and Strength of Materials. 247 
together with the values b, h and n dependent 
onit, is changed, and must first be determined. 
Cor. When xh, the depth of the surface 
of compression is indefinitely small, » being 
then = 0, the fulcrum is on the edge, and the 
strength of the triangle becomes 
shh? ‘ ? 
Le (o3 ~ o43)" 
We might in one of the preceding exam- 
as in article 6th. 
ples have put the sum of the forces of tension 
equal to those of compression, and thence, the 
neutral line being supposed given, have deter- 
mined the ratio of s tor, and from thatthe ratio 
of the forces necessary to produce a given ex- 
tension and compression in a fibre, which 
ratio must be constant in the same kind of 
body for any given extension or compression. 
We shall not however seek for that ratio, 
but suppose it known, and make it the sub- 
ject of a problem. But we will first give the 
following lemma. 
19. Lemma. In the bending of any body, 
this proportion will obtain: as the extension 
of the outer fibre on one side is to the contrac- 
tion of that on the other, so is the distance of 
the former from the neutral line to that of 
the latter. 
Demonstration. Let kl (fig 6th,) be an 
imaginary line perpendicular to the upper 
