228 On the Transverse Strain, 
vote 
a a Lay neh . ¢ . re 
2 > v2” 1n y summation of series | + 
n+} 
243+44&c. lom= — ~m being infinitely 
n 
greater than the unity here made use of.) 
é ba2 
And if v=o, the strength, or sae becomes 
sba” 
, which is the theorem of Galileo. 
If v= 1, or the forces are as the extensions, 
. sba? is 
the strength is, —; and this is the theorem 
of Mariotte and Leibnitz. And according to 
one or other of these suppositions, authors 
have generally estimated the strength of 
materials. 
5. Again: Let the section of fracture be 
the frustum ABCD, (fig. 2.) of a triangle. 
Then if a be the height of the segment, 6 its 
base, h the whole height of the triangle, and 
# any variable distance from AB as before, 
b 
we shallhaveh: b:: h—a#.: 7 (h-x) = de, 
or y, which substituted in the foregoing for- 
vo+1 
: ; v+1 v2 
mula —" ,» will give, Lai (2 — x ) 
v hav 
= the strength of de. And if as before the 
distance a be divided into an infinite number 
of equal parts, whereof the breadth of de is 
one, the strength of ABCD will be express- 
