[T4 
PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
B. 
— CONSEQUENCES OF THE ASSUMPTIONS 
Notation 
220. It will be useful for what follows to consider the La- 
place transform ¢(u) of the function 
(220-1) 
b(u)= = / Blo) as 
vith 
— A 
dR _, dR, 
—— = 09 — 
A 
R R, 
in continuous notation, relation (2) becomes relation (211-1) of the text. 
If we put 
b, = T (0) 
BR - 
we have 
LR=La+T B(o) L [T7,] +T B(1) L [T7] +. +T B(6) L [TR] +. 
=[La+} T 8(6) LT] + X T B(6) L7e 
If we suppose that T tends towards zero and that we have 
limit [La+E T B(6) LT]=La(t) 
and if we put 
we finally derive 
T 
ade 
LR = af?) + | 7 8(0) LA, db 
0 
which is the relation (211-1) of the text. 
(*} The meaning of hypothesis (b) is in particular that, at least over 
a large range, there exists a valid index of real national consumed in- 
come R,. This last property corresponds to the general hypothesis I have 
made in the first Part (§ 117 and 119) [in particular relations (117-1), 
211-1) and 211-2)] 
11] Allais - pag. 78