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