and Strength of Materials. 277 
Cor. If d=a, the equation for the whole 
triangle becomes x? + 972 x = 5882. 
Whence x = 5. 799337, whichis the distance - 
of the neutral line from the vertex.* 
34. The: situation of the neutral line hav- 
ing been determined by the foregoing rule, 
or by direct experiment, the strength of the 
piece may be obtained by the following for- 
mula ee (Art. 16th, Cor. 2d,) where 
sis the direct longitudinal strength of the 
fibres contained in a unity of surface; A the 
area of the section of tension, a its depth, g 
the distance of its centre of gravity from the 
neutral line, p and p’ the distances of the 
centres of percussion of the sections of tension 
and compression respectively, Lthe length of 
the piece, and C the cosine of its deflection. 
—But when the flexure is moderate C may 
be omitted without much error, and we will 
do so in the following examples. 
Example Ist. Required the strength of a 
joist of Dantzic fir, nine feet long, one 
foot deep, and three inches broad, the weight 
being applied at its end ? 
* The above example, as well as some other parts in the 
‘conclusion of this paper, have been added by permission, since 
the paper was read. 
