406  ME.  EAIEBAIEN  ON  THE  EESISTANCE  OF  TTBES  TO  COLLAPSE. 
8-incli  Tubes. 
No.  of 
experiment. 
D. 
L. 
P. 
P.  L. 
P.D. 
P- 
13 
8 
2i 
39 
97-5 
312 
780-0 
14 
8 
34 
32 
104-0 
256 
832-0 
15 
8 
34 
31 
103-3 
248 
826-4 
3)2438-4 
Mean  value  of />  ...  812-8 
10-inch  Tubes. 
No.  of 
experiment. 
D. 
L. 
p. 
P.  L. 
P.  D. 
P- 
16 
10 
19 
79-1 
190 
791 
17 
10 
36 
90-0 
360 
900 
2)1691 
Mean  value  ofjo  845-5 
A comparison  of  the  numbers  in  the  sixth  columns  with  the  numbers  given  by  the 
experiments  on  tubes  of  the  same  length,  clearly  shows  that  the  strength  varies  veiv' 
nearly  in  the  inverse  ratio  of  the  diameters ; and  moreover,  since  the  mean  values  of  p 
for  the  ditferent  sets  of  tubes  nearly  coincide  with  one  another,  we  infer  that  the 
strength  varies  inversely  as  the  product  of  the  length  by  the  diameter,  or  that  j)  = PIJ)= 
a constant. 
12-inch  Tubes. 
No.  of 
experiment. 
D. 
L. 
p. 
P.  L. 
P.D. 
P- 
18 
12-2 
421 
^2  4 
11-0 
53-6 
123-2 
654 
19 
12 
5 
12-5 
62-5 
150-0 
750 
20 
12 
22-0 
55-0 
264-0 
660 
3)2064 
Mean  value  ofjo 688 
Here  the  mean  value  of^  is  somewhat  below  the  value  determined  from  the  other 
tubes.  This  discrepancy  is  no  doubt  owing  to  the  difficulty  there  is  in  maintaining  such 
thin  tubes  of  large  diameter  exactly  in  the  cylindrical  form.  This  cii’cumstance  seems 
to  suggest  that  a small  correction,  depending  on  the  ratio  of  the  diameter  of  the  tube 
to  its  thickness,  may  be  requisite  to  render  formula  (2.)  mathematically  exact.  This 
correction  will  assume  the  form  of  — E X where  the  constant  E remams  to  be  deter- 
mined from  the  data  of  the  experiments. 
Mean  value  of  p derived  from  the  foregoing  results. 
^=|{891-6-f884-5  + 812-8-f  845-5  + 688}  =824. 
