328 
PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 2 
Any hope of doing this is illusory, since it has been shown 
hat whatever the function 3(8), for small values of à and © we 
have 
(331-2) 
0 ~ ry, 
(1) 
In practise, the rates à and p are quite small and it is there- 
fore practically certain that the order of magnitude of the 
value of © should be about the same as yc. But if this con- 
cordance does occur in fact, it only shows that the reasoning 
based on the composition of the working population is correct; 
in no way does it demonstrate the validity of the model pro- 
posed. This demonstration would only be possible if the deter- 
mination of the function ¢(8), and therefore of ©, from the 
composition of the working population, could be done accura- 
tely enough for the difference yc- © itself to be determined 
sufficiently precisely. As has already been noted, this is an 
undertaking which appears to be impossible, at least in the 
present state of knowledge (?). 
The Influence of the Function [3(0) 
332. It is interesting to examine what the results which 
correspond to the exponential model become when a non-expo- 
aential expression is used for B(6). 
Appendix I contains a study of the case in which the quite 
acceptable hypothesis is postulated that B(8)e*® can be repre- 
(") Relation (227-6). 
For i=-n=0, we have 
mn 
3) § 312 to 314. 
‘111 Allais - pag. 132