On the Resistance of Solids. 419 
When:a beam is compressed in the direction of its length, the 
deflexion is always in the direction of the diagonal, when the 
section is nearly square; this has been shown by the experiments 
of Girard, Lamandé, and Navier; and it is only a modification 
of the transverse strain, which confirms the general principles of 
the theory, aud at the same time shows that a cylinder is the 
best form for an insulated post *. 
19. When the neutral line divides the section into two parts, 
that are neither equal nor similar; assuine the distances of the 
upper and lowcr sides of the beam from the neutral line, and 
find the force exerted on each side of the neutral line by art. 13. 
Make those forces equal to each other, and from this equation 
the distance of the neutral line from the upper side may be ob- 
tained ; which being substituted for the assumed distance in the 
expression for the force of the part above the neutrai line, will 
give half the strength of the beam. 
In this manner the rule for the strength of a triangular beam 
has been found, which is inserted in the Philosophical Magazine, 
vol. xivii. p. 22. 
20. As the cohesion of their parts not only serves to charac- 
terize different substances, but also to determine their relative 
value in the various uses to which they may be appropriated; I 
have endeavoured to collect from various sources, the best experi- 
“ments on this important subject; and to preseut them in the 
form which appeared to me best adapted to render them capable 
of universal application. 
For this purpose they are reduced to a common standard, from 
which, by a simple operation, they may be reduced to any kind 
of weights or measures. 
I have adopted plate glass as a standard, because it is a sub- 
stance tolerably uniform in its nature, its defects may be readily 
perceived, and it is not used where its strength need be caleu- 
lated; and therefore, the strengths of different kinds of it will 
not be required, ‘The experiments were made on the transverse 
strength, and the direct cohesion was calculated by art. 14. The 
pieces were loaded by letting sand run slowly into the scale till 
they broke. The results were regular, and the highest was taken. 
* This remark extends only to the form of the section. 
+ The rule for the resistance to crushing (Phil. Mag. xlvii. 22) was an 
attempt to apply the principles which M. de Prony has used in his investi- 
gation of the push of the earth agains: retaining walls to the resistance to 
crushing—neglecting the effect of the cohesion in determining tie angle of 
fracture. Since that time I have found that the angle of fracture will vary 
with the cohesion ; therefore any rule where it is neglected can only be a 
rude approximation.—It may not be improper here to state, that in M. de 
Prony’s investigation of the push of the earth, one very material element is 
omitted ; viz. the friction against the back of the wall. The existence and) 
effect of this friction may readily be seen from the results of Col. Pasley's 
experiments. ‘* Course of Military Instruction,” iii, 563, 
Dd2 Experi- 
