222 



CENTRE OF GRAVITY. 



Fig. 1. 





must necessarily characterize it. Let A B, fig. 1, be a solid body placed near 

 the surface of the earth. Its particles are all solicited downward, in the di- 

 rections represented by the arrows. Now, if there be any single force equiva- 

 lent to these combined effects, two properties may be at once assigned to it : 

 1, it must be presented downward, in the common direction of those forces to 

 which it is mechanically equivalent ; and, 2, it must be equal in intensity to 

 their sum, or, what is the same, to the force with which the whole mass would 

 descend. We shall then suppose it to have this intensity, and to have the di- 

 rection of the arrow D E. Now, if the single force, in the direction D E, be 

 equivalent to all the separate attractions which affect the particles, we may 

 suppose all these attractions removed, and the body A B influenced only by a 

 single attraction, acting in the direction D E. This being admitted, it follows 

 that if the body be placed on a prop, immediately under the direction of the 

 line D E, or be suspended from a fixed point immediately above its direction, 

 it will remain motionless. For the whole attracting force in the direction D E 

 will, in the one case, press the body on the prop, and, in the other case, will 

 give tension to the cord, rod, or whatever other means of suspension be used. 



But suppose the body were suspended from some point P. not in the direc- 

 tion of the line D E. Let P C be the direction of the thread by which the 

 body is suspended. Its whole weight, according to the supposition which we 

 have adopted, must then act in the direction C E. Taking C F to represent 

 the weight, it may be considered as mechanically equivalent to two forces (74), 

 G I and C H. Of these, C H, acting directly from the point P, merely pro- 

 duces pressure upon it, and gives tension to the cord P C ; but C I, acting at 

 right angles to C P, produces motion round P as a centre, and in the direction 

 C I, toward a vertical line P G, drawn through the point P. If the body A B 

 had been on the other side of the line P G, it would have moved, in like man- 

 ner, toward it, and therefore in the direction contrary to its present motion. 



Hence we must infer, that, when the body is suspended from a fixed point, 

 it. cannot remain at rest, if that fixed point be not placed in the direction of the 

 line D E ; and, on the other hand, that if the fixed point be in the direction of 

 that line, it cannot move. A practical test is thus suggested, by which the 



