ME.  FA  TEE  A TEN  ON  THE  EESISTANCE  OF  TUBES  TO  COLLAPSE. 
407 
Eeduction  of  the  Results  of  Experiments  22,  24,  33  on  the  Collapse  of  Sheet-iron  Tubes 
to  unity  of  length  and  diameter. 
No.  of 
experiment. 
D. 
L. 
k. 
Thickness. 
P. 
P- 
22 
18-! 
^ 1 
^12 
•25 
420 
40,030 
24 
9 
Q I 
^12 
•14 
378 
10,495 
33 
145 
5 
•125 
125 
9,140 
To  find  the  Value  of  the  Constants  a and  C in  the  General  Formula. 
In  equality  (4.),  taking ^=40,030,  Tc^'Tb.,  ^^=820,  ^^=-043;  we  get 
log 40,030— log 820  ^ 
log -25- log -043  — ^ 
Similarly,  taking ^=40,030,  ^=‘25,  ^,=9140,  and  A:^=T25  ; we  get 
log 40,030-  log9140_^ 
log  *25— log '125  — 
and  taking ^3  = 10,495,  ^5:= -14,  ^9^=820,  ^^='043;  we  get 
log  10,495  -log  820  ^ 
log '14- log -043 
and  taking  the  mean  of  these  values,  we  get  a=2'19. 
For  the  value  of  the  constant  C,  we  have  from  (5.), 
C=|;=;o||?,,=806,300. 
Substituting  these  values  in  (2.),  we  get 
i2'19 
P=806,300x-ld’ 
which  is  the  general  formula  for  calculating  the  strength  of  wrought-iron  tubes  subjected 
to  external  pressure  *,  within  the  limits  indicated  by  the  experiments ; that  is,  provided 
their  length  is  not  less  than  1'5  foot,  and  not  greater  probably  than  10  feet. 
In  order  to  facilitate  calculation,  formula  (6.)  may  be  written, 
log P=1'5265H-2'19  log  100 k-  log (LD); 
* By  taking  2 instead  of  2 19  for  the  index  of  h,  this  formula  becomes 
P=806,300x=p^, (ff.) 
JLi.  Jj 
whence  the  value  of  P,  the  collapsing  pressure  may  be  readily  calculated  by  ordinary  arithmetic. 
For  thick  tubes  of  considerable  diameter  and  length,  this  formula  may  be  regarded  as  sufficiently  exact 
for  practical  purposes. 
For  example,  let  ^=^inch,  L= 10 feet,  D= 86 inches;  then 
P= 806,300  X , ffi!-..  = 560  lbs. 
10x36 
By  formula  (6.),  - P=l-5265  + 2-191og60-log360=5021bs. 
It  will  be  observed  that  these  results  do  not  differ  widely  from  each  other 
MDCCCLVIII.  3 I 
