114 SYSTEMS OF FORCES. [CHAP. VII. 



component forces between particles, viz. of the forces exerted by 

 the other particles of A upon the particle at P. 



The two resultant forces thus defined are equal and opposite, 

 since otherwise the particle at P (of infinitesimal mass) would 

 have infinite acceleration. 



We can imagine two cases: (1) where the reaction of A on B 

 is directed along the common normal at P, it is then the force 

 required to maintain the condition; (2) where the reaction of A 

 on B is not directed along the common normal, but nevertheless 

 the condition is maintained. 



In the first case the reaction is known as the pressure between 

 the bodies at P, and the surfaces are said to be smooth at P. 



In the second case the resolved part of the reaction along the 

 common normal is called the pressure between the bodies at P, 

 and the resolved part at right angles to the normal is called the 

 friction at P, and the surfaces are said to be rough at P. 



When the surfaces are in contact over a finite area we are 

 at liberty to assume reactions, such as those described in the case 

 of contact at points, to act upon the bodies at every point of the 

 area of contact, such reactions having finite resultants and finite 

 sums of moments about any axis. 



118. Constraints. More generally, when a system moves 

 so that one of its particles always lies on a prescribed geometrical 

 curve or surface, this condition can be maintained by a force 

 applied to the particle along the normal to the curve or surface, 

 and then the force is known as a constraint. We may say that 

 constraints are forces applied to the particles of a system moving 

 in a field of force, in directions at right angles to the paths of the 

 particles, and required for the maintenance of geometrical condi 

 tions. Constraints must arise from the actions of particles, but 

 the particles producing them are not necessarily particles of a 

 body on whose surface the constrained particle moves. 



119. Friction. We have already defined the friction between 

 two rough bodies at a point of contact to be the resolved part 

 of the reaction at right angles to the common normal. 



As before, let A and B be the bodies, P a point of contact, R 

 the pressure, and F the friction at P. 



