and Strength of Materials. 229 
ed by ~ (i x ui re free to ala 
al gaa th ae oe ) which, by summing 
the series as ai becomes 
o+2 
sb ha zit ys _ sb ha? 
Rae No-2., | ¥ ae v2 aS 
6. And if the strength sf the whole trian- 
gle be sought, it will, putting a = h, be ex- 
pressed by sh (5 sips a) 4 
b 
If then v —o, the strength = - 6 
z 
> 
as with 
Galileo. And if v=1, strength =", which 
is the value according to Leibnitz. i 
7. Now from the form of the expression, 
£ ie — T 73) which designates the strength 
of ABCD, it seems probable that there may be 
some height, a, less than h, at which the 
frustum may resist with more energy than the 
whole triangle :—We will put the fluxion of 
sb fha* a3 
a9 spa) and seek for the height at 
which the strength would be greatest. We 
b ¢2haa 3a*a . 
have then ; ae oa)- o And by di- 
ha ay ea _ 246 | 
vision, Pre v3 =o Ora= 3v-+6- ° 
Where if v =o, or all the fibres resist with 
