. The Civil engineer and architect's journal, scientific and railway gazette. Architecture; Civil engineering; Science. Suppose the mass ABDC, tig. 1, to be acted upon liy ajiy number of force among which is the force Q being the resultant of certain resistances, suj)- plied by different points in a surface BU, connuou to the intersected mass aiul to an immoveable obstacle BE. Now it is clear that under these circumstances we may vai'y the force P, Ijoth as to its amount, direction, and point of apiiHeatiou, without disturbing the equilibrium, provided only the form and direction of the line o
. The Civil engineer and architect's journal, scientific and railway gazette. Architecture; Civil engineering; Science. Suppose the mass ABDC, tig. 1, to be acted upon liy ajiy number of force among which is the force Q being the resultant of certain resistances, suj)- plied by different points in a surface BU, connuou to the intersected mass aiul to an immoveable obstacle BE. Now it is clear that under these circumstances we may vai'y the force P, Ijoth as to its amount, direction, and point of apiiHeatiou, without disturbing the equilibrium, provided only the form and direction of the line of resistance continue to satisfy the conditions imjiosed by the equilibrium of the system. These have been sliown to be tlie following,—tliat it no where cut the surface of the mass, except at P, anrl within the sjiace BD, and that it no where cut any section MN of the mass, or the common surface BD of the mass and obstacle, at an angle with the perpendicular to that surface, greater than the limiting angle of resistance. Thus, varying the force P, we may destroy the equiUbriuni, either, first, by causing the line of resistance to take a direction without the limits prescribed by the resistance of any section MN through which it passes, that is, witliout the cone of resistance at the jjoiut w here it intersects that sm-face; or, secondly, by causing the point Q to fall irithoiit the surface BD, in which case no resintatice can be o\)posed to the resultant force acting in that point; or, thirdly, the point Q lying within the surface BD, we may destroy the equilibrium by causing the line of resistance to cut the surface of the mass somewhere between that point and P. Let us suppose the linnts of tlie variation of P within which the first two conditions are satisfied, to be known ; and varying it, within tlujse limits, let us consider what may be its least and greatest values so as to satisfy the third condition. Let P act at a given point in AC and in a given direction. It is e
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