76 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28

For a system of points M, of mass m., we have

220-10) Xm, OM. = OC Em,+Em, GM’

where G is the center of gravity. In all cases therefore

(220-11)

2m, OM: >CC Em

(equality arises only when the entire mass is wholly concenrated
 in the point G).
We then have by simple transposition

220-12) / 0 (6)de =

glade?
/3(e)de

and from (211-3), (220-5) and (220-6) it follows that of necessity


(220-13)

A

A will be equal to 1/2 only if the distribution of the É(6)do,
whose overall value is k, is concentrated at a given point. and
of course this cannot happen in reality (1).
As will be shown, the value A=1 is a particularly significant
 one (2).

(*) Taking account of (112-1), the same analysis applied to the function
0(0) shows that

JE (60) do=er
(?) § 251, relation (251-1)

-1| AÂllais - pag. 80