ON THE STRENGTH OF PILLARS. 
401 
The results from the pillars with rounded ends in Table I. are as follow : 
Diameter 
of pillar. 
Length. 
Breaking 
weight. 
Value of x. 
Mean 
value of x. 
Error from using 
the mean, in parts 
of the value of x. 
inch. 
inches. 
feet. 
lbs. 
lbs. 
•50 
60-5 
= 5-04166 
143 
30309 
+ -L 
1 9 - 8 
•50 
30-25 
= 2-5208 
539 
35162 
1 
197 
•50 
15-125 
= 1-2604 
1904 
38230 
1 
T 8 
•497 
7-5625 
= -6302 
5262 
33263 
1 28'9 
•77 
60-5 
= 5-0416 
780 
32603 
+ J_ 
' 42 
•77 
30-25 
= 2-5208 
2726 
35070 
1 
m 
207 
•76 
15-125 
= 1-2604 
9223 
38360 
fl 
O 
1 
“ rS 
•76 
10-083 
- -84028 
17506 
36547 
fH 
O 
Ob 
_ 1 1 
11*5 1 
•99 
60-5 
- 5-04166 
1902 
30902 
|H 
II 
+ — 
1 12*4 
•99 
30-25 
= 2-5208 
6105 
30529 
m 
r-O 
+ -L 
‘ 107 
36639 
Ob 
1 
11*2 
1-00 
20-1666 
= 1-6805 
15737 
CO 
CO 
CO 
•99 
15-125 
= 1-2604 
19752 
30401 
+ — 
r 10*2 
1-29 
60-5 
= 5-04166 
5707 
34273 
_ 1 
38-2 
1-29 
30-25 
= 2-5208 
17235 
31857 
+ — 
~ 20*9 
1-5275 
60-5 
= 5-0416 
10750 
34229 
1 ! 
40-2 
1-52 
30-25 
= 2-5208 
32531 
32447 
+ -L 
' 34-8 J 
1-772 
60-5 
= 5-0416 
16562 
30092 
+ W 
1-95 
60-5 
= 5-0416 
23551 
29901 
+ — 
“ 8-6 
The enumeration above includes pillars varying in length from 121 times the dia- 
meter down to 15 times, or as 8 to 1. Through this range the greatest error arising 
from using the mean value of x here obtained is or somewhat more than one-eighth. 
We shall, therefore, take 33379 lbs., or 14‘9 tons, as a unit of measure for the strength 
of a solid uniform cast-iron pillar, of Low Moor iron, No. 3, one foot long and one 
inch diameter, the ends of which are rounded. 
36. For solid pillars of other dimensions with rounded ends, in the same material, 
taking the length in feet and the diameter in inches, and using the same notation as 
before, we have w the strength as below : 
d 3 ' 76 
w = 33379 -jyf for the strength in lbs. 
d 3 ' 76 
w = 14*9 -jt for the strength in tons. 
3 F 
mdcccxl. 
