48 ES 



1117, = )'. . ami ii similar notation 

 tor the other forces, the above njuati>:is may In 1 



an I # = (}> -Ay). 



To fnd the conditions for the equilibrium of a *>/ 

 of forces acting on a rigid body in one plane. 



system of forces acting in one plane may be red 

 to a single force 7?, and a couple whose i '/ If 



neither It nor G vanish equilibrium i> imp-; 



6 force cannot balance a couple. It // ah-ne v.-inNi equi- 

 librium is impossible, because there remains an unlal, 

 couple (!\ it' G alone vanish equilibrium is impossible, 

 cause there remains an unbalanced force. Eence, l'>r -qui- 

 librium we must have .72 = and G = 0. Also 11 = U requires 

 that IA'=Oand 



ee G is equal to the sum of the moments of the forces 

 with respect to 0, we may enunciate the result thus: A sys- 

 tem of forces acting in one plane on a rigid l<></// ?//// 



in if the sums of tlie resolved parts of the forces pa- 

 fo two rectangular ayes in the plan r */////*//. ami M 

 moments round an origin in the plane also vanishes. 



Conversely, if the forces are in equilibrium the sum -i' 



the resolved parts of the forces parallel to any i will 



;i. and also the sum of the moments of the round 

 any origin. 



58. If tlrre forces acting in on< 



1 "<I>I in "i>ti'ii.i'inm tht ir diru-tiuns ( itlu r ail m'.t at a point or 

 are all parallel. 



For suppose two of the 1 - to meet at a ]vint. and 



take this point for the origin; then the moment of each of 

 these two forces vani- I iati<>n (,' = o ivquire- 



that the moment of the third force should vanish, that is. the 

 third force must also pass throuirh the criirin. I 

 two of the forces meet, the third must pass through their point 

 uf intersection, which proves the proposition. This pro- 



