
  and 
  

   more 
  closely 
  with 
  the 
  theoretical 
  Curve 
  III 
  (which 
  is 
  drawn 
  

   for 
  a 
  homogeneous 
  tube 
  of 
  hard 
  brass) 
  as 
  the 
  proportion 
  of 
  

   material 
  affected 
  by 
  the 
  drawing 
  process 
  increases. 
  In 
  other 
  

   words, 
  we 
  should 
  expect 
  that 
  in 
  the 
  case 
  of 
  any 
  actual 
  tube 
  

   they 
  will 
  give 
  points 
  lying 
  between 
  Curves 
  III 
  and 
  IV, 
  and 
  

   this 
  is 
  found 
  to 
  be 
  the 
  case. 
  But 
  if 
  the 
  tube 
  be 
  subjected 
  to 
  

   practical 
  conditions 
  tending 
  to 
  anneal 
  it, 
  we 
  may 
  expect 
  that 
  

   it 
  will 
  approach 
  more 
  and 
  more 
  nearly 
  a 
  limit 
  which 
  is 
  

   represented 
  by 
  the 
  Curve 
  IV. 
  Imperfect 
  circularity 
  and 
  

   want 
  of 
  uniformity 
  in 
  thickness 
  or 
  material 
  will, 
  as 
  in 
  every 
  

   case, 
  result 
  in 
  further 
  weakening, 
  and 
  we 
  are 
  therefore 
  led 
  

   to 
  the 
  conclusion 
  that 
  by 
  employing 
  in 
  design 
  formulae 
  which 
  

   have 
  been 
  obtained 
  from 
  hydraulic 
  testing 
  apparatus, 
  we 
  are 
  

   making 
  serious 
  over-estimates 
  of 
  strength, 
  unless 
  we 
  can 
  

   rely 
  upon 
  the 
  maintenance 
  under 
  practical 
  conditions 
  of 
  

   the 
  high 
  elastic 
  limit 
  which 
  is 
  induced 
  by 
  the 
  drawing- 
  

   process. 
  

  

  I 
  am 
  not 
  competent 
  to 
  say 
  exactly 
  how 
  far 
  the 
  treatment 
  

   to 
  which 
  boiler-flues 
  are 
  subjected 
  in 
  practice 
  will 
  tend 
  to 
  

   anneal 
  them 
  ; 
  but 
  it 
  would 
  appear 
  that 
  the 
  only 
  safe 
  course 
  

   is 
  to 
  allow 
  for 
  thorough 
  annealing, 
  and 
  to 
  regard 
  the 
  estimates 
  

   given 
  by 
  Curve 
  IV 
  for 
  the 
  strength 
  of 
  brass 
  flues 
  as 
  absolute 
  

  

  * 
  Equation 
  (9) 
  was 
  given 
  by 
  Carman 
  for 
  thin 
  tubes. 
  The 
  numerical 
  

   ■coefficient 
  is 
  quite 
  a 
  representative 
  value 
  of 
  E 
  for 
  brass. 
  

  

  