DETERMINATION OF CENTRES OF GRAVITY 33 



experimented with is hung from a smooth nail, by means of a hole 

 bored in the body, the vertical line must be drawn with the help of 

 a plumb-line. The point of support is then shifted and the operation 

 repeated. Since the centre of gravity of the plate is in both straight 

 lines it must be located at their intersection. 



Plates of all shapes balance about their centres of gravity. 

 After the centre of gravity of a sheet of metal, or other stiff material, 

 has been determined by hanging it from a support in the manner 

 described in Experiment 14 i. (a) and (b), it will be found that if this 

 sheet be so arranged that a pointed upright is immediately under the 

 centre of gravity, the plate will be supported in a horizontal position. 

 This affords a convenient means of checking the correctness of the 

 experiment performed. 



Geometrical determination of centres of gravity. It has been 

 sufficiently explained that the centres of gravity of straight lines, 



ABC 



FIG. 25. Geometrical illustration of centre of gravity of a triangular plate. 



circles, squares, and other regular figures is at their geometrical 

 centres. Hence, the geometrical constructions for determining these 

 central points also locate the positions of their centres of gravity. 



The centre of gravity of a parallelogram is at the intersection of its 

 diagonals. 



The centre of gravity of a triangle is determined by bisecting any 

 two sides and joining the middle points so obtained to the opposite 

 angles. The intersection of the lines so drawn gives the centre of 

 gravity. The centre of gravity is found, by measuring, to be one- 

 third the whole length of the line drawn from the middle point of the 

 side to the opposite angle, away from the side bisected. 



In fact, a triangular plate may be considered as made up of a number 

 of narrow strips of material which decrease in length from the base 

 to the apex. The centre of gravity of each strip is the middle of the 

 strip ; hence the line drawn from the apex to the middle of the base 

 passes through each centre of gravity (Fig. 25, .4). By taking another 

 side as base, a similar line can be drawn from the middle to the opposite 

 angle (Fig. 25, B). These lines intersect at one-third the distance up 

 the line so drawn, measured from the base, and the point of intersection 

 is the centre of gravity of the triangular plate (Fig. 25, C). 

 J.G.S. c 



