516 ON THE EXPLOSION OF THE BOILER 
by the weight, w, at B. And, it is evident, that as B C in- 
creases, the velocity of the point, C, decreases, 
Therefore sd =— ue ; 
b g 
sy eeiCae wr? 
By Integration +F=- 7 + C; and when z=0, v=u; 
caw 
and, therefore, == - (w?—v*). 
: » ged he ; é 
When z=6 =v? — ae a where v is the velocity, with 
which the weight, w, will depart from, A, in the direction, B A, 
I 
after it has broken the first beam ; and, therefore, v is the ve- 
locity, with which the weight, w, will impinge upon the second 
beam. 
In the same manner, then, it appears, that 
II I 2acb 1) c 
vv" a ae wu _-— ; where v is the velocity, 
with which the weight, w, will depart from A, after it has 
broken the second beam. 
i" VIII 8 ch 
And, in the same manner v?=u? — cA 
; but, it is sup- 
Vu b 
posed, that v=o; and, therefore, u?= — 
But, it is necessary to find both b & c, before u can be known. 
To find 8, it is necessary to find the equation of the curve, 
DAE; and, to find c, we must find the weight, which, sus- 
pended at A, is just sufficient to break the given beam, D A E. 
ee See 
