ON PASSIVE STRENGTH AND FRICTION. 119 



the pressure, as the height of the inclined plane to its horizontal length, 

 when the inclination is barely such as to allow the continuance of any 

 motion which is imparted to the substance placed on the plane. 



It follows from the doctrine of the resolution of force, that when any 

 body is to be drawn along a horizontal surface, which produces a resistance 

 proportionate to the pressure, a part of the force may be advantageously 

 employed in diminishing the pressure produced by the weight of the body ; 

 hence, in order for the most advantageous application of the force, its di- 

 rection must be inclined to the horizon, and it may be demonstrated that 

 the inclination must be the same with that of a plane on which the relative 

 weight of the body is precisely equal to the friction. Thus, if we can de- 

 termine the inclination of a road which is barely sufficient for a carriage to 

 descend on it by its own weight, the same inclination will be the best pos- 

 sible for the application of any force by which the carriage is to be drawn 

 along a horizontal road of the same materials. 



It is obvious that an inclined plane on which a weight rests by means of 

 an adhesion proportionate to the pressure, can never be forced backwards 

 by any increase of that pressure, since the resistance increases in the same 

 proportion, and continues always sufficient to prevent the relative motion 

 of the weight and the inclined plane. Two such planes, put together, 

 would constitute a wedge, which would be equally incapable of giving 

 way to a pressure applied to its opposite surfaces, each of them possessing 

 similar properties with respect to friction. Thus, if the friction or adhe- 

 sion were exactly one eighth of the pressure, the height of the inclined 

 plane would be one eighth of its length, and the back of the wedge one 

 fourth. Such a wedge would therefore possess a perfect stability with 

 respect to any forces acting on its inclined surfaces. But the effects of 

 agitation, and the minute tremors produced by percussion, have a great 

 tendency to diminish the force of adhesion, by interrupting the intimacy of 

 contact : and where a pin, a nail, or a screw is required to retain its 

 situation with firmness, the inclination of the surfaces must be smaller 

 than the angle of such a wedge as is barely capable of affording a sufficient 

 resistance in theory. 



It appears, therefore, that the force of lateral adhesion, acting between 

 two bodies in contact, is of great importance in all mechanical arts ; the 

 firmness of architecture and of carpentry depends in great measure on it. 

 This kind of resistance being equally powerful, when the force is applied 

 in the direction of the surface, to whatever part of the surface it may tend, 

 it follows that any body which is subjected to friction on all sides, will 

 retain its situation with the same force that was used in overcoming the 

 friction in order to bring it into that situation, or rather with a greater 

 force, since the lateral adhesion is generally a little greater than the fric- 

 tion : so that a cylindrical wire cannot be withdrawn from a perforation in 

 a board, by any direct force less than that which'was employed in intro- 

 ducing it ; and this kind of stability, together with that of a wedge or nail 

 resisting a lateral pressure, constitutes the security of the lighter structures 

 of carpentry, while those of architecture receive a great part of their 



