226 CENTRE OF GRAVITY. 



edge placed under A E. Since, then, the centre of gravity of the plate is 

 under the line B D, and also under A E, it must be under the point G, at 

 which these lines cross each other ; and it is accordingly at a depth beneath G, 

 equal to half the thickness of the plate. 



This may be experimentally verified by taking a piece of tin or card, and 

 cutting it into a triangular form. The point G being found by drawing B D 

 and A E, which divide two sides equally, it will be balanced if placed upon 

 the point of a pin at G. 



The centre of gravity of a triangle being thus determined, we shall be able 

 to find the position of the centre of gravity of any plate of uniform thickness 

 and density which is bounded by straight edges. 



The centre of gravity is not always included within the volume of the body, 

 that is, it is not enclosed by its surfaces. Numerous examples of this can be 

 produced. If a piece of wire be bent into any form, the centre of gravity will 

 rarely be in the wire. Suppose it be brought to the form of a ring. In that 

 case, the centre of gravity of the wire will be the centre of the circle, a point 

 not forming any part of the wire itself: nevertheless this point may be proved 

 to have the characteristic property of the centre of gravity ; for if the ring be 

 suspended by any point, the centre of the ring must always settle itself under 

 the point of suspension. If this centre could be supposed to be connected 

 with the ring by very fine threads, whose weight would be insignificant, and 

 which might be united by a knot or otherwise at the centre, the ring would be 

 balanced upon a point placed under the knot. 



In like manner, if the wire be formed into an ellipse, or any other curve 

 similarly arranged round a centre point, that point will be its centre of gravity. 



To find the centre of gravity experimentally, the method explained in fig. 1 

 may be used. In this case two points of suspension will be sufficient to de- 

 termine it ; for the directions of the suspending cord, being continued through 

 the body, will cross each other at the centre of gravity. These directions may 

 also be found by placing the body on a sharp point, and adjusting it so as to be 

 balanced upon it. In this case, a line drawn through the body directly upward 

 from the point will pass through the centre of gravity, and therefore two such 

 lines must cross at that point. 



If the body have two fiat parallel surfaces, like sheet metal, stiff paper, card, 

 board, &c., the centre of gravity may be found by balancing the body in two 

 positions on a horizontal straight edge. The point where the lines marked by 

 the edge cross each other will be immediately under the centre of gravity. 

 This may be verified by showing that the body will be balanced on a point 

 thus placed, or that, if it be suspended, the point thus determined will always 

 come under the point of suspension. 



The position of the centre of gravity of such bodies may also be found by 

 placing the body on a horizontal table having a straight edge. The body being 

 moved beyond the edge until it is in that position in which the slightest distur- 

 bance will cause it to fall, the centre of gravity will then be immediately over 

 the edge. This being done in two positions, the centre of gravity will be de- 

 termined as before. 



It has been already stated that when the body is perfectly free, the centre 

 of gravity must necessarily move downward, in a direction perpendicular to a 

 horizontal plane. When the body is not free, the circumstances which re- 

 strain it generally permit the centre of gravity to move in certain directions, 

 but obstruct its motion in others. Thus, if a body be suspended from a fixed 

 point by a flexible cord, the centre of gravity is free to move in every direc- 

 tion except those which would carry it farther from the point of suspension 

 than the length of the cord. Hence if we conceive a globe or sphere to sur- 



