922 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
(517-8) are verified, whence it follows that the limited expan- 
sions derived in the case of the general model for the different 
quantities, and given in § 240, may be used. 
518. Secondly, since n >, it follows from (512-12), 
(512-13) and (512-14) that 
1 Ew'w,, Ac Into, 
5181) 2 Eros 0 ro] 
Assume that 
(518-2) w, =0 for n-1>= 9p 
so that the sums only cover p terms. Assuming further that the 
nw, _, are never-increasing, then applying the Tchebicheff ine- 
quality (1) 
(518-3) 
2 15 JF 
n° w 2X n 2 nw. 
nS sel n=1 n-1 
whence 
(518-4) 
A 
I En 
p En a, 
i.e. 
(518-5, 
N 
1 
13 
nm 
() BRONSTEIN-SEMENDJAJEW, 0d. cit., D. I35. 
T11] Allais - pag. 226