046 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28

For these values. we have

528-2)

i
À > —
2t)

and I/2w can of course be very large when w is very small (1).

First Limitation of the Value of A

520. Providing w is not too small, À will remain at a relatively
 low level. Indeed, it mav be noted in the first place that

() We have

=

on

an

>t

Hu

Thus A will differ from its limit value bv less than e, i.e. we will have

2 (1)

,

nt

æe if

17 >

rE

Thus, if for example w=1/100, A will differ from its limit value 50 by
less than 1/10 for n > 3000. It can thus be seen that A can only have
very high values if n is very large, and such values are incompatible with
observed reality, at least as far as can be judged

11] Allais - pag. 250