412 
ME.  EAIEBAIEN  ON  THE  EESISTANCE  OE  TTBES  TO  COLLAPSE. 
decrease  of  strength  holds  true,  within  no  great  limits  of  en’or,  to  tubes  of  much  greater 
length  than  in  the  preceding  experiments.  That  this  conclusion  is  not  empirical,  will 
be  seen  by  the  following  experiments  upon  boilers  of  full  size,  where  it  will  be  obseiwed 
that  the  flues  were  distorted  with  one-third  the  pressm’e  required  to  rapture  the  external 
shell. 
These  boilers  were  made  for  the  North-Eastern  Division  of  the  London  and  North- 
Western  Eailway  Company,  and  were  respectively  of  35  and  25  feet  in  length.  They 
were  7 feet  in  diameter,  and  composed  of  plates  
f ths  of  an  inch  thick.  Each  boiler  had  two  cylin-  f \ 
drical  flues  3 feet  6 inches  in  diameter,  and  of  the 
same  thickness  of  plates  as  the  outer  shell.  They 
were  fixed  in  the  position  shown  in  the  annexed 
diagram,  and  were  intended  to  resist  an  ordinary  working  pressure  of  only  40  lbs.  upon 
the  square  inch.  In  submitting  them  to  the  usual  test  of  double  pressure,  the  flues  of 
the  first  or  longest  boiler  gave  way  with  97  lbs.  upon  the  square  inch ; and  those  of  the 
shorter  boiler  required  127  lbs.  to  effect  the  same  distortion.  With  these 
large  tubes  a complete  collapse  was  not  accomplished,  but  the  cmcular 
form,  indicated  by  the  dotted  line,  was  distorted,  and  the  flue  became  i 
elliptical,  as  shown  dXhh*. 
The  weakness  of  the  flues  in  the  above  experiments  is  so  evident  as 
to  need  no  comment.  To  remedy  it,  it  has  been  already  stated,  we  need  only  resort  to 
a construction  so  simple,  and  yet  so  effective,  as  to  meet  at  a small  expense  all  the 
requirements  of  the  case. 
* Eeducing  the  above  results  to  unity  of  length,  which  with  flues  of  this  size  should  give  a nearly  con- 
stant quantity,  we  have — 
D. 
L. 
P. 
P.L. 
First  boiler  
42 
35 
97 
3395 
Second  boiler  
42 
25 
127 
3175 
The  correspondence  in  the  last  column  shows  that  these  flues  obey  the  law  of  inversely  as  the  lengtlis, 
very  nearly,  in  their  powers  of  resistance. 
It  may  be  well  to  test  the  accuracy  of  the  formula  which  has  been  found  to  apply  to  tubes  of  a length 
not  greater  than  10  feet,  by  determining  from  it  the  strength  of  flues  similar  to  the  above,  and  comparing 
the  results  with  those  derived  from  experiment. 
Here,  for  the  boiler  35  feet  long,  we  have  by  formula 
P = 806,300 
=78  lbs. ; by  experiment  97  lbs. 
This  difference  confirms  the  view  already  stated,  that  the  formula  for  short  tubes  does  not  applj'  strictly  to 
tubes  longer  than  10  feet. 
Eor  the  boiler  25  feet  long,  we  have 
P=1091bs. ; hj^  experiment  127  Ihs. 
A less  difference  between  the  experimental  and  calculated  result,  as  would  have  been  anticipated  from  the 
shorter  length  of  the  flue. 
It  will  he  observed,  that  even  these  experiments,  upon  friU-sized  boilers,  ai’e  remarkably  consistent,  and 
offer  no  discrepancies  which  cannot  he  easily  explained  consistentty  with  the  general  formula. 
