THIRD APPROXIMATION

for the path of a boomerang or a feather. If he shoulddo so, he would still fall short of actual conditions byassuming the wind to be constant in direction and ve-locity.

Scientific determination can never be perfectly exact.At best, science can only determine what would happenunder assumed conditions. It can never state exactlywhat does or will happen under actual conditions. 2

We have thus far stated verbally, geometrically, andalgebraically the laws determining interest under thesimpler conditions first, when it was assumed that theincome streams of individuals were both certain andfixed in amount, but variable in time shape, and, sec-ondly, when it was assumed that the income streamswere certain, but variable in amount as well as in timeshape. We have also considered verbally the interest prob-lem under conditions of risk found in the real world.

§2. The Six Sets of Formulas Incomplete

All that I shall attempt here is to point out the short-comings of the six sets of formulas in the second ap-proximation. Impatience Principle A in the second ap-proximation is expressed by formulas of the type:

/ = F <y + vf, y" ■+' x",..., y™ + x (m) )

indicating that a person’s impatience is a function of hisincome stream as specifically scheduled, indefinitely inthe future.

Of course, in the uncertainties of actual life no suchspecific scheduling is possible. The equation is true butincomplete, as / is properly not only a function of one ex-

3 See my article, Economics as a Science, in Proceedings of the Ameri-can Association for the Advancement of Science , Vol. LVI, 1907.

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