SO QUILIIU:!fM Of \ < "NMKAINr.I. BODY, 



\-o points be in contact, then the relations 

 -L, 



K = 



ami the equations of condition arc 



SA--0, Sr-0, tZ-- --O, and tf-0. 



throe points arc in contact, then the pressures arc 

 :nined irom the equations 



and the conditions of equilibrium are 



If more than three points are in contact, then the~] 

 are indeterminate, since they are connected by only three 

 equations; but the conditions of equilibrium arc still 



o N=O. 



91. The equations at the commencement of the preceding 



Article shew that if a body rests in equilibrium against a 



. liich press it against the plane must reduce 



to a single force acting in a direction perpendicular to the 



] ilano, for the condition 



isfied, since 2-XT, 2F, and ^"vanish. Hence the forces 

 reduce to a single force; and since 2X and Sl r vanish, this 

 force must be perpendicular to the fixed plane. 



, this single force must counterbalance the forces 

 - /,' '. - // ..., which are all parallel and all act in the same 

 direction. Hence, from considering the construction given 

 in Art. 66 for determining the centre of a system <>f 

 parallel forces, it follows that the point where this resultant 

 cuts the plane must be within a polygon, formed by so joining 

 the points of contact as to incluae them all and to have 

 no re-entering angle. 



