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XXI.  On  the  Resistance  of  Tubes  to  collapse. 
By  William  Faikbaien,  Esq.^  C.E.,  F.B.S.,  &c. 
Eeceived  April  21, — Read  May  20,  1858. 
The  following  experiments  were  undertaken  at  the  joint  request  of  the  Koyal  Society 
and  the  British  Association  for  the  Advancement  of  Science.  Their  object  is  to  deter- 
mine the  laws  which  govern  the  strength  of  cyhndrical  vessels  exposed  to  a uniform 
external  force,  and  then’  immediate  practical  application  in  proportioning  more  accu- 
rately the  flues  of  boilers  for  raising  steam,  which  have  hitherto  been  constructed  on 
merely  empmcal  data. 
It  is  well  known  that  the  immense  extension  of  the  application  of  steam  power,  and 
the  consequent  inducement  to  economise  as  far  as  possible  the  fuel  necessary  for  its 
production,  together  with  the  growing  tendency  to  employ  the  expansive  principle,  has 
caused  a general  increase  of  the  working  pressure  from  10  lbs.  to  50  lbs.,  and  even  in 
some  cases  to  150  lbs.  on  the  square  inch.  Unfortunately,  however,  our  knowledge  of 
the  principles  of  construction  has  not  kept  pace  with  our  desire  to  economise,  and 
hence  the  change  has  been  accompanied  by  an  increase  of  dangerous  and  fatal  acci- 
dents from  boiler  explosions.  Investigation  has  frequently  shown  these  lamentable 
catastrophes  to  have  arisen  from  ignorance  of  the  immense  elastic  power  of  steam,  and 
from  a want  of  knowledge  of  the  forms  of  construction  best  calculated  to  retain  an  agent 
of  such  potent  force;  and  as  explosions  become  more  frequent  in  proportion  as  the 
pressure  is  increased,  it  is  the  more  necessary  to  inquire  into  the  causes  of  such  disasters, 
and  to  apply  such  remedies  as  may  effectually  prevent  them. 
In  order  to  save  space  and  to  increase  the  generative  powers  of  boilers,  internal  flues 
and  tubes  have  been  generally  adopted,  and  that  without  sufficient  attention  to  propor- 
tioning their  diameter,  length,  and  thickness  of  plates,  so  as  to  ensure  safety  on  the  one 
hand,  and  economy  of  material  in  its  judicious  distribution  on  the  other.  Hitherto  it 
has  been  considered  an  undisputed  axiom  among  practical  engineers,  that  a cylindrical 
tube,  such  as  a boiler-flue,  when  subjected  to  a uniform  external  pressure,  was  equally 
strong  in  every  part,  and  that  the  length  did  not  affect  the  strength  of  a tube  so  placed. 
But  although  this  rule  may  be  true  when  apphed  to  tubes  of  indefinite  length,  or  to 
tubes  unsupported  by  rigid  rings  at  the  extremities,  it  is  veiy  far  from  true  where  the 
lengths  are  restricted  within  certain  apparently  constant  limits,  and  where  the  ends  are 
securely  fastened  in  frames,  which  prevent  their  yielding  to  an  external  forcO. 
In  some  experimental  tests  to  prove  the  efficiency  of  some  large  boilers,  the  author 
had  some  misgirings  as  to  the  strength  of  the  internal  flues  to  resist  a force  tending  to 
