INTRODUCTION TO MECHANICS. 



xix 



towards the side that is deficient ; and thus by changing the situation of 

 the centre of gravity, restores his equilibrium. 



A stick is poised on the tip of the finger, by supporting its centre of 

 gravity, and it is for want of this support that spherical bodies roll down 

 a slope. A sphere being perfectly round, can touch the slope but by a 

 single point, and that point is not perpendicularly under the centre of 

 gravity, which therefore is not supported. The centre of gravity in this 

 case coincides with the centre of magnitude, but when one part of the 

 body is composed of heavier materials than another part, the centre of 

 gravity, being the centre of the weight of the body, will generally no longer 

 correspond with the centre of magnitude, though it may accidentally do so. 

 We defined the centre of gravity to be that point about which all 

 the parts of a body balance each other : you must consider it as 

 an abstract point, since there are cases in which it may be situated 

 at some distance from the body. Such, for instance, is the centre 

 of gravity of a ring, which is situated in the centre of the space which the 

 ring encircles ; and that point cannot be supported unless the ring be 

 held so that the line of direction will fall within the base of the support, 

 which will be the case, either if you poise the ring on the tip of your 

 Fi: 15. finger, or if you suspend it by a string, as in Jig. 15. 



If a body be suspended by that point in which the 

 centre of gravity is situated, it will remain at rest in 

 any position indifferently ; but if it be suspended by 

 any other point, it can rest only in the two following 

 positions : Either when the centre of gravity is either 

 exactly above or below the point of suspension, so 

 that the point of suspension shall be in the line of 

 direction. 



Bodies having a narrow base are easily upset, for if they are the least 

 inclined, their centre is no longer supported, as you may perceive \r\fig. 16. 



\ 



Fig. 16. 



A person carries a single pail of water with great 

 difficulty, owing to the centre of gravity being 

 thrown on one side, and the opposite arm is 

 stretched out to endeavour to bring it back to its 

 original situation. But two pails, one hanging 

 on each arm, are carried with much greater facility, 

 because they balance each other. 

 When two bodies are fastened together by a line, string, chain, or any 

 power whatever, they are to be considered as forming but one body. If 

 the two bodies be of equal weight, the centre of gravity will be in the 

 middle of the line which unites them (Jig. 17), but if one be heavier 

 than the other, the centre of gravity will be proportionably nearer the 

 heavy body than the light one (fig. 18). Were you to carry a rod or 



Fig. 18. 



Fig. 19. 



c 2 



