348 



STABLE 



: : if an I 



boun*. area is great t when the 



straight lines are all chords of a circle. See also 1>< 

 Calculii ;. 



. The following is a simple e >f dist li- 



the nature of equilibrium. 



'teavy body rests on a -fixed body, to dct< rm 



'lie surfaces Icing supposed rough. 



Let UAC be a vertical section of the upper body n 



by a plane through its centre of gravity (r, and ]>M 

 section of the lower body made by the same plane. We 

 suppose these sections both circular; let r be the radius of 

 the upper section and R that of the l-.v.vr. L<-t tlie a 

 body be displaced into the position B'A'C', and sup]. 

 that point in the upper body which was originally at A : 

 at A tlie new point of contact draw the common normal 

 OA'N, meeting at the radius AO of the lower surface 

 at N the radius aN of the upper surfacr. Draw a 

 line through A' meeting aN at M ; let // be the, new position 

 of the centre of gravity of the upper body. I :pose 



the surfaces rough enough to prevent all si id in ir, the u 

 body will tuni round A', and the equilibrium will be umtdltli- 

 :'alls further from a than M. and stable if y be between 

 JM and a. 



