The national debt, at the conclusion of the war which ended in 1697, was
twenty-one millions and an half. (See Smith's Wealth of Nations,
chapter on Public Debts.) We now see it approaching fast to four hundred
millions. If between these two extremes of twenty-one millions and four
hundred millions, embracing the several expenses of all the including
wars, there exist some common ratio that will ascertain arithmetically
the amount of the debts at the end of each war, as certainly as the fact
is known to be, that ratio will in like manner determine what the amount
of the debt will be in all future wars, and will ascertain the period
within which the funding system will expire in a bankruptcy of the
government; for the ratio I allude to, is the ratio which the nature of
the thing has established for itself.
Hitherto no idea has been entertained that any such ratio existed, or
could exist, that would determine a problem of this kind; that is, that
would ascertain, without having any knowledge of the fact, what the
expense of any former war had been, or what the expense of any future
war would be; but it is nevertheless true that such a ratio does exist,
as I shall show, and also the mode of applying it.
The ratio I allude to is not in arithmetical progression like the
numbers 2, 3, 4, 5, 6, 7, 8, 9; nor yet in geometrical progression, like
the numbers 2, 4, 8, 16, 32, 64, 128, 256; but it is in the series of
one half upon each preceding number; like the numbers 8, 12, 18, 27, 40,
60, 90, 135.
Any person can perceive that the second number, 12, is produced by the
preceding number, 8, and half 8; and that the third number, 18, is in
like manner produced by the preceding number, 12, and half 12; and so
on for the rest. They can also see how rapidly the sums increase as
the ratio proceeds. The difference between the two first numbers is but
four; but the difference between the two last is forty-five; and from
thence they may see with what immense rapidity the national debt has
increased, and will continue to increase, till it exceeds the ordinary
powers of calculation, and loses itself in ciphers.