204 REPORT—1840. 
Experiments. 
With a view to develope the laws connecting the strength of cast- 
iron pillars with their dimensions, they were broken of various lengths, 
from five feet to one inch, and the diameters varied from half an inch 
to two inches, in solid pillars; and in hollow ones the length was 
increased to seven feet six inches, and the diameter to 35 inches. My 
first object was to supply the deficiencies of Euler’s theory of the 
strength of pillars*, if it should appear capable of being rendered 
practically useful; and, if not, to endeavour to adapt the experi- 
ments so as to lead to useful results. As the results of the experi- 
ments were intended to be compared together, it was desirable that 
all the pillars of cast iron should be from one species of metal ; 
and the description chosen was a Yorkshire iron, the Low Moor, 
No. 3. The pillars were mostly made cylindrical, as that seemed a 
more convenient form in experiments of this kind than the square; for 
square pillars generally break anglewise. The experiments in the first 
table were made on solid uniform pillars, rounded at the ends, that the 
force might pass along the axis; and the metal was cast in dry sand, to 
obtain, as far as possible, uniformity in its texture. In the second 
table the pillars were uniform and cylindrical, as before, but had their 
ends flat and at right angles to the axis. In this table the variety of 
the lengths and diameters of the pillars was considerable; and in the 
lengths it was greater than in the former table. The pillars were from 
the same models as before, but were cast in green (moist) sand. 
Results from the 1st and 2nd Tables. 
1st. In all long pillars of the same dimensions, the resistance to 
crushing by flexure is about three times greater when the ends of the 
pillars are flat, than when they are rounded. 
Qnd. The strength of a pillar, with one end round and the other flat, 
is the arithmetical mean between that of a pillar of the same dimen- 
sions with both ends round, and one with both ends flat. Thus, of 
three cylindrical pillars, all of the same length and diameter, the first 
having both its ends rounded, the second with one end rounded and 
one fiat, and the third with both ends flat, the strengths are as 1, 2, 3 
nearly. 
ard. A long uniform cast-iron pillar, with its ends firmly fixed, whe- 
ther by means of dises or otherwise, has the same power to resist 
breaking as a pillar of the same diameter, and half the length, with the 
ends rounded or turned so that the force would pass through the axis. 
4th. The experiments in Tables 6. and 7. show that some additional 
strength is given to a pillar by enlarging its diameter in the middle 
part; this increase does not, however, appear to be more than one- 
seventh or one-eighth of the breaking weight. 
5th. The index of the power of the diameter to which the strength 
of long pillars with rounded ends is proportional, is 3°76 nearly, and 
3°55 in those with flat ends, as appeared from the results of a great 
* Berlin Memoirs, 1757. 
