183.] FRICTION. 



Now if p be the horizontal distance of the point 5 from aft, 

 the bending moment at a/3 is R 1 -/ = o 3 -p. If a/3 intersect A'B' 

 in P, II III in Q, the triangles SPQ and #03 are similar, so 

 that their altitudes p and H are as the homologous sides PQ 

 and o 3 ; hence 



and the value of the bending moment is H PQ. As H is 

 constant, we find that the bending moment is proportional to the 

 vertical height, or ordinate, of the funicular polygon. 



5* FRICTION. 



182. The reaction between two surfaces in contact has so far 

 been regarded as directed along the common normal of the 

 surfaces. This is true when the surfaces are perfectly smooth. 



The surfaces of physical bodies are rough, i.e. they present 

 small elevations and depressions ; when two such surfaces are 

 "in contact" the projections of one will more or less enter into 

 depressions of the other ; the greater the normal pressure 

 between the surfaces, the more will this be the case. Hence 

 when a tangential force acting on one of the bodies tends to 

 slide its surface over that of the other body, a resistance will be 

 developed whose magnitude must depend on the roughness of 

 the surfaces and on the normal pressure between them. This 

 resistance is called the force of friction. 



The study of friction belongs properly to applied mechanics, 

 and will here only be touched upon very briefly. 



183. Imagine a body resting with a plane surface on a hori- 

 zontal plane. Let a small horizontal force P be applied at its 

 centroid (which is supposed to be situated so low that the body 

 is not overturned), and let the force P be gradually increased 

 until motion ensues. The value of P when motion just begins 

 is equal and opposite to the frictional resistance F between the 



