EMBANKMENT WHEN ONE FACE IS SLANTING. 31 



turn the embankment over its outer edge A. Hence, we 

 have 



the moment of P t = ^h 2 w 1 x $7t = ^h s w 1 ; (1) 



the moment of P z = dx^hw t x AH 



the moment of AFD = wt. of ADF x AF 



o 



= tyhw x f c = faphw ; 

 the moment of FECD = wt. of FECD x (AF + JFE) 



the moment of EBC = wt. of EEC x (AB f BE) 



= \dliw x (a \d) 

 = \dhw (3a 2d). 



r2 i 



.-. the moment of ABCD = \ '- + =b(2c+b) 



\ _ O li 



hw + (3a - d) hw v . (2) 



^ (3a - 2d) } 



If the embankment be upon the point of overturning on 

 A, the moments in (1) and (2) are equal to each other, and 

 we have 



w 

 or, W = [2c*+3b(2c+b) + d(3a-2d)~]+d(3ad), (3) 



1 



and the embankment will be overturned or not, according as 



in 

 or 



COR. 1. If the embankment is of the form of Fig. 11, 

 d = 0, and (3) becomes 



