410 
ME.  EAIEBAIEN  ON  THE  EESISTANCE  OE  TUBES  TO  COLLAPSE. 
square  inch ; hence  it  appears  that  a considerable  reduction  of  tenacity  must  be  made 
for  the  riveting  of  the  plates.  The  ratio  of  reduction  is  in  this  case  -f. 
One  remarkable  fact  distinctly  established  by  these  experiments,  is  the  comparative 
weakness  of  tubes  subjected  to  external  pressm’e.  If  ^ be  put  for  the  internal  pressm’e 
per  square  inch  at  which  a tube  is  ruptured,  then  for  tubes  of  the  same  thickness  and 
diameter,  we  find  from  (6.)  and  (7.)  the  following  relation  of  strength : — 
P 1 L 
P~  13-44 
If  L = 2^  and  ^=-043,  then  p=7-77 ; that  is  to  say,  in  this  case  the  tube  subjected 
to  internal  pressure  will  have  about  7^  times  the  strength  of  a similar  tube  subjected  to 
external  pressure.  When 
i>=P, 
we  find 
L=13-44y^^-’9. 
If  ^=-25,  then  we  find  L=3f  feet  nearly;  that  is,  a tube  of  this  length  and  thickness 
will  be  equally  strong  whether  subjected  to  external  or  internal  pressm-e. 
Taking  the  mean  of  Experiments  41  and  42  on  the  lead  pipes,  we  have  from  formula  (!.}. 
E=|^^=2220, 
2x-25  ’ 
which  gives  us  the  tenacity  of  lead  per  square  inch. 
Hence  we  find 
„ 4440/c 
D 
(8.) 
which  gives  the  formula  of  strength  of  lead  tubes  subjected  to  an  internal  pressure. 
Practical  Application  to  Construction  of  the  Results  of  the  Experiments. 
Throughout  the  whole  of  the  experiments  enumerated  in  the  precedmg  pages,  it  has 
been  proved  that  the  resistance  to  collapse  from  a uniform  external  pressure,  in  cylin- 
drical tubes,  varies  in  the  inverse  ratio  of  the  lengths.  This  law  has  been  tested  to 
lengths  not  exceeding  fifteen  diameters  of  the  tube ; but  the  point  at  which  it  ceases  to 
hold  true  is  as  yet  undetermined,  and  could  only  be  ascertained  by  a new  and  laborious 
series  of  experiments  on  tubes  of  considerably  greater  length,  in  which  the  strength  of 
the  material  modifies  the  above  law  of  resistance  to  collapse.  Such  experiments  are. 
doubtless,  very  desirable ; but  the  vessels  necessary  for  the  purpose  would  be  most 
expensive,  and  the  results  already  obtained  appear  to  supply  all  the  data  necessary  for 
calculating  the  strengths  and  proportioning  the  material  in  all  ordinary  cases. 
If  we  take  a boiler  of  the  ordinary  construction,  30  feet  long  and  7 feet  in  diameter, 
with  one  or  more  fines  3 feet  or  3 feet  6 inches  in  diameter,  we  find  that  the  cylindrical 
external  shell  is  from  three  to  four  times  stronger  in  its  powers  of  resistance  to  the  force 
tending  to  burst  it,  than  the  fines  are  to  resist  the  same  force  tending  to  collapse  them. 
This  being  the  case  in  boilers  of  ordinary  construction,  it  is  not  surprising  that  so  many 
