Sec. 5] VALUE OF CAPITAL 209 
which is supposed to be the rate,at which water will flow 
through an aperture of one square inch with a “head” 
of six inches. The “first’’ inches are often so sure to con- 
tinue as to be guaranteed. Again, if we overlook the 
element of risk, the hares in joint stock companies 
often exemplify perpetual annuities. 
Turning from capital proper y to capital wealth, we find 
in land an approximate example of capital yielding a per- 
petual annuity. Land is often capitalized on the basis of a 
perpetual and uniform income, in the form of erops or other 
uses. It is then valued at a certain number of years’ pur- 
chase. These so-called “natural and indestructible powers . 
of the soil,” however, which such a calculation assumes, do 
not always exist, and when they do exist, do not always 
yield a perpetual annuity. Mines and quarries become 
exhausted, while much land yields an irregular, increasing, 
or decreasing income stream. 
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We turn now from perpetual to terminable annuities. 
Suppose that a man possesses a ten-year annuity of $100 a 
year. Thismeans that he hasthe right to receive ten annual 
payments of $100 each, the first falling due one year from 
the present moment. It is clear that such an annuity differs 
from a perpetual one by lacking the infinite succession of 
payments after the ten years are past. In short, the 
terminable annuity is simply a perpetual annuity dated 
to-day, less a perpetual annuity deferred ten years. There- 
fore, the present value of the terminable annuity is simply 
the difference between the present value of the two perpet- 
ual annuities. Of these two perpetual annuities, the pres- 
ent value of the one which begins immediately, interest 
being four per cent, is $2500, and that of the one which is 
deferred ten years is gas, or $1689. Their difference is 
$2500 — $1689 or 811. Now such a difference as this, i.e. 
the difference between any particular sum (as $2500) and 
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