TRB OP GRAVITY OF A I'YIUMlh. 1 ".> 



if we suppose 1 to be made up of an indefu 



thin triangular slice* par 



base, < 'iiesc slices has its centre of gravi* 



H :. th centre of gravity of the pyramid U 



Again, take A7/- i / it O. Then, 



tre of gravity of the pyrami ; >e in 



hence (/, the point of intersection of 

 these stra: Centre of gra\ 



parallel to DD. Also because 

 heiefore /-'//- \DB, and 



pg-ytfi bat FII-\I>n, therefore FG-\DG-DF. 



centre of gravity is one-fourth of the way up the 



>g toe centre of gravity of the base wit! 

 vertex. 



the same way as the corresponding results were demon- 

 r the triangle, we may establish the following: 



The centre of gravity of a pyramid coincides with the cen- 

 tre of gravity of particles of equal mass placed at the angular 



; yraiiml. 



Let f lt y,, r, be the co-ordinates of one angular _point; 



coordinates of another; and so on : . 1 be 



the co-ordinates of the centre of gravity of the pyramid: then 



05-J(-r 



(5) To find tke centre of gravity of any pyramid having a 



ide the base into tria:u'l. -; if any part of the base is 

 vr then suppose the c ;to an in- 



great number of in j short straight lines. 



vertex of the pyramid with the centres of gravity of 

 all \. and also with all tkcir angles. Draw a 



iic base at a distance from the base equal to 

 . -urth of the distance of the vertex from the base; then 



