comparisons are not matters susceptible of dispute, being founded
on simple arithmetical computations, level to the capacity of any
intelligent schoolboy. A person who once wrote a very small pamphlet
made some show of objecting to calculations of thus kind, on the ground
that the highest dilutions could easily be made with a few ounces of
alcohol. But he should have remembered that at every successive dilution
he lays aside or throws away ninety-nine hundredths of the fluid on
which he is operating, and that, although he begins with a drop, he only
prepares a millionth, billionth, trillionth, and similar fractions of
it, all of which, added together, would constitute but a vastly minute
portion of the drop with which he began. But now let us suppose we take
one single drop of the Tincture of Camomile, and that the whole of this
were to be carried through the common series of dilutions.

A calculation nearly like the following was made by Dr. Panvini, and may
be readily followed in its essential particulars by any one who chooses.

For the first dilution it would take 100 drops of alcohol.

For the second dilution it would take 10;000 drops, or about a pint.

For the third dilution it would take 100 pints.

For the fourth dilution it would take 10,000 pints, or more than 1,000
gallons, and so on to the ninth dilution, which would take ten billion
gallons, which he computed would fill the basin of Lake Agnano, a body
of water two miles in circumference. The twelfth dilution would of
course fill a million such lakes. By the time the seventeenth degree of
dilution should be reached, the alcohol required would equal in quantity
the waters of ten thousand Adriatic seas. Trifling errors must be
expected, but they are as likely to be on one side as the other, and any
little matter like Lake Superior or the Caspian would be but a drop in
the bucket.

Swallowers of globules, one of your little pellets, moistened in
the mingled waves of one million lakes of alcohol, each two miles in
circumference, with which had been blended that one drop of Tincture
of Camomile, would be of precisely the strength recommended for that
medicine in your favorite Jahr's Manual, "against the most sudden,
frightful, and fatal diseases!" [In the French edition of 1834, the
proper doses of the medicines are mentioned, and Camomile is marked
IV. Why are the doses omitted in Hull's Translation, except in three
instances out of the whole two hundred