ON THE STRENGTH OF PILLARS. 
393 
thicker, compared with their lengths, than have usually been employed in this 
paper. Some results of the continental theory we shall, however, find of great service 
further on. 
Pillars with one End rounded and the other flat. 
15. In the first and second Tables we have the strength of cast-iron pillars, with 
both their ends rounded, and both flat ; we will now refer to Table V., which con- 
tains the results of experiments to ascertain the strength of pillars with one end 
rounded and the other flat, and in some cases with discs ; these results being placed 
between those from the pillars, with round and flat ends, as taken, with some addi- 
tions, from the first and second Tables. 
It has been shown, that the strength of pillars, with both their ends fixed, is to the 
strength, when the ends are rounded, in a constant ratio. It seems probable, there- 
fore, that the strength, when one end is fixed and the other rounded, must be related 
to the results of the other cases by some very simple law. Taking the mean results 
from Table V. and other places, and neglecting the slight differences in diameter 
among castings from the same model, we have as below : 
Both ends rounded 
One end rounded and one flat, or with a disc . . 
Both ends flat, or with discs. 
Breaking weights in lbs. 
143 
256* 
487 
3017 
6278 
9007 
7009 
13499 
20310 
7009 
13565 
22475 
16493 
33557 
16. The pillars in each vertical column in this abstract, are of the same length and 
diameter; the strengths, therefore, in the three different cases, reading downwards, are 
as 1,2, 3, nearly, the middle being an arithmetical mean between the other two. 
It is shown, moreover, by the experiments further on, upon timber, wrought iron, and 
steel, that the strength of a pillar with one end round and the other flat, is always an 
arithmetical mean between the strengths of pillars of the same dimensions with both ends 
rounded and both flat, however the ratio of the strength of these may vary-f~. We 
see, too, by the first and second columns in the preceding abstract from Table IV., 
which contain the ratio of the strengths in pillars with discs, that their results are in 
accordance with the rest. From these facts, as well as from other evidence not ad- 
duced, I conclude that the above mean would always take place, however the fixed 
ends were fastened. 
17- The case of pillars fixed at one end and moveable at the other, is not without 
its interest in practice ; as piston rods of steam-engines and the rods of force-pumps 
are instances of the use of materials in that form, it being the same thing in effect 
whether the pillar be rounded at the end, or turn upon a joint there. Other instances 
may often be seen in practice ; as where pillars are firmly based at the bottom, but 
* This pillar was weakened a little by a previous experiment upon it. 
t The experiments on wrought iron, show that it is, practically, the case even when the pillars are much 
crushed by the pressure. 
MDCCCXL. 3 E 
