862 
ME. HODGKIJs-SON’S EXPEEDUZS’TAL EESEAECHES 
machinery would break without injury to it. The great reduction in strength produced 
by taking away the external crust, shows that to ornament a pillar it would not be 
prudent to plane it. It may, however, be mentioned that the eighth pillar had many 
flaws in it. 
In experiments upon hollow piUars, it is frequently found that the metal on one side 
is much thinner than that on the other, but this does not produce so great a diminution 
in the strength as might be expected, for the thinner part of a casting is much harder 
than the thicker (Table VIII.), and this usually becomes the compressed side. 
The strength of a solid pillar, 10 feet long and I mch diameter, being, from the first 
mean above, 2085'2 lbs., that of a solid pillar, I foot long and I inch diameter, will, 
since I0‘'^=50TI9, be 2085-2 x 50TI9 = I04508 lbs., or 46-65 tons; the strength being 
supposed to vary directly as the 3-55 power of the diameter, and inversely as the I- 7 
power of the length, as obtained from the experiments in my former paper on this 
subject*. 
The larger and more varied pillars in the present research, have, by experiments 
deduced from most of the irons in the kingdom, given more precise results for the con- 
stants on which the strength depends. They show that it varies directly as the 3-5 
power of the diameter, much more nearly than as the 3-55 power, and inversely as the 
1-63 power of the length, from a mean of many experiments in each case (see pages 865 
and 866). 
From the second mean value of x in the preceding- summary, that depending on the 
3-5 power of the diameter, the strength of a pillar 10 feet long and 1 inch diameter 
is 2223-7 lbs., and this multiplied by 10*'®* or 42-658 (see Table II. page 860), gives 
94858-59 lbs. = 42-347 tons, for the strength of a pillar 1 foot long and 1 inch diameter. 
Whence w being the breaking weight in tons of a pillar whose length is ? in feet, and 
external and internal diameters D and d in inches, the ends being flat and well-bedded, 
we have, in Low Moor iron. No. 2 — 
j^3'55 __ 
46-65 X , from formulae in Philosophical Transactions, 1840; 
w=42-347 X 
J33-5_^3-5 
1-63 
, from formulae in the present paper. 
The preceding chapter contains the results of experiments on the strength of pillars 
10 feet long, solid as well as hollow, the hollow ones varying from 2-^ to 4 inches 
external diameter, and the solid ones cast fr'om models 2^ inches diameter. They ai-e 
all of Low Moor iron. No. 2, except two. Nos. 13 and 14, of Blaenavon iron. In the 
previous research f the fron used was that of Low Moor, No. 3, and there appears to he 
very little difference in their strengths, though the No. 2 seems to he rather the stronger. 
The experiments in Table IX. of the previous paper are on hollow pillai’s 1-75 mch 
external diameter and upwards ; and on solid pillars of the same diameter nearly, the 
* Philosophical Transactions, 1840, Part II. t Ibid. 
