and Strength of Materials: 243 
Cor. Ist. If v—w, or the forces are as 
the same power of the extensions and com- 
5 — sbad Ra - 
pressions, strength = 7G (p12) = @+2)LKE 
section of tension. 
sd 
Cor. 2d. Ifv=n —o, rong X sectionof 
tension. 
Cor. 3d. Ifv=w —1, strenoth=qq X sectionof 
, 2 on tension. 
16. And thus we might proceed to find the 
strengths of beams of other forms, as triangles, 
their frustums, &c. But to obtain that of 
any general form ABCD, figure 5th, it may 
be necessary to make use of fluxions; and 
if we call the depth of tension pe =a, any 
distance px = 7, de=X, depth of compres- 
sion pf=d, any distance py=y, »= Y, 
the neutral line ab — , and the rest as before, 
we shall then have the force exerted in de 
= — the breadth of de being unity, or the 
force = ——— X2'e when its breadthis = x, (art. 9). 
ne 
“=the product of the force in de 
sXx 
and - 
a 
when multiplied by the distance of the neutral 
line. And in the same manner the resistance 
wal patra 
ink = — ie »and = = “ = the productas 
before. 
