TRANSACTIONS OF THE SECTIONS. 205 
number of experiments; or the strength of both may be taken as the 
3°6 power of the diameter nearly. 
6th. In pillars of the same thickness the strength is inversely propor- 
tional to the 1°7 power of the length nearly. 
Thus the strength of a solid pillar with rounded ends, the diameter 
3-6 
[7 
The absolute strengths of solid pillars, as appeared from the experi- 
ments, are nearly as below. 
In pillars with rounded ends, 
of which is d, and the length J, is as 
e 
; of, a6 
Strength in tons = 14°9 al 
In pillars with flat ends, 
66 
Strength in tons = 44°16 ie 
In hollow pillars nearly the same laws were found to obtain ; thus, if 
D and d be the external and internal diameters of a pillar, whose 
length is /, the strength of a hollow pillar, of which the ends were 
-moveable (as in the connecting rod of a steam-engine), would be ex- 
pressed by the formula below. 
D3-6 — q3-6 
[\-7 i 
In solid pillars, whose ends are flat, we had from experiment as 
before, 
Strength in tons = 13 x 
D3-5— q3-6 
ea 
The formula above apply to all pillars whose length is not less than 
about thirty times the external diameter; for pillars shorter than this, 
it is necessary to have recourse to another formula, which has been 
investigated by the author*. 
Similar Pillars. 
In similar pillars, or those whose length istothe diameter in a constant 
proportion, the strength is nearly as the square of the diameter, or of 
any other linear dimension; or in other words, the strength is nearly 
as the area of the transverse section. 
In hollow pillars, of greater diameter at one end than the other, 
or in the middle than at the ends (Table 11.), it was not found that any 
additional strength was obtained over that of cylindrical pillars. 
The strength of a pillar, in the form of the connecting rod of a 
steam-engine, was found to be very small, perhaps not more than half 
the strength that the same metal would have given if cast in the form 
of a uniform hollow cylinder. 
Strength in tons = 44°3 x 
* Tn this case the formuia for the strength is » where b is the breaking 
be 
b+ic 
weight of the pillar, as calculated according to the previous formula for long 
flexible pillars ; and ¢ = the force which would crush a pillar of the same sec~ 
tion without flexure. 
