owledge 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.

I come now to apply the ratio as a rule to determine in all cases.

I began with the war that ended in 1697, which was the war in which the
funding system began. The expense of that war was twenty-one millions
and an half. In order to ascertain the expense of the next war, I add
to twenty-one millions and an half, the half thereof (ten millions and
three quarters) which makes thirty-two millions and a quarter for the
expense of that war. This thirty-two millions and a quarter, added to
the former debt of twenty-one millions and an half, carries the national
debt to fifty-three millions and three quarters. Smith, in his
chapter on Public Debts, says, that the national debt was at this time
fifty-three millions.

I proceed to ascertain the expense of the next war, that of 1739, by
adding, as in the former case, one half to the expense of the preceding
war. The expense of the preceding war was thirty-two millions and a
quarter; for the sake of even numbers, say, thirty-two millions; the
half of which (16) makes forty-eight millions for the expense of that
war.

I proceed to ascertain the expense of the war of 1756, by adding,
according to the ratio, one half to the expense of the preceding war.
The expense of the preceding was taken at 48 millions, the half of which
(24) makes 72 millions for the expense