320 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28

in which G is the centre of gravity of the points M,,, assumed
to be of mass m,.
But the points M, can be classified in two categories M,
and M; according to whether they lie between O and G or
between G and P of the abcissa p

(,

vi

©

For the M; points

(517-3)

GM, < OG .

Again, if the 0, do not decline too rapidly, G will be to
the right of the centre of the segment OP, and the image O’
of O with respect to G will be to the right of P. Then we will
have

(517-4)

GM. < 0G

so that

(517-5)

1 Em, GM°
2 OG'Em.

Thus under the assumptions made. that is to sav if

(517-6)

[S58

"111 Allais - pag. 224