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If the natural slope of the earth K'E be at an angleEK'D, then the slope of the wall will be K'G bisect-ing the angle IK'E which EK'D wants of 90°.

TO DETERMINE THE EXTRADOS OE AN ARCH AND OFITS PIERS.

Fig. 12. Let CV = c = the radius of curvature at the vertexof the extrados of an arch.

GF = gf=- LY = ON = AV = n, the height of thekey. AE = YM, or Ae ■= Vm = x = the versed sineof the intrados at any point BEF a horizontalline at the springing of the arch. KLOD a hori-zontal and base line, below which the foundation isincompressible in every direction. VD or vd = m —the height from the vertex of the extrados, to anyordinate KD or kd to it, OF = VD — VE — VD —

EA -f- VA — m — x -{- n, the height of the pier to thespringing of the intrados from the base line.

CONSTRUCTION.

In OF continued each way, take FG and ON eachequal AV. On the diameter NG describe the circle,cutting KLOXD in L and X. Make OK equal LX.Draw LY parallel and equal to ON. Join KY andYN. At right angles to KY is the direction of thelateral pressure, and at right angles to YN of the ver-tical pressure, or pressure in the direction of gravity.

From F at any angle, GFH less than the angleKYL, draw FH, cutting the horizontal line GI inH. Make III equal GH, and let fall the triangleH IK' similar to the triangle FGH, HI, and FG ho-