30 EMBANKMENT WHEN ONE FACE IS SLANTING. 



of the normal pressure P, and the angle which the direc- 

 tion of the normal pressure makes with the horizon ; then 

 we have, for the horizontal component, 



P! = P cos a 



= area of BC x |CE x w l cos (Art. 15) 

 = area of CE x \hw l , 



where h = CE, and w^ is the weight of a cubic foot of the 

 fluid. 



Similarly, P z = area of BE x^hw t ; 



but area of CE is the projection of BC on CE, and area of 

 BE is the projection of CB on EB ; i. e., the pressure 

 exerted by a fluid in any direction upon a surface 

 is equal to the weight of a column of the fluid, 

 whose base is the projection of the surface at right 

 angles to the given direction, and whose height is 

 the depth of the centre of gravity of the surface 

 below the surface of the fluid. 



Hence, since the projection at right angles to the vertical 

 direction is the horizontal projection, and that at right 

 angles to a horizontal direction is a vertical one, we find 

 the vertical pressure of the fluid against a surface by treat- 

 ing its horizontal projection as the surface pressed upon, and, 

 on the contrary, the horizontal pressure of the fluid in any 

 direction by treating the vertical projection of the surface at 

 right angles to the given direction as the surface pressed 

 upon, and in both cases we must regard the depth of the 

 centre of gravity of the surface below the surface of the 

 fluid as the " height of the column." 



Let g, G, and #, be the centres of gravity of AFD, 

 FECD,' and EBC ; let AB = a, DC = b, AF = c, EB = d, 

 and w = the weight of each cubic foot of the embankment. 

 The horizontal pressure of the water acting at M tends to 



