492 EEPOKT— 1891. 



some thickness being fixed upon. The width h is then de- 

 termined from the condition that the portion of the wall above 

 h must satisfy the conditions for stability. Then the widths 

 c, d, e, &c., are determined in order, from similar considera- 

 tions. Since the section of the wall will be independent of the 

 length of the wall, to simplify calculations the wall may be 

 sujiposed to be of unit length. 



An easy calculation in statics shows that the distance from 

 the face of the wall of the centre of gravity of the top segment 

 of the wall, included between a and b, is given by the formula, 



b'^ -i- a^ + ab 

 3 {a + b) 

 Similarly, the distance of the centre of gravity of the next 

 segment from the face of the wall is — 

 &2 + c 3 -f be 



and similarly for every other segment. 



Also, the moment of overturning in foot-pounds for the top 



62'5 



segment, due to the water-pressure, is -^ . /i^ ; the moment of 



62*5 



overturning for the first two segments is "" - . 2' . /r; for the 

 o ^ 6 ' 



62"5 

 first three segments, -^^ . 3^ . /r, &c. 

 6 



Let us suppose that by some means the first four widths, 

 ((, b, c, d, have been correctly determmed, and we wish to find 

 the next width, e. Since the centre of pressure on the base is 

 at the extremity of the middle third, taking moments about 

 that point, the condition for stability will give us the following 

 equation to determine e : — 

 a + b\2e b'^ + a^±ab]j b + c\2s b^ + c"- + bc]-, 



,d + c\^& d2 + c2 + cZc), d + cj2e c2-f^g + ecZ ) , 

 + 2-13^" 3Tcr+cr) "^"S-iT" 3(^ + e) )"''- 



6 



where w denotes the weight of a cubic foot of masonry. 



Now, the previous width, d, would be determined by a 

 precisely similar equation, i.e., — 



a^bl2d_l^±^±ab] bJ^^U_h^±l + bc], _^ 



'2 (3 3(a+&)] ^ 2 l3 3{c + b)\ 



d + c\M_ d^ + c^ + dc U_^, 62j5 ^3 

 ■^2 13' 3 (rf. + c) I ■ 6 ■ ■ 



