The centre of mass, G, of a system of particles (masses mr at Pr ) can be defined by the relation, O being an arbitrary point,

This is equivalent to finding the point Q1 which divides P1P2 in the ratio m2 : m1 ; then the point Q 2 which divides Q 1 P 3 in the ratio m3 : (m1 + m2 ) ; then the point Q 3 which divides Q 2 P 4 in the ratio m 4 : (m1 + m2 + m3 ), and so on until finally G is reached.