TRANSMISSIBILITY OF FORCE 95 



The body is now held at rest by the two forces P A , P , and is 

 therefore in equilibrium under the forces P A) P , W A , W B . Tak- 

 ing moments about a line through A perpendicular to AB y we find 

 that the moments of P A , W A , W B vanish, so that in order that the 

 sum of the moments of the four forces taken about this line may 

 vanish, we must have the moment of P B equal to zero, and there- 

 fore P B itself equal to zero. Thus the only force required to keep 

 the body at rest is the force P A at A. 



A condition for equilibrium is now that the sum of the com- 

 ponents of W A , W B) and P A shall vanish in any direction. The 

 components of W A and W B are, however, equal and opposite, so 

 that the component of P A must vanish in every direction. That 

 is to say, we must have P A = 0. 



It has now been proved that the rigid body is in equilibrium 

 under the action of the two forces W A , W B . 



70. This establishes at once a principle known as the transmissi- 

 lility of force. 



The effect of a force acting on a rigid ~body depends on its mag- 

 nitude and on the line along which it acts, but not on the particular 

 particle in this line to which it is applied. 



For, let the same force be applied at any 

 two points Q, R of its line of action. An 



equal and opposite force at R can neutralize either of the two 

 forces, which are therefore equivalent. 



COMPOSITION OF FORCES ACTING IN A PLANE 



71. Suppose that we have two forces P, Q acting at two points 

 A, B of a rigid body, it being supposed that the two lines of action 

 of these forces lie in one plane. Then the two lines of action, 

 produced if necessary beyond the points A, B, will meet in some 

 point C. 



By the principle of the transmissibility of force it is imma- 

 terial whether the force P acts at A or at (7; let us suppose it to 

 act at C. In the same way let us suppose the force Q to act at C 



