and Strength of Materials. 245 
gy are the distances of the centres of gravity 
of the sections of tension and compression 
respectively from the neutral line. 
Cor. 2d. Ifo=w=], 
Sf sx°Xe + fsxXe x tt 
aL.C 
(when «=a and y—d) = (by corollary 
2d, art. 9th, and the last corollary above) 
sgp tse - $8) Sis 
aL.c * section of tension + aLo * section of 
Strength — 
p’g Xx section compression sg 
g’ x section compression — aL.C * sec- 
tion of tension x (p+p’), where p and p’ are 
the distances of the centres of percussion of 
the surfaces of tension and compression from 
the neutral line, and g and y’, as before. 
17. Example. Let the surface of fracture 
ABCD, (fig. 5th, ) be the segment ofatriangle, 
whose base is CD and vertex E; the part 
ABba being that of tension, Call pE, the 
distance of the neutral line from the vertex, 
=h, and the rest as before: And to express 
pe and pf, or the depths of the surfaces of 
tension and compression, in terms of h, let 
mand be such numbers that a or pe may be 
designated by mh, and d or pf by nk. Then 
by similar triangles Ep: ab:: Ex: de. In 
symbolsh:b::h—a: _ (h—a) =de—X. And 
tension x 
in like manner h: bi: hy: = (hey) aii 
