872 
ME. HODGKIXSOX’S EXPEEDIEXTAL EESEAECHES 
Formulae for computing the Breaking Weights of Solid Pillars of the Irons in the 
preceding summary ; where W is the breaking weight in lbs. or in tons. D the 
diameter in inches, and I the length in feet. 
Description of Iron in the Pillar. 
Strength of a pillar 
from formula 
W = m 7 
where wz is as below, 
according as the weight 
is in lbs or tons. 
Strength of a pillar 
from formula 
\> =m. , 
^1-63 
where rn is as below, 
according as the weight 
is in lbs. or tons. 
lbs. tons. 
lbs. tons. 
Old Park Iron, No. 1 
125502 = 56-03 
111858 = 49-94 
Derwent Iron, No. 1 
117872=52-62 
105079 = 46-91 
Portland Iron, No. 1 
116802 = 52-14 
104098=46-47 
Calder Iron, No. 1 
116862=52-17 
104137 = 46-49 
London Mixture 
104137 = 46-49 
92862=41-46 
Level Iron, No. 1 
105700 = 47-19 
94202 = 42-05 
Coltness Iron, No. 1 
101130 = 45-15 
90119 = 40-23 
Carron Iron, No. 1 
100929 = 45-06 
89949=40-16 
Blaenavon Iron, No. 1 
96659 = 43-15 
86114=38-44 
Old Hill Iron, No. 1 
84435 = 37-69 
75270 = 33-60 
Second London Mixture 
117408 = 52-41 
104623 = 46-21 
Low Moor Iron, No. 2 
' 101676=45-39 
90674 = 40-48 
Blaenavon Iron, No. 3 
103515=46-21 
92329=41-22 
The numbers above represent the strength of a pillar 1 foot long and 1 inch diameter. 
To compare the direct strength of long pillars of cast iron ivith their transverse strength. 
— If the pillars be cylindrical, and have their ends turned hat and perpendicular to their 
D" 
axes, the ultimate strength of a solid pillar will be represented by 'W=m—. where D 
is the diameter, I the length, and m, n, p constants. My former experiments* gave 
n=3-55 and j9 = I’7, but the present experiments on larger pillars give o' 5 and I '6 3 for 
their values much more nearly. 
The transverse strength of a cylinder, laid with its ends upon supports, and broken by 
a weight at its middle, is 
v,=h.—- 
Whence the ratio of the direct strength of a pillar to its transverse strength is 
vp_m 
td b ' 
If w be taken as 3-55 and^^ as I'7, we shall have 
w m D 
w' b 1"^ ’ 
and if be taken as 3‘5 and^ as I ‘6 3, 
tv m D ^ 
w' b 
* Philosophical Traiisactious, 1840. 
