ON PRESSURE AND EQUILIBUIUM. 7r 



The same principles are applicable to the ecpiilibrium of the wedge. A 

 we<ige is a solid which has . tla-ee plane faces inclined to each other, and 

 two triangular ends ; and we suppose the faces perfectly polislied, so as to 

 be free from friction, and that no force can act on them otherwise than in a 

 perpendicular direction. Now in order that three forces, acting on the faces 

 or sides of a wedge, may hold each other in equilibrium, each of them must 

 be in proportion to the length of the side on which it acts : they must also be 

 applied at such parts that their directions may meet in one point ; for other- 

 wise they will not be completely opposed to each other, and a rotatory mo- 

 tion will be produced. (Plate IV. Tig. 64.) 



If each face of the wedge were conceived to be capable of receiving a pres- 

 sure, not only in a perpendicular direction, but in any other direction at plea- 

 sure, as some authors have supposed, the instrument wowld lose its essential 

 character as a wedge ; but in such cases, the proportion of the forces required 

 for the state of ecjuilibrium, may always be determined by drawing a triangle 

 with its sides parallel to their directions. 



It happens, however, not uncommonly, that the force actually operating 

 on the wedge is derived from another foice, acting in a direction more qr less 

 ohli(]ue, as when a heavy body rests on one of the faces of tlie wedge which is 

 inclined to the horizon, the body being retained in its situation, by an obstacle or 

 a thread which confines it to a vertical line, and the sliding away of tlie wedge 

 being prevented by a horizontal force. A wedge so situated, and supposed to 

 be capable of sliding without friction on a horizontal surface, is sometimes 

 called a moveable inclined plane, and it will support the weight resting on it, 

 if the horizontal force be to the weight, as the height of the plane is to its 

 horizontal length. If the thread, or the obstacle helping to support the weight, 

 be placed in any other direction, tlie magnitude of the forces must be determined 

 from the general law of the composition of three pressures. (Plate I V.Fig 65.) 



If a prop or bar, leaning against a smooth vertical surface or wall, be em- 

 ployed to support or to raise a weight, by means of a force which draws its 

 base along a smooth horizontal surface, the horizontal force must be to the 

 weight as the distance of the bottom of the prop from the wall to its perpcn- 



