404 
ME.  FAIEBAIEN  ON  THE  EESISTANCE  OE  TUBES  TO  COLLAPSE. 
which,  to  a certain  extent,  is  independent  of  the  length  of  the  tube,  whilst  the  pressnie 
producing  the  compression  is  always  approximately  proportional  to  the  longitudinal 
section.  Now  let  us  assume  for  these  tubes, — 
P'  = the  external  pressure  of  the  fluid  in  lbs.  to  produce  ruptme  or  collapse ; 
P = this  pressure  per  square  inch ; 
R = the  resistance  of  the  material  to  compression  or  to  crumpling ; 
L = the  length  of  the  tube  in  feet ; 
D = the  diameter  of  the  tube  in  inches ; 
h — the  thickness  of  the  plates  in  inches ; 
p = the  pressure  P reduced  to  unity  of  length  and  diameter,  or  =PLD ; 
C,  a,  constants  to  be  determined  from  the  data  supplied  by  the  experiments. 
Since  P',  the  total  pressure  on  the  tube,  varies  directly  as  the  longitudinal  section, 
that  is,  as  the  product  of  the  length  by  the  diameter,  we  have 
F=C'.  P.  L.  D. 
Now  it  has  been  determined  by  experiment,  that  the  resistance  of  thin  ii-on  plates  to 
a force  tending  to  crush  them,  or  rather  to  a force  tending  to  crumple  them,  varies 
directly  as  a certain  power  of  their  thickness,  the  number  indicating  the  power  lying 
between  2 and  3 ; hence  we  assume, 
R=C".^*; 
but  when  rupture  takes  place,  P'=R,  and 
C'.P.  L.D=C''.^, 
For  tubes  of  the  same  thickness,  we  readily  derive  from  this  equality, 
P.L.D=P,L,.D^; (3.) 
that  is,  the  continued  product  of  the  pressure,  the  length  and  the  diameter  is  constant  ; 
or  in  other  words,  for  tubes  having  the  same  thickness,  the  pressm’es  of  collapse  reduced 
to  unity  of  length  and  diameter  [p)  are  equal  to  one  another. 
To  determine  the  values  of  the  constants  a and  C in  (2.),  we  have 
PLD  /^Y 
PAD,”  W ■ 
But  in  order  to  embrace  a range  of  experiments  by  taking  the  mean  of  theii’  results, 
we  have,  putting  p for  the  value  of  P,  when  the  tube  is  reduced  to  unity  of  length  and 
to  unity  of  diameter. 
(4.) 
■ _ logp-logj?, . 
logA  — log  A:,  ’ 
