Harriet Hall in The Skeptical Inquirer:
In 1800, conventional medicine was a disaster. Doctors weakened patients with bloodletting and purging, they poisoned them with mercury and other harmful substances, and they often killed more patients than they cured. Dr. Samuel Hahnemann was looking for safer, more effective ways to help his patients. He had an epiphany after he took a dose of cinchona bark and developed symptoms similar to those of malaria, the disease cinchona was supposed to treat. He extrapolated from this one observation to conclude that if any substance causes a symptom in healthy people it can be used to treat the same symptom in sick people. He formulated this as the first law of homeopathy,similia similibus curentur, usually translated as “like cures like.” He diluted his remedies so that they would no longer cause symptoms; this led to his second law of homeopathy, the law of infinitesimals, which states that dilution increases the potency of a remedy. When he observed that his remedies worked better during house calls than in his office, he attributed it to jostling in his saddle bags, so he added the requirement of “succussion,” specifying that remedies must be vigorously shaken (not stirred) by striking them against a leather surface at every step of dilution.
Homeopathic remedies are usually labeled with the notation X or C, corresponding to ten and one hundred. 15C would mean that one part of remedy was diluted in 100 parts of water, one part of the resulting solution was again diluted in 100 parts of water, and the process was repeated fifteen times. Hahnemann died before Avogadro’s number was available to calculate how many molecules are present in a volume of a chemical substance. Today we can calculate that by the thirteenth 1:100 dilution (13C), no molecules of the original substance remain. Hahnemann typically used 30C remedies.
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