ON THE STRENGTH OF PILLARS. 
411 
with great care, and were either perfectly straight, or they were rendered so in the 
lathe, where their ends were turned flat and parallel. The pillars intended to be 
used with rounded ends, were made about two inches shorter than the rest, or 7 feet 
4f inches long, in order to allow room for the rounded caps upon the ends, as before 
mentioned, the whole length of the pillar with caps being 7 feet 6f inches. 
Description of the Tables. 
48. The first column in the Tables on hollow cylinders contains the number of the 
experiments only, and needs no explanation. The second column, in giving the in- 
ternal diameter of the pillar, gives it as calculated as well as measured. This was 
done because there was great difficulty in measuring correctly the internal diameters, 
which were in some degree irregular. The weight of a solid pillar of a certain dia- 
meter, and the given length, being known, from a mean of three experiments, and 
the weights of the hollow cylinders, together with their external diameters, being also 
known, from these data, the internal diameters of all the cylinders were computed; 
and a mean between the calculated and the observed results was taken for the internal 
diameter. This extra trouble was taken, as I was desirous of avoiding every possible 
inaccuracy in experiments which, from the expense and labour attached to them, 
were not likely to be soon repeated. The third and fourth columns of Tables VIII. and 
IX. contain the deflections caused by different weights laid upon the pillar, and the 
weights themselves. The fifth column contains what is denominated the breaking- 
weight, but which means only that weight which was sufficient to overcome the 
greatest resistance of the pillar. This was frequently attained when a long pillar had 
been bent through a space perhaps not exceeding its radius. From the first experi- 
ment on long hollow pillars with rounded ends, it was evident that so little flexure of 
the pillar was necessary to overcome its greatest resistance (and beyond this a smaller 
weight would have broken it), that the elasticity of the pillars was very little injured 
by the pressure, if the weight was prevented from acting upon the pillar after it 
began to sink rapidly, through its greatest resistance being overcome. 
By attending carefully to this point, the pillar was frequently saved uninjured for 
another experiment. The small flexure that it had got was straightened, and the 
rounded ends being removed, the pillar, with its flat ends well bedded against the crush- 
ing surfaces, was broken, and the results in Table IX. were recorded. The sixth 
columns in Tables VIII. and IX. contain the strength of a solid pillar, 7 feet 6f inches 
long, and one inch diameter, as calculated on a theoretical supposition* mentioned 
further on. This value is always calculated for the full length, 7 feet 6f inches, 
though some of the pillars in Table IX. were two inches shorter than that. This re- 
duction, as well as others of a similar nature, was made on the supposition that the 
strength of pillars of the same thickness varies inversely as the T7th power of the 
length, as was found to be the case in solid pillars. 
It had been shown, Table VI., that a solid cylindrical pillar, with rounded ends, 
* Poisson, Mecanique, 2nd edition, vol. i. pp. 619 and 620. 
3 g 2 
