ON THE STRENGTH OF PILLARS. 
389 
diameter (the ratio of the strengths of the pillars with rounded and with flat ends 
being uniform), required and of the crushing weights to break them. 
The lengths of these pillars were thirty times their diameters, which were *51 and 
T01 inch respectively; but the pillars *777 inch diameter, and 20‘166 inches long, 
(the length being twenty-four times the diameter), were broken with of the 
crushing weight. These last pillars, which were broken with a little less than one- 
third of the crushing weight, showed themselves injured by the compression, since 
they gave a ratio less than the mean. On the other hand, the pillars just mentioned 
as - 51 inch diameter were broken with from one-fourth to one-third of the crushing 
weight; and those T01 inch diameter with somewhat less than one-fourth, neither 
of these being injured by the pressure. We may, therefore, conclude that about one- 
fourth of the crushing weight is the greatest load which a cast iron pillar, flat at the 
ends, will bear without producing a crushing or derangement of the materials, which 
would lessen its breaking weight ; and that the length of such a pillar should be 
thirty times the diameter, or upwards. Pillars whose length is less than in this 
proportion, give the ratio of the strengths of those with rounded and with flat ends, 
from 1 : 3, down to 1 : 1^, or less, according as we reduce the number of times which 
the length exceeds the diameter, as will be seen by the abstract. 
A circumstance may be mentioned, which, perhaps, tended a little to equalize the 
strengths of the shortest pillars mentioned above. It became necessary to render 
those which were rounded at the ends more flat there, than if the ends had been 
hemispheres ; whilst in the experiments upon pillars, whose length was greater with 
respect to the diameter than these, the ends were more prominent than in the hemi- 
spherical form. This change became necessary on account of the splitting of the 
ends in the short pillars ; it having been found that the pillars whose diameter was 
one-thirteenth of the length or upwards, with rounded ends, failed in many instances 
by the ends becoming split. In these cases a portion of the rounded end of the pillar 
formed the base of a cone, whose vertex was in or near the axis of the pillar. This 
cone acting as a wedge whose sides were in the angle of least resistance, and having 
its vertex sharp, split and cut up the sides of the pillar, of which it formed a part*. 
All the pillars in the preceding abstract became bent, and broke in the middle, as 
if the breaking weight had been transverse. This was the case with all the pillars 
tried, till those of *52 inch diameter became only two inches long, the length being 
less than four times the diameter. 
Some of the short pillars, it will be noticed, bore more than the average crushing 
weight, arising from these having been cast very small, and therefore being harder 
and resisting with more than the average strength of the metal. 
* For more detailed information on the crushing of short masses of cast iron, and the interesting forms of 
its fractures, see the Report in the volume of the British Association before referred to. 
