ON THE STRENGTH OF PILLARS. 
413 
The third and fourth pillars in Table XI., are two hollow pillars 2 \ inches external 
diameter at bottom, and If at top nearly. They tapered regularly from the bottom 
to the top, where there was a disc to increase the stability of fixing. The mean weight 
of these was 36‘8lbs., and the mean breaking weight 29488 lbs. But we have seen 
above, that a uniform hollow pillar 2’02 inches diameter, and 36^ lbs. weight, would 
require 305 18 lbs. to break it. Therefore these pillars, like the former ones, are weaker 
than uniform hollow pillars. Experiment 5. was with a uniform pillar having rounded 
ends. The section was of the form , three inches across ; the pillar weighed 62 lbs., 
and was broken with 1 7578 lbs. But a uniform hollow pillar 3’01 inches diameter, 
and 50f lbs. weight (Experiment 13., Table VIII.), required 2670 7 lbs. to break it. 
Whence we see, that pillars of this form, which is nearly that of the connecting rod of 
a steam-engine, are very weak compared with uniform hollow cylindrical ones ; the 
strength being as the T88 power of the weight nearly (Art. 46.), the hollow cylinder, 
if of the same weight, 62 lbs., as the pillar above, would have required 39645 lbs., or 
more than twice 17578, to break it. 
Experiment 6. is the result from a model differing from the last in having the sec- 
tion of the form This was considerably stronger than the preceding, but much 
weaker than a hollow cylinder of the same weight. 
Experiments 7 and 8. show the strength of solid pillars when the pressure is applied 
to some point intermediate between the centre and the circumference ; and exhibits 
a great falling off, from what it would have been, if the pressure had been through 
the axis, as in pillars from the same model in Table I. 
Experiment 9. is on a pillar so fixed that the pressure is in the direction of the 
diagonal; and comparing its strength with that of one of the same dimensions, with 
rounded ends, in Table I., it is nearly the same. The strength is, therefore, only one- 
third of what it would have been, if the pillar had been erect, with its ends well sup- 
ported, as in Table II. 
The long pillars referred to in this paper will, I conceive, comprise most of the 
forms at present used in practice, including the best of those employed by the an- 
cients. With respect to pillars so short as to break by crushing, experiments on 
twenty-eight species of timber are given at the end of the paper ; and on this subject 
I would beg to draw the attention of the reader to my Report on cast iron, in the 
Sixth Volume of the British Association, before referred to. The experiments upon 
crushing, by M. Rondelet (Art de Batir), and by Mr. George Rennie, will be known 
to most of my readers. 
pillar, and D\ E the diameters of the two ends of that in the form of a truncated cone. But if we compute the 
diameter of a uniform cylindrical pillar of the same length and solid content as one with unequal diameters, 
we shall find the uniform pillar stronger than the other, and the more so according as the inequality of the 
diameters of the latter is greater. 
