Prof. Hodgkinson on the Strength of Pillars of Cast Iron. 15) 
length is / in feet, and the external and internal diameters D and d 
in inches, the ends being flat and well bedded—are as below : 
3°55 3°55 
w=46°65 x ——— 
from formula in Phil. Trans. 1840 ; 
D*=—q?* 
w=42°347 x Ts 
from formula in present paper. 
To obtain some idea of the relative strengths of pillars of different 
British irons, I applied, at Mr. Stephenson’s suggestion, to Messrs. 
Easton and Amos, who procured for me twenty-two solid pillars, each 
10 feet long and 23 inches diameter, cast out of eleven kinds of iron 
(nine simple irons and two mixtures). The pillars were all from the 
same model, and were east vertically in dry sand, and turned flat at 
the ends, as the hollow ones had been ; two being cast from the same 
kind of iron in each case. The simple unmixed irons tried were as 
below, and all of No. 1. 
Mean breaking weight. 
Old Park iron........ Stourbridge ...... 29°50 tons. 
Derwent iron ........ Durham .......,:. 38°03 |), 
Portland iron ........ Tovine, Scotland .... 27°30 ,, 
Calder iron,.......... Lanarkshire ,....... 27:09 ,, 
Level iron .......... Staffordshire ...... 24°67 ,, 
Coltness iron ..,..... Edinburgh ...,.... 23°52 ,, 
Warron iON. .,; «sess Stirlingshire....,... 23°52 ,, 
Blaenavon iron ......South Wales ...... 22°05 ,, 
Old Hill iron ........Staffordshire ...... 20°05 ,, 
The mean strength of the pillars from the irons above varies from 
20°05 to 29°50 tons; or as 2 to 3 nearly. 
The pillars formed of mixed irons were found to be weaker than 
the three strongest of the unmixed series. 
From many experiments, it was shown that the weight which 
would crush the pillars, if they were very short, would vary as 5 to 9 
nearly. 
The pillars in general were broken of four different lengths, 10 feet, 
7 feet 6 inches, 6 feet 3 inches, and 5 feet, the ends of all being turned 
flat, and perpendicular to the axis. It was found that when the 
length was the same, the strength varied as the 3°5 power of the 
diameter ; and when the diameter was the same and the length varied, 
the strength was inversely as the 1-63 power of the length. Both 
of these were obtained from the mean results of many experiments. 
The formula for the strength of a solid pillar would therefore be 
35 
w= Mm X Tas» 
where w is the breaking weight, d the diameter in inches, / the length 
in feet, and ma weight which varied from 49°94 tons in the strongest 
iron we tried, to 33°60 tons in the weakest. 
The ultimate decrement of length, in pillars of various lengths but 
of the same diameter, varies inversely as the length nearly, Thus 
the ultimate decrements of pillars 10 feet, 7 feet 6 inches, 6 feet 
