

1 ",7 



volume of the slice between the planes whose a 

 A* respectively is ultima 



i w sin a f 1 



MOT we obtain for the volume of one of the hells ulti- 



; sin ti> by 



[(' !{- }<.**]' 



- ultimately 



mu w M*n a Aos 



The centre of gravity of each shell is on the axis of * At a 

 tne vert 



dUtanoc from tne vertex of the cone, which is OJIKI! in three 

 fourths of the abscissa . base of the 



cone is situated (see Ex. (5) of Art. 109). v the 



absciMa of the centre of gr :.- proposed solid ; ti. 



k and A- U- 1)10 abscissa: of the plane bases of the two cones, 



sin a sin a _^ 



':>-! 



"(/ 8 





shall conclude this Chapter with a few general pro- 

 po*i: :ig properties ol the centre of gravi: 



mate of each of a system of particles be m*/- 

 '<> the square of its distance from point, ths 



SUM of the products is least when the given point is the centre 

 >y of the system. 



centre of gravity of the system be made the 



& 7, be the coordinates of the given point; 



te co-ordinates of the first par : , y,, s^ 



tiie second ; and so on j m,, m. masses ot the 



particles; p t , p |f ... the distances of the particles from their 



