858 
ME. HODGKUTSOX’S EXPEEBIEXTAi EESEAECHES 
6. The great difference between the strength of a pillar with both ends rounded and 
both ends flat, is rendered obvious by their different modes of fracture, the fonner 
breaking in one place only, the middle ; and the latter in three, at the middle and at 
each end. 
7. In pillars with one end rounded and one end flat, fractm’e takes place at about 
one-thu’d of the distance from the rounded end ; and if the base of the pillar be enlarged 
with a disc, the distance of the place of fractm’e from the top of a pillar 30|- inches 
long is but ’28 inch from one-third of the whole length from the top, deduced fi’om a 
mean of two experiments, in which one pillar broke at 10 ’42 inches, and the other at 
10’30 inches (mean, 10’36 inches) from the rounded end (see p. 439 of foi-mer research). 
8. If the pillar had had both ends rounded, then the centre of fractm’e would have 
been at the middle, at h (first piUar, Plate XXXII.), or at half the height : in the cases 
before us, fracture took place at two-thirds of the height nearly, or at b (second pfflar). 
Hence, comparing the distances A5, Ah of the points of fractm’e from the rounded ends 
of two pillars of equal diameter and height, one with both ends rounded, and the other 
with one end rounded and one end flat, we have those distances as to or as 3 to 2 
nearly. 
9. The relative strengths of the two pillars should therefore be inversely as the I’Tth 
or l’6th powers of then’ lengths, Ab, Ab, or as 3’249:6’473, or 3’031:5’8, differing not 
undely from 1 to 2, as is shown by various experiments in Tables I., II., V., XII., XIII. 
of the former research. 
10. Moreover, it will appear that in the curve indicating the form of flexm’e to the 
third pillar, Plate XXXII., the distance Abe wffl apply to the first pillar. Abed to the 
second pillar, and bedef to the third pillar ; these distances being inversely as 2, 3, 4, the 
l’7th powers of which are 3’249, 6’473, 10’556, and the l’6th powers 3’031, 6’8, 9-19, 
or as 1, 2, 3, nearly. 
11. Hence, of three pillars of the same length and diameter, one with both ends 
rounded, one with one end rounded and one end flat, and the other with both ends flat, 
the strengths are as 1, 2, 3. 
The follo’wing facts, from the subsequent experiments, illustrate the last of the pre- 
ceding figures. See also forms of fracture, Plate XXXIII. 
In pillars of “ Second London Mixture,” 2 feet 6 inches long and 1-^ inch diameter, 
fracture took place near to the middle and by breaking across near’ each end. 
A pillar of Old Hill iron, 5 feet long and 2^ mches diameter, broke in the middle, 
and broke across near each end. 
In piUars 6 feet 3 inches long, Aacture took place in the middle, and each end became 
split. This was the case in all these pillars. 
In pillars 7 feet 6 inches long and 2-| inches in diameter — that of Derwent iron broke 
in the middle and split off at each end ; one of Old Park and one of London Mixtm’e 
broke in three pieces, and split off at one end : there would appear to have been more 
points of contrary flexure in each of these two pillars than in the other cases. 
