GENERAL PRINCIPLES 



27 



The centre of gravity of homogeneous bodies is the centre of 

 their shape ; that of a surface (parallelogram, rectangle) is the 

 point where the diagonals intersect ; that of triangles (fig. 45 

 above) is at the intersection of their diagonals ; that of a circle 

 is its centre, and, in general, if any surface can be cut into 

 traingles, the centre of gravity of the surface will be the result- 

 ant of those of all the triangles. 



Solids, having the preceding surfaces for sections, have similar 

 axes of gravity, on which at equal distances, from the two faces, 

 the centres of gravity lie. 



If an iron triangle weighing 60 kilogrammes, 

 is held by three workmen at the corners, each 

 would support 20 kilogrammes. 



The position of the centre of gravity can be 

 found on the plan, or on the axis of symmetry 

 of a body, when there is one, as is the case 

 when two equi-distant points of the body are 

 are found in the perpendicular to that plan or 

 axis (figs. 46 and 47) . But tne centre of gravity 

 can be found on a plane called the diametrical 

 plane whenever this plane divides all the 

 surfaces which cross it into two equal parts. 

 Thus in a prism the plane which bisects the 

 sides is the diametrical plane (fig. 48) . 



It is shewn in treatises on geometry or statics 

 that: 



1. The centre of gravity of a prism is in the middle of the 

 straight line which joins the centres of gravity of its two bases 

 B and B 1 , and this rule applies also to a cylinder. 



2. The centre of gravity of a pyramid is at a quarter of the 

 distance from the base on the straight line which joins the apex 

 to the centre of gravity of the base, and the same applies to a 

 cone. 



All that has just been said concerns homogeneous bodies. The 

 experimental determination of the centre of gravity of any body 

 can be made in the following way : 



1. The body is suspended by two of its points successively. 

 The two directions of the suspension intersect at the centre of 

 gravity. 



2. The body is placed on a knife edge, so that it balances, that 

 is to say, it is in equilibrium. 



F 48 



