236 On the Transverse Strain, 
ing fibres takes place. And hence we see 
that in the bending or fracture of any mate- 
rial, the particles on one side are dilated, 
whilst those on the other are compressed ; 
and it will not be difficult to perceive, that 
there must be a line somewhere in the surface 
of the fracture, where neither extension nor 
compression is sustained. 
13. If then in figure 3d, in which adbe is 
intended to represent the surface of fracture, 
ab be the neutral line, or that of which we 
have been speaking, and if abd be the sur- 
face of extension, and acb that of compres- 
sion, it is evident that the extensions, or com- 
pressions of any particles, within those sur- 
faces, will be as their distances from the line 
ab; and the forces necessary to produce them 
may be considered as in proportion to some 
powers v and w of those distances. 
And in order to estimate the strength of the 
piece whose section is achd, if F and f repre- 
sent the points at which the forces, rising 
from extension and compression, being col- 
lected, would produce the same effects as 
they do at their respective distances from 
the neutral line: f will be the fulerum on 
which all the horizontal forces may be con- 
ceived as sustained, and Ff one arm of a 
bended lever, while the length Gf is the 
