and Strength of Materials. 287 
— .64437 x B = b. And by substituting 
these in the theorem above, we have the 
_ 5x .64437x Bx (5.7993)? 
meth = CX 
5519 (.5519)? 
e: gn ey aa i 3 ri 4 
at ta) (a 3) x : 5519 
2 eae Ae 
= 3.1794 x — = strength of the beam when 
no part of ithas been taken away. And neg- 
lecting the deflection in the two cases as in- 
considerable, we shall have: 
Strength of the part = 3.4793 he 
of the whole = 3.1794 = 
Difference — .2999 xX fe = the 
excess of the strength of the part above that 
of the whole; a quantity nearly equal to 
vo of the strength of the whole beam. 
This curious conclusion is analogous to 
what was shown to be the case in incompres- 
sible bodies (arts. 7 and 8), and the reason, 
why :th of the height was here chosen to be 
cut off, was that § was found there to be the 
height of maximum strength. 
For the values of s and C, in the preced- 
ing examples, and for information connected 
with the history of this subject, see Mr. 
Barlow’s work, which we have so frequently 
