ON THE STRENGTH OF PILLARS. 
421 
The following abstract contains the lengths, lateral dimensions, and breaking 
weights of the three kinds of pillars tried. 
Length. 
Pillars with both ends 
rounded. 
Pillars with one end flat, and 
the other rounded. 
Pillars with both ends flat. 
Diameter. 
Breaking weight. 
Diameter. 
Breaking weight. 
Diameter. 
Breaking weight. 
Wrought iron. 
inches. 
90f 
601 
30| 
301 
151 
inch. 
1-017 
1-015 
1-015 
1-015 
1-005 
lbs. 
1808 
3938 
15480 
15480 
23535 
inch. 
1-02 
1-03 
1-015 
1-015 
1-005 
lbs. 
3355 
8137 
21355 
21187 disc. 
26227 
inch. 
1-02 
1-02 
1-015 
1-015 
1-005 
lbs. 
5280 
12990 
23371 
25387 disc. 
27099 
Steel. 
29-95 
•87 
10516 
•87 
20315 
•87 
26059 
Timber. 
m 
Side of 
square. 
1-75 
3197 
Side of 
square. 
1-75 
6109 
Side of 
square. 
1-75 
9625 
The pillars in each horizontal line in this abstract are of equal length, and nearly 
of equal diameter, the only essential difference being in the form of their ends. 
Taking the longest pillars, those of 90f and 60^ long, the strengths are 
Ends rounded. 
In iron . . . 1808 
In iron . . . 3938 
In timber . . 3197 
Ends rounded and flat. Ends flat. 
3355 5280 
8137 12990 
6109 9625 
The strengths in these three cases are, therefore, as one, two, three nearly, the 
middle being an arithmetical mean between the other two. These results are a cor- 
roboration of those from cast-iron pillars (Art. 16.). We see, too, from the wrought- 
iron pillars 30| and 15^ inches long, as well as from those of steel, which appear to 
have been slightly crushed by the weight (Art. 6.), that this ratio one, two, three, does 
not obtain in short pillars, but that the difference of the strengths of the three forms 
of pillars becomes less, according as the number of times which the length of the 
pillar exceeds the diameter decreases. But whatever may be the ratio of the strengths 
of pillars with rounded ends to those with flat ones, the strength of those with one 
end rounded and one flat, is nearly an arithmetical mean between the strengths of 
the other two, as will be seen from the numbers below. 
Mean from strengths of 
pillars, with both ends 
rounded and both flat. 
Strengths of pillars, one 
end rounded and one 
flat. 
lbs. 
lbs. 
3544 
3355 
8464 
8137 
19426 
21355 
20434 
21187 
25317 
26227 
18287 
20315 
6411 
6109 
