910 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28

i~p (!). Thus, from (511-1) and (511-2) the values of T and
of the w must satisfy the condition

aT) — 4 La 01 aie
(51211) To] "Ee ET * b=)

where the value of ¢(i - p) is given.
Thus, the weights w,_, are subject to the two conditions
(510-10) and (512-11). For given weights w,_, satisfying the
condition (512-10), the relation (512-11) determines T and the
relation (512-9) determines A. Relation (512-8) determines ©,
once T is known.
As the expression for A as a function of the w,_, is independent
 of T, discussion of the value of A can be carried on
Independently of the conditions (512-8) and (512-11), taking
account only of the condition (512-9).
Equation (512-9) can be rewritten as follows (for simplicity
 the subscripts of the © have been omitted)

512-12)

Mn? Ww, A,
eel
à]
Un Wy]

for nl

with

(512-13)

I
LS b Sl
2 n

where A, | denotes the value of A for the function 8, , (2.

(}) $ 312.
For example. we have

relation 226-2).
(3) Relations (220-6) and (=10-7)

1] Allais - pag. 214