Principle of Virtual Velocities* 131 



224. The three straight lines AB, EC, AC, are to each other 

 as the faces of the wedge to which they respectively belong, for 

 these faces are parallelograms of the same base, and whose al- 

 titudes are JiB, BC, AC; it follows, therefore, that the power pGeom. 

 and its two components, are to each other as the back and two 175t 

 sides of the wedge, or in other words, that the power being repre- 

 sented by the back of the wedge, the force exerted against the two sides 



will be represented by these sides respectively. A very acute wedge, 

 therefore, or one whose sides are very long compared with the 

 back, possesses an advantage in the same proportion, and may 

 be made to exert a great power by means of a very moderate 

 blow on the back. 



225. There has not been a perfect agreement among mechan- 

 ical writers as to the theory of the wedge. The direction of the 

 resistance has sometimes not been sufficiently attended to, and 

 the circumstance of one of the resistances proceeding from an 

 immoveable obstacle in certain cases, has sometimes been over- 

 looked. 



226. To the wedge are referred all cutting instruments, as 

 knives, scissors, the teeth of animals, &c. A saw is a series of 

 wedges on which the motion impressed is oblique to the resist- 

 ance. A wimble is a combination of the screw and the wedge. 



To the wedge of the pyramidal form, are reduced all piercing 

 instruments, as nails, bayonets, stakes, piles, &c. 



General Law of Equilibrium in Machines. 



227. By combining together, in different ways, the machines 

 above considered, we can form others, the number of which may 

 be multiplied without end. With respect to compound machines, 

 we determine the ratio of the power to the resistance necessary 

 to an equilibrium, by having regard to the tensions of the cords 

 that connect the different parts, this ratio being supposed to be 

 known for each of the component parts. 



But however complicated the machine, there is a simple rule 

 by which the ratio of the power to the resistance is obtained 



