fs ee 
and Strength of Materials. 237 
other, (the points F and G being supposed to 
be connected by the chain FG, merely to 
give the lever the appearance of greater 
strength.) And to obtain the strength of the 
body we shall have 
W x /G = sum of the forces in abd x Ff. 
sum of the forces inabd x Ff 
Whence W= jhe length. 7G , where 
the deflection of the beam is neglected ; or in- 
troducing that, as in art, 9, we have W (the 
sum of the forces in abd % (FP-+ Pf) 
Length X cosine of Deflection 
weight) = 
— TXD+TX4, where T= sum of the 
ene ckaved. 
forces rising from tension, D and A the dis- 
tances of the centres of tension and com- 
pression from the neutral line, L the length of 
the piece, and C the cosine of its deflection. 
14. A necessary consequence of this reason- 
ing is, that the sums of the forces of extension 
and compression are just equal to one ano- 
ther :* For the weight W, acting in the di- 
* The mode of reasoning adopted above has been ob- 
jected to by Mr. Barlow, who conceives that the forces in 
F and f, or those of extension and compression, instead of 
being equal, should be inversely as their distances from 
the neutral line, or that the forces in F % PF = forces in 
J X Pf, and that these taken collectively are — the rec- 
tangle under the weight and the length of the beam, which 
is supposed to turn as on a pivot round the neutral line. 
Whence LX W = the forces in F % PF + forces in f 
