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 inde- 
pendent 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 simpli- 
city 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