ON THE STRENGTH OF PILLARS. 
391 
mities, their strength would be increased, so that they would bear the same as pillars 
of equal diameter and of half the length with the ends rounded. 
To ascertain whether this would be the case, experiments were made upon pillars 
60| inches long, from the same models as were made in Tables I. and II., but with 
this addition, the pillars were now cast with strong discs upon their ends, of about 
double the diameter of the pillar. These discs were turned flat and perpendicular to 
the axis, and therefore rendered the ends of the pillar, when placed between the 
parallel crushing surfaces, perfectly immoveable. The results of these experiments 
are given in Table IV. 
11. Comparing the mean breaking weights in Table IV. with those of the corre- 
sponding pillars in Table II., we shall find that pillars with discs on the ends are 
somewhat stronger than those without them. I will select the mean results from the 
second and fourth Tables, from models of the same diameter and length ; and from 
the first Table, those from pillars of the same diameter and half the length ; affixing 
to each result a number in a parenthesis, indicating the number of experiments the 
mean has been derived from. 
Abstract from Tables I., II., and IV. 
Pillars "with their ends turned flat. 
Length 60§ inches. (Table II.) 
Pillars with discs on the ends 
turned flat. 
Length 60) inches. (Table IV.) 
Pillars with the ends rounded. 
Length 30£ inches. (Table I.) 
Diameter. 
Breaking weight. 
Diameter. 
Breaking weight. 
Diameter. 
Breaking weight. 
inch. 
lbs. 
inch. 
lbs. 
inch. 
lbs. 
•51 
487 (2) 
•50 
539 
:s; 
•77 
2456 (2) 
•775 
2719 (2) 
•77 
2726 
1 
•997 
6238 (3) 
1-00 
6830 (4) 
•99 
6105 
y 
1-29 
16064 (3) 
1*28 
16369 (2) 
1-29 
17235 
y 
1.56 
28962 (3) 
1-53 
30789 (2) 
1-52 
32531 
A 
12. These results are, as we see, the means from a considerable number of experi- 
ments, agreeing moderately well among themselves : they show, as has been observed 
before, that the discs give the pillar a small increase of strength above that of a pillar 
with flat ends only ; and the approach to equality between the strengths of the pillars 
with discs, and of those of the same diameter, and half the length with rounded ends, 
is perhaps as near as can be expected in experiments of this nature. Hence we may 
conclude, that a long uniform cast-iron pillar, with its ends firmly fixed ( whether hi/ 
means of discs or otherwise), has the same power to resist breaking, as a pillar of the 
same diameter and half the length with the ends rounded, or turned so that the force 
would pass through the axis. 
It may here be observed, that, in comparing the strengths, I have, as before, 
neglected the slight differences of diameter in pillars from the same model, and 
supposed them all of equal diameter. 
13. Of the general conclusion arrived at above, I would offer the following as an 
explanation. Suppose a long uniform bar, or bolt of cast iron, were bent by a press- 
