416 
MR. HODGKINSON’S EXPERIMENTAL RESEARCHES 
same, the strength varies inversely as the 1 *7th power of the length, as a sort of 
general average. Adopting this number, and calculating by it the strength of a pillar 
one foot long, from the strength of one 7 feet 6f inches long, we have the strength 
of solid pillars one foot long and one inch diameter, 
In pillars with rounded ends 29074 lbs. = 12*979 tons ; 
In pillars with flat ends . 99318 lbs. = 44*338 tons. 
The mean strengths of pillars one foot long and one inch diameter, as obtained 
(Art. 35 to 37.) from the experiments on solid pillars, are 33379 lbs. and 98922 lbs. 
respectively ; which, in pillars with flat ends, is pretty nearly in agreement with that 
above. But the defective specimens in the first hollow pillars, with rounded ends, 
has caused the number to be 29074, whilst the solid cylinders gave 33379 lbs. 
51. Taking the numbers above, as deduced from the hollow pillars, we have for 
the strength of hollow cylindrical pillars in general, 
j)376 _ ^376 
29074 jr 7 5 in pillars with rounded ends ; 
t 
j^3*55 ^3'55 
99318 tpt 5 in pillars with flat ends. 
i 
In using these formulae, which answer for solid cylinders when d = 0, it must be 
borne in mind that they do not apply to pillars whose length is less than about thirty 
times the external diameter when the ends are flat, nor to those of less than half 
that length when they are rounded. 
Short hollow Pillars. 
52. When pillars are shorter than as above, we have seen (Art. 6.) that there is a 
falling off" in their breaking strength, on account of a change being produced in the 
material through the great weight necessary to break them. This falling off has been 
attempted to be accounted for (Art. 41.), and a formula given by which the strengths 
of pillars, however short, could be calculated from the theorems used for long pillars, 
by means of the crushing strength of the body, the latter being shown to be an 
element in the resistance of pillars to fracture by flexure. 
This formula for short pillars (Art. 43.) is 
b c 
y - bWfc 
where h is the strength of the pillar, as calculated by the rules for long pillars (Art. 
51.), and c the weight which would be required to crush the pillar without flexure. 
Table X. contains the results of experiments upon thirteen pillars varying in length 
from twenty-four times the external diameter down to less than eight times. In this 
table, the deflections were not observed, as they were very small, and required much 
care ; and there was considerable danger in observing them, for the pillar usually 
broke, with violence, into many pieces. They were made, however, with great care: 
