Regarding homeopathic dilutions, a calculation nearly like the following was made by Dr. Panvini.
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.
One of your little pellets is 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.