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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1914 edition. Excerpt:...0 and G acts downwards. Call the angle that AC makes with the horizontal y, and the angle FAC, ft. On drawing the parallelogram o forces as shown, we have, since E and G are proportional to the sines of the opposite angles in the triangle ONL, E _ sin ONL G sin NLO It is easily seen from the figure that ONL = y--, and that NLO = $ ] ft-f f' hence the above general relation becomes, E __ sin (/--f).j. G sin ( + + ft);' Now, if we conceive the plane AC, always passing through the point A, to vary its position, that value of E, corresponding to the greatest value obtained by the construction above, is the thrust actually exerted against the wall; for, if AC is the plane of rupture corresponding to this greatest trial thrust, any less value of the resistance of the wall E will cause S to make an angle greater than f with the normal to AC, which (Art. 21) is inconsistent with the law of stability of a granular mass (also see Art. 25): hence the least thrust consistent with equilibrium corresponds to the greatest value of.Ethus obtained; and this is the actual active thrust exerted against the wall, when the wall simply resists the tendency to overturning or sliding on its base, caused by the tendency of the prism of rupture to descend. If there is a thrust exerted on the wall towards the earth, from any external force acting on the left of the wall; from left to right; then, if this be supposed to increase gradually, the active thrust of the earth on the right is first overcome; then, as the external force increases, the directions of S, on all planes as AC, approach the normals to those planes, pass them, and finally the full passive resistance of some prism of earth to sliding upwards along its base is brought into play. The...