760 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
The Functions R(t) and ot, 0) 
128. Lastly, it is possible to deduce from the invariance 
of ¢ and from equations (111-6) and (111-7) 
a + p(u)du 
(128-1) Ral6) ©(t,0)=R,(t) p(0)e ” 
from which it follows that 
(128-2) 1 Ro, 1 0¢ 1 dR, 
R, dt § ot TR. at "le(t}-e(t0)| 
Thus from (110-6) we have 
(128-3) 
R A 
= Axe ® PS OF (48) = o(t-6) 
R, dt @ Ot 
Nothing further can be said about the functions R.(#) and 
(2, 6). 
Changes in i and op over Time 
129. Attention is drawn to the fact that the only assumption 
implied in the preceding formulas is that the difference i(¢) - p(2) 
is constant. They therefore hold where 7 and ¢ are functions 
of time. 
[11] Allais - pag. 64