388 
MR. HODGKINSON’S EXPERIMENTAL RESEARCHES 
column, that the ratio of the strengths of pillars, with rounded and with flat ends, is 
nearly constant for all pillars, from those which are the longest compared with their 
diameters, to those whose length is about thirty times the diameter; which is the case 
with the pillars 30| inches long, and TOl inch diameter; and also those of 15*125 
inches long and *51 inch diameter. In all pillars, therefore, whose length is thirty 
times the diameter, or upwards, the strength of those with flat ends seems to be about 
three times as great as the strength of those of the same dimensions with rounded 
ends, the mean ratio being 1 : 3*167. In the pillars shorter than thirty times the dia- 
meter, the ratio is not constant : and it will be seen that it decreases when the length 
compared with the diameter decreases. This uniformity in all pillars down to a 
certain length, compared with their diameter, and the departure from it in shorter 
pillars, were matters which for a considerable time arrested my attention. Experi- 
ments were made upon wood and wrought iron, and the results were in accordance 
with these ; but the reason of the deviation was first made evident by the experiments 
upon wrought iron, from which it appeared that short specimens of that metal became 
slightly crushed, and perceptibly changed in their form, by a weight which was nearly 
the same as that which produced a falling off in the strength of a long pillar of the 
same diameter. Thus it was found that a weight of 22679 lbs. produced a very ob- 
vious change in the form of a short cylinder, 1*015 inch diameter (as will be seen 
from the experiments further on) : and a pillar of that diameter and 30| inches long, 
with the ends flat, exhibited a great falling off in strength. It was evident, therefore, 
that incipient crushing or derangement of the parts was the cause of the change. 
Cast iron does not often admit of such an alteration in its form as to be perceptible 
to the eye ; but its strength begins to fall off with weights which differ not widely from 
those which deranged the form, and reduced the strength of wrought iron. I have, 
therefore, made the preceding abstract to include, in addition to the mean breaking 
weights from the first and second tables, a column containing the weights which 
would crush, without flexure, short cylinders of cast iron (the Low Moor, No. 3.) of 
the same diameters as the pillars with flat ends. These crushing weights were ob- 
tained from the experiments further on (Art. 55.), in which it was shown that prisms 
of this iron, perfectly bedded at the ends, and so short as not to be bent with the 
pressure, were crushed with a force of about forty-nine tons per square inch. The 
mean of my experiments gave 86238 lbs. for the crushing force of a cylinder one inch 
diameter ; and the resistance to crushing, in the cylinders of other diameters, was 
calculated from this, on the supposition that the resistance is as the area of the sec- 
tion ; which supposition was proved to be true in my Report on the strength of hot 
and cold blast iron*. 
7. It will be seen at a glance from the preceding abstract, what portion of its 
crushing strength each pillar required to break it, whether the ends were rounded 
or flat. The pillars with flat ends, whose length was the least number of times the 
* Transactions of the British Association for the Advancement of Science, vol. vi. 
