GENERAL PRINCIPLES 



29 



To produce a state of equilibrium, a body placed on a surface 

 must have its axis of gravity passing through the point on which 

 it rests, A, or within the base on which it rests, S (fig. 51). 



That base is called the base of support. If a body is inclined, 

 and still remains, in contact with its base of support, its centre of 



gravity will be displaced. 

 ,.... It can either be raised or 

 ': lowered, and it is easy to 



:' \ | G,\ r\ Q' I see (% 52) that the equili- 

 '/ brium is most stable when 

 the centre of gravity is as 

 low as possible and unstable 

 (G x ) when the centre is as 

 high as possible. But a 

 f sphere which rolls on a 



horizontal surface possesses 

 a centre of gravity always 



at the same distance from that surface, the equilibrium, in this 

 case being said to be indifferent. It is not enough that the axis 

 of gravity should fall within the 

 base of support for the equilibrium 

 to be the most stable ; the centre of 

 gravity must be at the minimum 

 distance from that base. But it is 

 clear that in all cases it is a necessary 

 condition of equilibrium that the 

 axis of gravity should fall within 

 the surface of support (fig. 53). 



Fi. 53. 



22. The stability of a material edifice depends both on the 

 size of its base of support and on the small height of its centre 

 of gravity. Subject to a lateral force which tends to overturn 

 it, it resists by virtue of its thickness in the direction of that 

 force, and its weight. Take a vertical wall of thickness E in the 

 direction of the horizontal force, H, tending to overturn it on its 

 edge, AA' (fig. 54). The moment, M, of that force in relation to 

 the point B, is the product : 



M = H X BC (see 16). 



Let the section BCDE (fig. 55) be examined as if it represented 

 the projection of the whole wall (the wall seen in profile). Then 



M- HxEI. 



Now the force H and the weight P of the wall have a resultant 

 in the direction of RK, and the reaction of the ground is equal 

 and opposite in the direction KR'. This reaction, applied to the 



