CENTRE OF GRAVITY. 



223 



line D E maybe at once discovered. Let a thread be attached to any point of 

 the body, and let it be suspended by this thread from a hook or other fixed 

 point. The direction of the thread, when the body becomes quiescent, will be 

 that of a single force equivalent to the gravitation of all the component parts of 

 the mass. 



An inquiry is here suggested : Does the direction of the equivalent force, 

 thus determined, depend on the position of the body with respect to the surface 

 of the earth, and how is the direction of the equivalent force affected by a 

 change in that position 1 This question may be at once solved if the body be 

 suspended by different points, and the directions which the suspending thread 

 takes in each case relatively to the figure and dimensions of the body exam- 

 ined. 



The body being suspended in this manner from any point, let a small hole 

 be bored through it, in the exact direction of the thread, so that if the thread 

 were continued below the point where it is attached to the body, it would pass 

 through this hole. The body being successively suspended by several differ- 

 ent points on its surface, let as many small holes be bored through it in the 

 same manner. If the body be then cut through, so as to discover the direc- 

 tions which the several holes have taken, they will be all found to cross each 

 other at one point within the body ; or the same fact may be discovered thus : 

 a thin wire, which nearly fills the holes, being passed through any one of 

 them, it will be found to intercept the passage of a similar wire through any 

 other. 



This singular fact teaches us — what, indeed, can be proved by mathematical 

 reasoning without experiment — that there is one point in every body through 

 which the single force, which is equivalent to the gravitation of all its parti- 

 cles, must pass in whatever position the body be placed. This point is called 

 the centre of gravity . 



In whatever situation a body may be placed, the centre of gravity will have 

 a tendency to descend in the direction of a line perpendicular to the horizon, 

 and which is called the line of direction of the weight. If the body be alto- 

 gether free and unrestricted by any resistance or impediment, the centre of 

 gravity will actually descend in this direction, and all the other points of the 

 body will move with the same velocity in parallel directions, so that, during 

 its fall, the position of the parts of the body with respect to the ground will be 

 unaltered. But if the body, as is most usual, be subject to some resistance 

 or restraint, it will either remain unmoved, its weight being expended in 

 exciting pressure on the restraining points or surfaces, or it will move in 

 a direction and with a velocity depending on the circumstances which re- 

 strain it. 



In order to determine these effects — to predict the pressure produced by 

 the weight if the body be quiescent, or the mixed effects of motion and pres- 

 sure if it be not so — it is necessary in all cases to be able to assign the place 

 of the centre of gravity. When the magnitude and figure of the body, and the 

 density of the matter which occupies its dimensions, are known, the place of 

 the centre of gravity can be determined with the greatest precision by mathe- 

 matical calculation. The process by which this is accomplished, however, is 

 not of a sufficiently elementary nature to be properly introduced into this trea- 

 tise. To render it intelligible would require the aid of some of the most ad- 

 vanced analytical principles ; and even to express the position of the point in 

 question, except in very particular instances, would be impossible, without the 

 aid of peculiar symbols. 



There are certain particular forms of body in which, when they are uni- 

 formly dense, the place of the centre of gravity can be easily assigned, and 



