400 
MR. HODGKINSON’S EXPERIMENTAL RESEARCHES 
33. We see from the preceding abstracts, that the values of x never rise so high as 
two, but approach toward it accordingly as the breaking weight becomes smaller. 
In the pillars 77 inch diameter and 60^ inches long, where the length is seventy- 
eight times the diameter, the value of x is 1’805 in one case, and 1*843 in another; 
and in the pillars *50 inch diameter, and 60^ inches long, the length being one hun- 
dred and twenty-one times the diameter, the value of x is 1*914. These facts, and 
the regular increase in the value of x according as the breaking weight is dimi- 
nished, show that 2 is the value to which x would approximate if the breaking weight 
were infinitely small, or the body perfectly incompressible. 
Computations of the Strength of Long Pillars hy means of the preceding Numerical 
Results. 
34. We have found that the strength of cast-iron pillars, whose diameter is the 
same, is inversely as the 17 th power of the length nearly; and where the diameter 
differs, the strength varies according to a power of the diameter which is nearly con- 
stant. This, in cylindrical pillars, whose ends are rounded, we have found to be 
3736, and in those with flat ends 3*568, the pillars with discs upon the ends giving 
3*679. 
The earlier experiments gave 3*76 for the pillars rounded at the ends, and 3*55 for 
the flat ones ; and these numbers will be retained in the following computations, 
whatever the form of the section may be ; it having been shown that the power was 
nearly the same, whether the pillars were round or square. 
35. As a convenient unit of comparison, we may determine the strength of a solid 
pillar whose length is one foot and diameter one inch, as obtained by calculation 
from most of the experiments in the first and second Tables. 
Putting then d for the diameter of a given pillar in inches, l for its length in feet, 
w for its breaking weight, and x for that of a pillar one inch diameter and one foot 
<f 76 
long, we have -jY as a comparative measure of the strength in pillars with rounded 
ends. Whence 
d 3 ' 76 T 76 
JT : '* : w : x 
w l x ‘ 
. . X — ^376 5 
for pillars with their ends rounded. 
In the same manner, for pillars with their ends flat, 
wl v7 
X — ^ ' 
