MECHANICS. 



43 



(97.) In the inclined plane, therefore, 

 like every other mechanical power, \ve 

 lose velocity in proportion as \ve increase 

 the force. In some instances, however, 

 this is an advantage. For instance, in 

 an inclined plane constructed forlaunch- 

 ing a ship. Here the plane is slightly in- 

 clined, and the power which would sus- 

 tain the vessel on the plane (allowing 

 the effects of friction) is equal to the 

 force with which the vessel descends, 

 which, owing to the small elevation, is 

 comparatively trifling. 



CHAPTER X.On the Wedge. 



(98.) A WEDGE is a solid figure, which 

 is called in geometiy a triangular prism. 

 Its two ends are equal and similar tri- 

 angles, and its three sides are rectan- 

 gular parallelograms. This figure is 

 represented in figs. 78, 79. 

 The wedge is very generally used in 



Fig. 78. 



cleaving timber, in which case its edo:e 

 is introduced into a cleft already maide 

 to receive it, and it is urged at the 



Fig. 



back by percussion. The friction of 



the faces of the wedge xvith the timber 

 ought to be sufficient to prevent its 

 recoil. 



The wedge may be considered as formed 

 by two inclined planes placed base to 

 base, their altitudes forming the back of 

 the wedge. The power being generally 

 applied perpendicularly to the back will 

 be parallel to the common base. But it 

 is a more difficult matter to say in what 

 direction the resistance is to be consi- 

 dered as acting against the face of the 

 wedge. 



In the theory of the wedge, there are 

 introduced so many conditions, which 

 are perfectly inapplicable in practice, so 

 many gratuitous assumptions and sup- 

 positions so inconsistent with practical 

 truth, that the whole doctrine has little 

 or no value. 



One of the circumstances, which 

 creates the greatest difficulty in the 

 theory of the wedge, is the very hetero- 

 geneous nature of the resistance, and the 

 force or power by which it is overcome. 

 The resistance is generally that modifi- 

 cation of force called pressure. The 

 power, which is opposed to this resist- 

 ance, is commonly that species of action 

 called percussion. These are modifica- 

 tions of force so totally different as not 

 even to admit of comparison. It has 

 been generally thought that there is no 

 blow or impact, however slight, which 

 will not overcome a pressure or resist- 

 ance however great. From which it 

 would seem to follow, that an infinitely 

 small impact is equivalent to an infi- 

 nitely great pressure. Be this as it may, 

 however, the great difference between 

 these modifications of force, is suffi- 

 ciently evident to demonstrate the total 

 impossibility of establishing the condi- 

 tion of equilibrium of a machine in 

 which the weight or resistance is a force 

 of the one, and the power is a force of 

 the other species. 



Nothing, therefore, can more plainly 

 demonstrate the inutility of the theoiy 

 of the wedge than that, in this theory, 

 the power is supposed to be a pressure 

 exerted on the back of the wedge, which 

 is supposed to be capable of balancing 

 the effect of the resistance in producing 

 the recoil of the wedge. In all cases, 

 where the wedge is practically used, the 

 friction of its faces with the resisting 

 substance, is sufficient to prevent the re- 

 coil ; so that, strictly speaking, no force 

 whatever is necessary to sustain the 

 machine in equilibrium, and to move it, 

 pressure is never resorted to, inasmuch 



