AHK  , that of the second by twice the

area BKL, and so on . The quadratic moment of the whole system is there-fore represented by twice the area AHEDCBA . Since a quadratic moment is essentially positive, the various areas are to taken positive in all cases . If k be the radius of gyration about p we find k2 =2 X area AHEDCBA X ON 4- aP, where a¢ is the line in the force-diagram which represents the sum of the masses, and ON is the distance of the pole 0 from this line . If some of the particles lie on one side of p and some on the other, the quadratic moment of each set may be found, and the results added . This is illustrated in fig . 6o, where the total quadratic '~miIIIII~~~ii~~~II~IIII~IIIIpII~I P moment is represented by the sum of the shaded areas . It is seen that for a given direction of p this moment is least when p passes through the intersection X of the first and last sides of the funicular; i.e. when p goes through the mass-centre of the given system; cf. equation (15) .