and Strength of Materials. 249 
are equal to those of compression (art. 14,) 
we have 
vs =f (when a —a,andy =d), 
a’ 
s being the resistance of the most extended 
fibre, and r that of the most compressed. If 
then, in figure 6th, hk be unity, s will be the 
force necessary to produce the extension 
hk, and r the resistance answering to the 
compression li. Now by the lemma mp: 
pn:: hk: = = li: Hence li= <, putting 
a for mp, d for pn, and hk being unity. 
And since the forces are as the » power of 
the compression of a fibre, and the compres- 
sion caused by c= unity, we have l*:e¢:: 
~ cd» : : 
(£) <= which is a new value of r; and 
this substituted for r, in the equation of the 
forces above, gives f= us StS eYyig : 
a’ a 
Cor. 1. If v=w-—o, or all the forces 
are constant 
Xx"; 
of a Au = Xe = sx section of tension, 
a’ 
cYy”) ] h : 
and f—* = ex fi —cx section of compression. 
But these quantities are equal, and there- 
fore section of tension: section of compres- 
sion ::¢: 8s, a constant ratio, determinable 
by experiments. 
Ti 
