114-117] TRANSMISSIBILITY OF FORCE. 113 



system is the same as that of an equal parallel force of like sense 

 applied to any other particle of the system which lies in the line 

 of action of the force. 



We may express this result by saying that forces applied to 

 particles of a rigid system may be regarded as vectors localised in 

 their lines of action instead of vectors localised at the positions 

 of the particles. 'This is the result referred to in Article 76. 



The result is known as the Principle of the Transmissibility of 

 Force. 



116. Inviolable conditions. A rigid system is an example 

 of a system which moves in such a way that certain geometrical 

 relations are maintained, and the internal forces between the 

 particles of the system are so adjusted from instant to instant 

 that the conditions are never violated. 



The notion thus introduced may be extended to cases where 

 the system is not rigid, or where external forces are adjusted so 

 that certain geometrical conditions are never violated. In such 

 cases generally some external forces are given, and others are in 

 our power, and the latter can be adjusted as stated. 



117. Reaction of bodies in contact. The Postulate 5 

 of Article 87 frequently involves a geometrical relation which is 

 to be maintained. 



This happens when two bodies are in contact. So long as 

 they are not separated their surfaces touch, they never intersect. 



The maintenance of this condition requires a particular appli- 

 cation of force to both. 



When the surfaces touch at isolated points, or at a point, the 

 forces required to maintain the condition may be regarded as 

 applied to the particles which are at the points of contact in the 

 directions of the common normals. 



Let A and B be the bodies, P a point of contact. Then the 

 forces applied to P, considered as a particle of A, are of two sorts, 

 forces exerted by the other particles of A, and forces exerted by 

 the particles of B, the latter are regarded as having a finite result- 

 ant, known as the reaction of B upon A at the point P. In like 

 manner the reaction of A upon B at the point P is made up of 

 L. 8 



