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 con- 
ditions of two sets of six equal chances. Whether these 
assumed conditions existed was a question, not of mathe- 
matics, 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 prob- 
lem 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