and Strength of Materials. 285 
‘where r = radius, A — area ACB, anda 
— CEH. 
If in like manner P be the centre of per- 
cussion of a circular arc ACB, and E the 
point of suspension, the distance EP will be 
expressed by 
(=- oa +5 r) A'43(a—r) (2ra—a )* 
(—-1) A’ + 2(2ra- a i 
where A’ is=— the arc ACB, andr, and aas 
before. 
Example 6. Let it be required to find 
the strength of a beam, the section of frac- 
? 
ture of which was that frustum of a triangle 
whose neutral line we found in art. 33, and 
to compare it with the strength of the beam, 
supposing its section to «ibs been the whole 
triangle. 
From art. 17th it will appear that the 
strength of the frustum, ABCD, when its ex- 
tended side is that nearest the vertex, is— 
.C 
mn n* 
ea Se) me ae m? wat pa 
v4+2 043 (Ha ae) i n 
w+l * w+2 
and calling v =mw—1, since the extensions 
and compressionsare as the OE eh it becomes 
n® 
s+ 
bh? , 
tos ~<a) tG* mesg a tere 
2 
