106 



. It was shewn : that there is a point in . 



body such that, if tin- partiel.-s of tin M 1,\ 



'el forces and this point be fixed, the body will rest in 

 whatever position it be placed. 



fa body may be considered as the resultant 



,< different elementary portions of the 



.llel and lines, "in thi< case the point 



above de MIC of parallel forces is called the 



centre of grar b body. \\ '< may d< tin- :re of 



j system of heavy partiele. as a point 



if it be supported and the par;' idly connected with it, 



the ill rest in any position. 



In the present Chapter we shall determi; >n of 



the centre of gravity in bodies of various forms. We shall 

 first give a few elementary examples. 



(1) Gi nitres of grar it)/ ' ////// <r><, 

 a body, to find the centre ofgra< 



I. t G l denote the centre of gravity of one par / the 



centre of f the other part; let m l denote the mass of 



the first part and m t the mass of the second part. Join f.i\ f>\ 



and divide it in G so that 777^= /2 , then G is the o 



', m v 



of gravity of the whole body (Art. 37). 



(2) G' 'fy of a lody and also ' 



'tj ,,f 

 the remainder. 



Let G denote the centre of gravity- of the bod; , the 



centre of gravity of a pai t of the 1> ;nte the 



of the body, and m l the mass of the part. Join G^G and pro- 



y~f y^f 



duce it through G to G t> so that -*', ~ L ~ > ^ cn ^t ^ s lm ' 



c of gravity of the remainder. 



(3) To find the centre of gravity of >re of 



ness and density. 



