426 
MR. HODGKINSON’S EXPERIMENTAL RESEARCHES 
Lamande’s Experiments upon Oak ( from Tredgold’s Carpentry ). 
These experiments were upon square pillars of different lengths, varying as 1, 2, 3, 
and the sides of their squares as 2, 3, 4. This writer has, in most instances, given 
four experiments or more to determine the breaking weights of pillars of each size. 
The longest pillars, compared with their thickness, in this series are 6-375 feet long, 
and 2*126 inches square, the length being about thirty-five times the side of the 
square ; and the average breaking weight from four experiments was 7769 lbs. We 
bl* d 4 
therefore get a = = 15455 lbs., whence b = 15455 -p- Further on, I shall endea- 
vour to compute the results of Lamande’s experiments. 
Short Pillars of Timber . 
65. We have seen that pillars of cast iron, wrought iron, and timber, follow in a 
great measure the same laws as to their strength (Arts. 5. 58.). In these different 
materials, pillars with rounded ends have their strength in a constant ratio to that of 
those with flat ends. This, however, only applies to pillars whose length is so many 
times the diameter or thickness, that they are not sensibly crushed by the breaking 
weight. 
My experiments have not shown what part of their ultimate crushing weight pillars 
of timber will bear without suffering such a diminution of their strength, from this 
cause, as to need correcting for, as was done in estimating the strength of short 
pillars of cast iron (Art. 41.). In that metal there appeared to be a slight falling off 
in the strength of even the longest pillars, which I accounted for by the shifting of 
the position of the neutral line, but it was not such that the results of the general for- 
mulae then used (Art. 36 to 38.) needed modifying ; nor was there shown a defect in 
comparing the breaking weight of the pillars with rounded ends with those with flat 
ones, till the breaking weight was about one-fourth of the weight which would have 
crushed the whole pillar without flexure (Art. 6.). 
It seems probable, from the experiments in Table XIII., that timber will bear, 
without much reduction of the breaking weight from crushing, considerably more 
than one-fourth of the ultimate crushing weight ; for the pillars 1*75 inch square 
and 60^ inches long, with flat ends, exhibited no reduction in comparison of strength 
with those with rounded ends, though the mean breaking weight of the former was 
more than one-third of the weight which would have crushed the whole section. It 
may, however, be remarked, that the circumstance of a pillar with flat ends bearing 
upwards of three times as much as one of the same diameter with rounded ends, does 
not prove that the former had not its breaking weight in some degree reduced by 
crushing, since both descriptions of pillars were considerably compressed. In the 
absence of other information, therefore, I shall in calculating the strengths of short 
b c 
pillars of timber by the formula y — c (Art. 42.), suppose d, as in cast iron, 
