22 Rules for ascertaining the Strength of Materials. 
and _ if supported at both ends. 
In this case d is the diagonal. The strength of a square 
beam is the least when the force is in the direction of the dia- 
gonal, The lateral strength of a solid cylinder is 
y 4. 
tik if supported at one end, 
and une if supported at both ends. 
In this case r is the radius, and p = 314159 &c. 
The lateral strength of a tube or hollow cylinder, is 
SF p(RA—r4) 
41 
fp(R4—r) 
d Rl 
if supported at one end. 
an if supported at both ends ; 
Randr being the radii of the exterior and interior circles. 
The section of the tube is supposed to retain its circular form 
at the time of fracture. It has been said that we cannot deter- 
mine from theory the proper thickness of material for the tube, 
so that its form may not be sensibly altered by the pressure ; but 
this is a mistake, for by a very simple investigation the thickness 
can be determined sufficiently near for any practical purpose. 
The lateral strength of a triangular beam or bar is 
05645 fb de . 
. ees supported at one end, 
i 
29572 f 
l 
! ba. 
pry) eS i supported at both ends. 
In this case J is the base of the triangle, and d_ the height 
or the dimension in the direction of the pressure. The strength 
is the same when the edze is uppermost as it is when the op- 
posite side is uppermost. The strength of a solid cylinder, pil- 
lar, or column, to resist a force acting in the direction of its 
axis is 
8 fra 
=p? Where e is the extension of the mate- 
rial at the time of fracture. The diameter of a column may 
be so great in proportion to its length, that a less force than that 
necessary to bend it, would crush it. 
The force necessary to crush a homogeneous solid cylinder is 
8 fpr. 7 
The last rule has not yet been compared with experiment, 
indeed I do not know of any to compare it with. A set of ex- 
periments, on this kind of fracture, would be useful, not only 
to the architect and engineer, but also to the philosopher, “ It 
is 
