390 
MR. HODGKINSON’S EXPERIMENTAL RESEARCHES 
8. We see, therefore, that when pillars of cast iron, with flat ends, are shorter than 
about thirty times the diameter, the ratio of the strength of those of the same dimen- 
sions, with flat and with rounded ends, is very variable. But when the length is 
thirty times the diameter, or more, up to one hundred and twenty-one times, we have 
shown it to be nearly constant ; and we may infer that the ratio would be constant, 
however greatly the length might exceed the diameter ; since the uniformity seems to 
depend upon the circumstance that the weight necessary to break these long pillars 
by flexure, is not sufficiently great to produce much compression in them, and there- 
fore does not alter sensibly the position of their neutral line. In this respect, cast 
iron has the advantage of most other metals, on account of its great power of resisting 
crushing, which is, on the average, from six to seven times as much as that necessary to 
tear it asunder*. Wrought iron, on the other hand, does not require nearly so much 
force to crush it, so as in a great measure to destroy its utility -f, as is required to tear 
it asunder (Art. 60.) ; and therefore the ratio of the strength of equal pillars, with 
rounded and flat ends, becomes variable somewhat sooner in it than in cast iron, 
though the comparative results are the same in long pillars. The experiments on 
timber, and on steel, so far as they have gone, give the same results with respect to 
long pillars. 
9. Confining our researches, for the present, exclusively to what may be termed 
long cast-iron pillars, or those whose length, in pillars with flat ends, is thirty times 
the diameter, or upwards, since these are but little compressed by the breaking 
weight, we shall obtain some interesting properties. These properties, doubtless, 
would be common to all rigid bodies, where the length, compared with the diameter, 
was so great that the breaking weight was not sufficient to diminish sensibly the 
power of the body to resist a transverse force. Till recently, in all inquiries respect- 
ing the strength of materials, bodies have been assumed to be incompressible ; and 
if they really were so, the constant ratio above-mentioned, and some other properties, 
which I shall deduce from the results of the experiments upon cast-iron pillars, would 
be found in them, whatever might be their length, compared with their diameter. 
Some descriptions of stone may perhaps approach much nearer than cast iron to this 
state of ultimate incompressibility, compared with their power of resisting tension. 
Strength of Long Pillars of Cast Iron. 
10. We have seen, that in all long pillars, where the dimensions are the same, the 
resistance to crushing by flexure is about three times as great when the ends are flat 
as when they are rounded. This general agreement, and the near approach in point 
of strength, in pillars with flat ends, to those of the same diameter and of half the 
length with rounded ends (as may be seen by comparing the preceding abstract), led 
me to conceive, that if the pillars with flat ends were more firmly fixed at the extre- 
* Transactions of the British Association, vol. vi., before referred to. 
f The valuable experiments of Mr. Barlow refer to a further destruction of the material. 
