54 LECTURE VII. 



it were simply applied in the direction of the motion, as the length of any 

 part of the rope uncoiled is greater than the perpendicular distance of its 

 extremity from the axis. So that when the rope becomes very oblique, a 

 great force is required, in order to counteract a much smaller one- acting 

 perpendicularly. This remark may be in some measure illustrated by 

 considering the method used by joiners and stone cutters for keeping a saw 

 straight : two ropes or braces are twisted together by means of a pin or 

 lever passing between them, and serve each other in place of an axis, round 

 which they are coiled obliquely, so that they act with great force, when 

 they are sufficiently tight and not too much twisted. (Plate IV. Fig. 62.) 



It appears from the laws which have already been laid down, respecting 

 the motions of bodies on inclined surfaces, that a weight acting vertically 

 will hold in equilibrium another weight resting on an inclined plane, with- 

 out friction, when the first is to the second as the height of the plane to its 

 oblique length. The pressure on the plane is in this case to the weight 

 resting on it, as the horizontal length of the plane is to its oblique length. 

 This pressure may be measured experimentally, by substituting for the 

 resistance of the plane that of a thread perpendicular to it. (Plate IV. 

 Fig. 63.) 



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

 wedge is a solid which has three plane faces inclined to each other, and 

 two triangular ends ; and we suppose the faces perfectly polished, 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 otherwise they will not be completely opposed to each other, and a 

 rotatory motion will be produced. (Plate IV. Fig. 64.) 



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

 pressure, not only in a perpendicular direction, but in any other direction 

 at pleasure, as some authors have supposed, the instrument would lose its 

 essential character as a wedge ; but in such cases the proportion of the 

 forces required for the state of equilibrium 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 force acting in a direction more or 

 less oblique, as when a heavy body rests on one of the faces of the 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 the wedge being prevented by a horizontal force. A wedge so 

 situated, and supposed to be capable of sliding without friction on a hori- 

 zontal 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, the 



* See Whewell's Mechanics. 



