ME.  FAIEBAIEN  ON  THE  EESISTANCE  OE  TUBES  TO  COLLAPSE. 
409 
Eediicing  the  values  of  P by  this  formula,  we  derive  the  following  results : — 
No.  of 
experiment. 
D. 
Diameter. 
L. 
Length. 
k. 
Thickness. 
P. 
Pressure. 
P',  or  value 
of  P reduced 
to  unity  of 
thickness, 
viz.  •!. 
Value  of 
P'.  L.  D. 
5 
4 
5 
•043 
43 
273 
5400 
22 
00 
•250 
420 
57 
5400 
24 
9 
•140 
00 
CO 
190 
5300 
33 
14^ 
8 
5 
•125 
125 
76 
5600 
The  remarkable  approximation  of  the  numbers  in  the  last  column  to  one  another, 
distinctly  establishes  the  law  (P.L.D  = P^.L^.DJ  in  relation  to  tubes  composed  of  thick 
plates. 
Deduction  from  the  Besults  of  the  Experiments  on  the  Collapse  of  Elliptical  Tubes. 
By  comparing  the  result  of  experiment  (34.)  on  the  elliptical  tube  with  the  result  of 
the  experiments  on  the  cylindrical  tubes,  we  find  that  the  general  formula  (6.)  will  apply 
approximately  to  elliptical  tubes,  by  substituting  for  D in  that  formula  the  diameter 
of  the  circle  of  curvature  touching  the  extremity  of  the  minor  axis.  Thus  we  have. 
Diameter  of  the  cu’cle  of  curvatime  =-^= — — =20  nearly. 
Now  the  pressure  on  this  elliptical  tube  was  6'51bs.,  which  reduced  to  unity  of 
length  and  diameter,  gives  650  lbs.,  which  result  nearly  agrees  with  688  lbs.,  the  mean 
pressure  of  the  12-inch  tubes  also  reduced  to  unity  of  length  and  diameter. 
Although  this  deduction  is  based  on  merely  one  experimental  result,  yet  it  appears 
to  be  confirmed  by  the  following  proposition  derived  from  mathematical  analysis. 
The  pressure  P per  square  inch,  requisite  to  flatten  equal  angular  portions  of  a tube 
of  variable  cun  ature,  \ ai’ies  inversely  as  the  diameters  of  curvature. 
Hence  it  will  be  observed  how  very  much  the  strength  of  a tube  subjected  to  external 
pressure  is  deteriorated  by  a delation  from  the  cylindrical  form. 
Strength  of  Cylindrical  Tubes  subjected  to  Internal  Pressure. 
Taking  the  mean  of  the  results  of  Experiments  36  and  39  on  iron  tubes,  we  have 
from  formula 
E=^^^^=30,000  nearly. 
2 X ‘043  ’ ^ 
Hence  we  find 
60,000^ 
^ “ D ’ ^ 
which  gives  the  formula  of  strength  of  thin  sheet-iron  tubes  subjected  to  internal 
pressure. 
Now  the  tenacity  of  boiler  plates  has  been  found  to  be  23  tons,  or  51,520  lbs.  per 
3 I 2 
