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II.— ON THE PEESSURE OF EARTH AGAINST A RETAININGl 

 WALL. Br ARTHUR HILL CURTIS, LL.D., D. Sc. 



[Read, June 19, 1882.] 



When a mass of earth is supported by a wall, it is an important 

 matter to determine what the stability of the wall should be in 

 order that equilibrium should be maintained. To solve this prob- 

 lem, it is necessary to determine the magnitude of the pressure 

 and the point of its application. 



• The investigation which determines the magnitude of the pres- 

 sure is based on a principle due to Coulomb, in accordance with 

 which we suppose that the mass of the earth which presses against 

 any portion of the wall, measured from the top downwards, seeks 

 to lower its centre of gravity by sliding along some plane inclined 

 to the horizon, at an angle not less than the angle of friction (or 

 repose) of earth on earth, and compute the horizontal force which 

 will be suflScient to prevent this tendency taking effect along the 

 plane which requires the greatest possible resistance to counteract it. 

 The force thus obtained is equal and opposite to the greatest pres- 

 sure which can result, and is thus, in one sense, a maximum, but 

 yet it is the minimum force which will ensure equilibrium, on the 

 supposition that the wall is perfectly rigid. 



The problem in the case in which the surface of the earth is in 

 the form of a cylinder round a horizontal line parallel to the top of 

 the wall, which is supposed to present a vertical surface to the 

 earth, is solved by a theorem due, I believe, to Dr. Hart, Vice- 

 Provost of Trinity College, Dublin : this theorem is as follows : — 



Let a vertical plane OADB (fig. 1) be drawn perpendicular to 

 the wall at a point A, situated on the horizontal line coinciding 

 with the top of the wall, and bisecting a unit of its length — one 

 foot, suppose : let this plane cut the surface of the earth in the line 

 AZDB, and at any point C on OA ; let CB be drawn inclined to 

 the horizon at the angle (p, the angle of friction of earth on earth ; 

 then, if CD be drawn in such a way that, drawing DJE perpendi- 

 cular to CBy the area CAZD shall be equal to the area CDE, the 



