854 
IHE. HODGEIXSOX’S EXPEEDIEXTAL EESEAECHES 
it soon became evident that pillars of the same size with their ends flat, and well sup- 
ported or bedded throughout, would require a much greater weight to break them than 
those with rounded ends ; a large number of both kinds were made and broken by 
experiment to determine their relative strength to resist fracture, and it was found that 
so long as the pressure required had not been more than about one-fourth of that neces- 
sary to crush short specimens of the same material, the strength of a solid pillar with 
flat ends was a little more than three times that of one with rounded ends, the mean 
being 3'167, as shown in the abstract, page 387 of that research, hut in other experi- 
ments it is still nearer to 3. 
5. If the pressure necessary to break the pillar were much greater than about one- 
fourth of that which would crush short specimens of the same material, then the ratio 
1 to 3 would become 1 to 2, or even less. 
6. In the following abstract, pages 856 and 857, which iacludes experiments on hoUow 
pillars with rounded and with flat ends, as above, and upon solid pillars of wrought 
iron and timber, the ratio of the strengths of the two kinds of pillars is nearly as I to 3, 
varying not widely from the former. From this abstract we see that pillar's which have 
been loaded with more than about one-fourth of the crushing weight ar-e hr some degree 
injured, and the ratio in them difiers from 1 : 3, becoming 1 : 2'6, 1 : 2'4, &c. 
In the last column of the abstract, page 857, denomurated it may be seen at a glance 
what portion of the crushing weight was requu’ed to break each pillar; and in those 
where it amourrted to '282, '272, or above '25*, they were generally injured by the 
pressure. 
7. Irr the abstract, p. 393 of the former research, the relative strengths of pillars — ^with 
both ends rounded, one end rounded and one end flat, and both ends flat, — are determined 
in a great number of experiments, and found to be nearly as I, 2, 3, from experiments 
on cast iron, wrought iron, steel and timber. 
8. In the abstract, page 391 of the former research, pillars 60^ inches long, with their 
ends turned flat, are compared, as to their strengths, uith pillars of the same size nith 
discs on their ends turned flat : the strengths of these two classes of pillars difiered but 
little, but the pillars with discs on the ends are rather the stronger. In this abstract it 
was shown that pillars one-half the length of the precedmg, and of the same diameter 
but with the ends rounded, were of the same strength as the preceding ones neai'ly, as 
shown by many experiments. 
Attempt to account for the principal Results in the preceding description of the abstracts. 
I. Of the general conclusion arrived at in the abstract last referred to, I would offer 
the following as an explanation. Suppose a long uniform bar of cast iron were bent 
by a pressure at its ends so as to take the form Ahcdef^, where all the cui'ves Abe, ede, 
e/B, separated by the straight line AceB, would be equal, since the bar was supposed to 
T> 
^ The pillars of the “ Second London Mixture,” 6 feet 3 inches long, gave the same result when — =-26. 
L 
