Curtis — Pressure of Earth against a Retaining Wall. 13 



The case in which the surface of the earth is curved is not 

 practically of much importance, but it may be •well to consider 

 the case in which the surface of the earth, except in the vicinity of 

 th* wall, is a plane inclined to the horizon at an angle less than 

 ^, and intersecting the plane of the face of the wall in a horizontal 

 line. If the wall be supposed to carry a surcharge of earth, the 

 portion adjacent to the wall will weather away, and form a plane, 

 AZ (fig. 3), inclined to the horizon at the angle ^, and therefore 



Fig. 3. 



parallel to CB. The solution of the problem will be obtained by 

 determining, in the trapezium AZBG, the line CD such that, 

 drawing BE, inclined to CB at the complement of the angle 

 a + 0', the area CDE shall be equal to the area CAZD. 



To solve the problem : Suppose it done, and bisect EB in iV; 

 then the rectangle CN . DM = 2ACDN' = trapezium AZBC, and 

 therefore known ; but as the triangles DBM, DBE, and DBN are 

 all known in species, it follows that the ratio of DM: NB is known, 

 and from these two conditions it follows that CN . NB is known, 

 and the problem is solved by cutting CB in the point N, such 

 that CN . NB shall have this known value, taking EN = NB, and 



making angle CED = ^ - (a + ^') : the line CD solves the problem. 



