CENTRE OF GRAVITY. 



225 



A straight wand, of uniform thickness, has its centre of gravity at the centre 

 of itiklength ; and a cylindrical body has its centre of gravity in its centre, at the 

 middle of its length or axis. Such is the point C, fig. 6. 



Fig. 6. 



Fig. 7. 



A flat plate of any uniform substance, and which has in every part an equal 

 thickness, has its centre of gravity at the middle of its thickness, and under a 

 point of its surface, which is to be determined by its shape. If it be circular 

 or elliptical, this point is its centre. If it have any regular form, bounded by 

 straight edges, it is that point which is equally distant from its several angles, 

 as C in fig. 7. 



There are some cases in which, although the place of the centre of gravity 

 is not so obvious as in the examples just given, still it may be discovered with- 

 out any mathematical process, which is not easily understood. Suppose ABC, 

 fig. 8, to be a flat triangular plate of uniform thickness and density. Let it be 



Fig. 8. 



imagined to be divided into narrow bars, by lines parallel to the side A C, as 

 represented in the figure. Draw B D from the angle B to the middle point D 

 of the side A C It is not difficult to perceive that B D will divide equally all 

 the bars into which the triangle is conceived to be divided. Now, if the flat 

 triangular plate A B C be placed in a horizontal position on a straight edge 

 coinciding with the line B D, it will be balanced ; for the bars parallel to A C 

 will be severally balanced by the edge immediately under their middle point, 

 since that middle point is the centre of gravity of each bar. Since, then, the 

 triangle is balanced on the edge, the centre of gravity must be somewhere im- 

 mediately over it, and must therefore be within the plate, at some point under 

 the line B D. 



The same reasoning will prove that the centre of gravity of the plate is un- 

 der the line A E, drawn from the angle A to the middle point E of the side 

 B C. To perceive this, it is only necessary to consider the triangle divided 

 into bars parallel to B C, and thence to show that it will be balanced on an 



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