^lE.  FAIEBAIEN  ON  THE  EESISTANCE  OE  TUBES  TO  COLLAPSE. 
403 
narrow  slit ; Zj  ruptured  similarly ; and  on  measuring  the  expanded  circumferences  at 
the  broadest  part,  it  was  found  that  the  metal  of  the  former  had  elongated  1^  inch,  and 
that  of  the  latter  1|^  inch. 
These  experiments  seem  to  show  pretty  conclusively,  that  the  length  has  very  slight 
influence  on  the  resisting  powers  of  tubes  of  wrought  iron  to  internal  pressure.  Beyond 
the  hmit  of  one  or  two  feet  in  length,  it  appears  to  aflect  the  strength  so  slightly,  that 
it  may  be  almost  enth’ely  disregarded  in  practice. 
GENEEALIZATION  OE  THE  EESULTS  OE  THE  EXPEEIMENTS. 
In  the  reduction  of  the  experiments,  I have,  as  on  former  occasions,  been  ably  assisted 
by  my  friend  IVIi’.  Tate,  whose  sound  philosophical  views  and  high  mathematical  attain- 
ments are,  from  his  numerous  publications,  so  well  known  to  the  public.  To  that  gentle- 
man I am  indebted  for  many  seivices,  and  among  others  for  an  elaborate  inquiry  into 
the  specific  gravity  and  properties  of  steam,  which  I hope  will  be  shortly  forthcoming 
as  a new  addition  to  our  knowledge,  and  that  more  particularly  in  its  application  to  the 
wants  and  necessities  of  the  present  high  state  of  civihzation. 
On  this  question  I am  personally  gratified  to  find  the  subject  in  such  able  hands,  and 
aided  by  the  industry,  care  and  perseverance  of  my  own  assistant,  Mr.  W.  Unwin,  I 
entertain  hopes  of  rendering  the  researches  now  in  progress  of  such  a character  as  fully 
to  justify  the  application  of  the  word  useful,  which  of  all  others  is  probably  the  best 
calculated  to  express  the  true  value  of  these  investigations. 
Formulce  of  Strength  relative  to  Cylindrical  Tubes. 
The  strain  which  the  material  of  a cylindrical  vessel  undergoes,  when  a uniformly- 
distributed  external  pressure  is  applied  to  it,  is  very  difierent  from  the  strain  produced 
when  the  pressure  acts  internally.  In  the  latter  case  the  material  is  equally  extended 
throughout  all  its  parts,  and  its  cylindrical  form  is  preserved  at  all  stages  of  the 
pressm-e,  with  the  exception  of  a small  portion  closely  bordering  upon  the  inflexible 
plates  closing  the  extremities.  The  tube  under  a high  internal 
pressm’e  will  assume  the  form  represented  in  the  annexed  dia- 
gram, and  the  relation  of  the  force  of  rupture  to  that  of  resist- 
ance will  be  approximately  expressed  by 
p=?^, (1-) 
where  P represents  the  pressure  requisite  to  produce  rupture,  E the  ultimate  resistance 
of  the  material  to  extension,  D the  chameter  of  the  tube,  and  k its  thickness ; whereas 
in  the  former  case,  the  material,  being  compressed,  becomes  crumpled  in  longitudinal 
lines  near  the  middle ; the  tube  loses  its  original  cylindiical  shape  at  and  near  to  that 
part,  whdst  the  portions  towards  the  extremities  being  supported  by  the  inflexible  end 
plates,  retain,  or  nearly  retain,  their  original  form ; so  that,  in  fact,  the  material  virtually 
resisting  compression  is  the  comparatively  small  portion  at  and  near  the  middle,  and 
