Centre of Gravity 113 



that the scale, when standing on end, is in a very 

 unstable position. We will next consider the reason 

 for these differences in behaviour of the scale. Fig. 33 

 shows such a long wooden lath as the scale already used 

 resting on the ground on 



(a) a flat face; 



(6) a narrow long face ; 



(c) an end. 



The approximate position of the centre of gravity 

 of the lath is shown by a black dot. In each position 

 of the lath, the centre of gravity, when the lath is at 

 rest, is vertically over some point on the ground covered 

 by the part of the lath in contact with the ground. 

 It will be noticed, however, that the height of the centre 

 above the ground is least when the lath is on one of 

 its flat sides, and greatest when the lath is standing 

 on end. Further, it is clear that the base of support 

 of the lath is of greatest area when it is in position (a), 

 and least in position (c). This leads to the idea that the 

 stability or otherwise of a body is directly connected 

 with the height of its centre of gravity above its base of 

 support, and also with the area of the base of support. 

 Suppose the lath standing on end to be displaced from 

 this position. A very small displacement in any 

 direction will cause the perpendicular from the centre 

 of gravity to the ground that is to say, the line of 

 action of the weight of the lath to fall on some part 

 of the ground not included within the area of the 

 portion of ground upon which the lath was supported 

 when at rest. The lath, if unsupported in any way, 

 will now fall, and come to rest with its centre of gravity 

 nearer to the ground in one of the positions (a) or (6). 

 This is due to the moment of the weight of the lath 

 about the point or points at which it touches the 



H. D. S. 8 



