MR.  FAIEBAIRN  ON  THE  RESISTANCE  OE  TUBES  TO  COLLAPSE. 
405 
and  similarly,  we  find 
C=£ (5) 
A glance  at  the  results  of  the  experiments  recorded  in  Tables  I.  II.  III.  IV.  V., 
where  the  thickness  of  the  plates  composing  the  tubes  is  the  same,  is  sufficient  to  show, 
— 1st,  that  the  strength  of  the  tubes  varies  nearly  inversely  as  their  lengths ; 2ndly, 
that  the  strength  also  varies  nearly  inversely  as  the  diameters.  The  following  reduc- 
tion of  these  experiments  will  not  only  render  these  laws  apparent,  but  will  also  show 
that  in  tubes  of  the  same  thickness  the  strength  varies  inversely  as  the  product  of  their 
lengths  by  their  diameters,  or,  what  amounts  to  the  same  thing,  that  PLD  (=j?)  is 
nearly  a constant  quantity. 
Reduction  of  the  Results  of  the  Experiments  on  the  Collapse  of  Sheet-iron  Tubes 
■043  inch  thick,  to  unity  of  length  and  diameter. 
Experiments  1,  2 and  6,  were  performed  on  tubes  of  the  same  length  and  diameter, 
and  also  Experiments  7,  10  and  11 ; hence  we  have  for  the  mean  values  of  P, — 
Mean  value  of  P from  Experiments  1,  2 and  6= 
Mean  value  of  P from  Experiments  7,  10  and  11 
170+137H-140 
=149. 
48  + 52  + 65 
=55. 
4-inch  Tubes. 
D. 
L. 
p. 
P.  L. 
P.  D. 
P- 
No.  of 
Pressure 
Pressure 
Pressure 
Pressure 
experimeut. 
Diameter  in 
inches. 
Length  in 
feet. 
of  collapse  in 
lbs. 
reduced  to 
unity  of  L. 
reduced  to 
unity  of  D. 
reduced  to 
unity  of  L 
and  D. 
1,  2,  6 
4 
149 
232-5 
596 
930-0 
3 
4 
65 
216-6 
260 
866-4 
4 
4 
65 
205-8 
260 
823-2 
5 
4 
5 
43 
215-8 
172 
860-0 
27 
4 
5 
47 
235-0 
188 
940-0 
29 
4 
*^2 
93 
232-5 
372 
930-0 
6)5349-6 
Mean  value  of p 891-6 
The  approximation  of  the  numbers  to  one  another  in  columns  5 and  7,  shows  how 
very  nearly  the  strength  varies  inversely  as  the  lengths.  This  observation  applies  with 
equal  exactness  to  all  the  reductions  which  follow. 
6-inch  Tubes. 
No.  of 
experiment. 
D. 
L. 
P. 
P.  L. 
P.D. 
P- 
7,  10,  11 
6 
55 
137-5 
330 
825 
9 
6 
4H 
32 
157-3 
192 
944 
2)1769 
Mean  value  of p ...  884-5 
