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 concen- 
rated 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 ne- 
cessity 
(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 signifi- 
cant 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