402 
MR. HODGKINSON’S EXPERIMENTAL RESEARCHES 
This rule is only intended to apply to pillars whose length is fifteen times the dia- 
meter or upwards, and in the largest pillars, perhaps, not so low. It appears pro- 
bable that we should find a falling off in the strength of these when they are con- 
siderably more than fifteen times the diameter in length. 
This reduction in the resistance of the thicker pillars, compared with what we are 
led to expect from the results of the smaller, arises, as appears to me, from the greater 
softness of the metal when cast in large masses than in small ; and this cause, I con- 
ceive, has some influence upon the strength of all cast-iron pillars. 
37- To find x, the strength of a pillar one inch diameter and one foot long, in solid 
cylinders flat at the ends, from the mean results in Table II. 
Using here the formula 
w t 7 
and restricting ourselves to cylinders whose length is upwards of twenty-five times 
the diameter, we have. 
Diameter of 
pillar. 
Length of pillar. 
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. 
•51 
60-5 
— 
5-04166 
487 
83182* 
W 
•77 
60*5 
= 
5-04166 
2456 
97175 
£ 
O 
•50 
30-25 
2-5208 
1662 
93735 
CO 
•77 
30*25 
= 
2-5208 
8811 
107300 
T 1 
•777 
•997 
20-166 
60-5 
z 
1-6805 
5-0416 
15581 
6238 
92229 
98638 
II 
4- - 1 - 
1 1378 
1-01 
30-25 
— 
2-5208 
20310 
94403 
CO 
1-29 
60-5 
5-0416 
16064 
101770 
5 
1*56 
60-5 
5-0416 
28962 
93455 
CM 
•51 
20-166 
= 
1-68055 
3830 
101063 
0-5 
QO 
•51 
15-125 
= 
1-2604 
6764 
109445 
9'4 
The abstract above contains pillars varying in length from 25 to 121 times the 
diameter, and omitting the first, for the reason given in the note, the greatest error 
which has occurred by using the general mean 98922 lbs., is ^ 4 th. Hence we may adopt 
98922 lbs., or 44’ 16 tons, as the strength of a cast-iron pillar, one inch diameter and 
one foot long, flat at the ends ; this number, however, only to be applied to pillars 
whose length is 30 times the diameter, or upwards. 
38. Retaining the same notation as before, we have, for solid cylindrical pillars of 
any given size, the lengths being as above : 
d 3-55 
w = 98922 X ~jyT’ f° r s t ren gfh in lbs. 
d 3 ' 55 
w — 44’ 16 X-jpj-, for the strength in tons. 
* I conceive this result to be too low, on account of the difficulty of having slender pillars quite straight. 
It is, therefore, not included in the general mean value of x. 
