Skc. 3] THE RISK ELEMENT 271

probable cases and that only one of these will give double
sixes. Mathematics could not obtain the result unaided
by experience. All that mathematics accomplished with
the dice was to derive a result from the assumed conditions
 of two sets of six equal chances. Whether these
assumed conditions existed was a question, not of mathematics,
 but of concrete opinion. If the dice were known to
be “loaded,” the case would be materially altered.

§3
Tn order to apply this theory of chance to the valuation
of capital, we observe that both the future rate of interest
and the future items of income are uncertain. In the problem
 of capital-valuation, however, the uncertainty in the
rate of interest does not always enter, for only present
and not future rates are employed at the time at which
the valuation of the capital is made. When we call a rate
a “ present” rate we mean, of course, that the contract
or estimate to which it relates is a present contract or
estimate. The very fact of valuation implies a known
rate or rates at which the valuer is contrasting present
and future goods. There may be several “ present ” rates.
Thus if the “ present” be the year 1906, we may imagine
a whole series of rates of interest holding true in 1906 for
such a man; for instance, 4 per cent for a 1-year contract,
6 per cent for a 5-year contract, and 5 per cent for a 15-year
 contract, all originating at the present moment. All
of these rates are fixed and known and hold true in the
year 1906, but they do not determine the rates which
will hold true for the contracts or estimates of 1907 or
1914.
In valuing capital, therefore, it is not necessary to regard
the rate of interest as uncertain except when the rate in
question is a future rate.

Let us suppose that in
due at the end of the time FA

Figure 10 the income AB is
, and that the rate of interest