Ae 
oe 
and Strength of Materials. 233 
v1 
sist with equal forces, A ees (putting the 
double ordinate de for yx, the fluxion of thesur- 
face) = sx Sum of the de x « =s x the section 
of fracture X dist. of its centre of gravity from 
b: which distance if called g, will give 
ke o+i 
syx x 1 sg X section | 
eo section; and W = eeerqins 
Cor. 2d. Ifv=1,or the extensions are as 
x 
eo 
SYX § 
the forces, _— =X Sum of the dex gz? 
= “3h x the section, where p is the dis- 
tance of the centre of percussion of the section 
of fracture, and g that of gravity, as before 
(Emerson’s Mechanics, Prop. 57, Cor. 1). 
o+l 
SYR xr 
D 
But since “8? x the section= = 1x 
a 
sgp X section 
W xXcos. Defl.; we have W= 727 y cos. defi. 
10. In the preceding investigations we have, 
agreeably to custom, supposed that the com- 
pressed fibres or particles were confined to a 
very small space on the edge of the beam ; 
and that all the rest were in a state of ten- 
sion, less or more. And this may probably 
be not far from the case in such bodies 
as glass or marble: But (as Dr. Robi- 
Gs 
