Dilutions
Three logarithmic potency scales are in regular use in homeopathy. Hahnemann created the "centesimal" or "C scale", diluting a substance by a factor of 100 at each stage. The centesimal scale was favored by Hahnemann for most of his life. A 2C dilution requires a substance to be diluted to one part in 100, and then some of that diluted solution diluted by a further factor of 100. This works out to one part of the original substance in 10,000 parts of the solution. A 6C dilution repeats this process six times, ending up with the original substance diluted by a factor of 100−6=10−12 (one part in one trillion or 1/1,000,000,000,000). Higher dilutions follow the same pattern. In homeopathy, a solution that is more dilute is described as having a higher potency, and more dilute substances are considered by homeopaths to be stronger and deeper-acting remedies. The end product is often so diluted as to be indistinguishable from the dilutant (pure water, sugar or alcohol).
Hahnemann advocated 30C dilutions for most purposes (that is, dilution by a factor of 1060). In Hahnemann's time, it was reasonable to assume the remedies could be diluted indefinitely, as the concept of the atom or molecule as the smallest possible unit of a chemical substance was just beginning to be recognized. The greatest dilution reasonably likely to contain even one molecule of the original substance is 12C.
Some homeopaths developed a decimal scale (D or X), diluting the substance to ten times its original volume each stage. The D or X scale dilution is therefore half that of the same value of the C scale; for example, "12X" is the same level of dilution as "6C". Hahnemann never used this scale, but it was very popular throughout the 19th century and still is in Europe. This potency scale appears to have been introduced in the 1830s by an American homeopath, Constantine Hering. In the last ten years of his life, Hahnemann also developed a quintamillesimal (Q) or LM scale, diluting the drug 1 part in 50,000 parts of diluent. A given dilution on the Q scale is roughly 2.35 times its designation on the C scale. For example, a remedy described as "20Q" has about the same concentration as a "47C" remedy.
| X Scale, D Scale | C Scale | Ratio | Note |
|---|---|---|---|
| Ø | Ø | 1:1 | mother tincture (undiluted) |
| 1X, D1 | — | 1:10 | described as low potency |
| 2X, D2 | 1C | 1:100 | called higher potency than 1X by homeopaths |
| 6X, D6 | 3C | 10−6 | |
| 8X, D8 | 4C | 10−8 | allowable concentration of arsenic in U.S. drinking water |
| 12X, D12 | 6C | 10−12 | |
| 24X, D24 | 12C | 10−24 | Has a 60% probability of containing one molecule of original substance if one mole of the original substance was used. |
| 60X, D60 | 30C | 10−60 | Dilution advocated by Hahnemann for most purposes; the patient would need to consume 1041 pills (a billion times the mass of the Earth), or 1034 gallons of liquid remedy (10 billion times the volume of the Earth) to consume a single molecule of the original substance.
Moreover, since even in a 15C solution, very likely be no molecules of the original substance would be left, the 30C solution would probably contain no molecules of water that had come into contact with the original substance. |
| 400X, D400 | 200C | 10−400 | Dilution of popular homeopathic flu remedy Oscillococcinum |
| Note: the "X scale" is also called "D scale". 1X = D1, 2X = D2, etc. | |||
Critics and advocates of homeopathy alike commonly attempt to illustrate the dilutions involved in homeopathy with analogies. Hahnemann is reported to have joked that a suitable procedure to deal with an epidemic would be to empty a bottle of poison into Lake Geneva, if it could be succussed 60 times. Another example given by a critic of homeopathy states that a 12C solution is equivalent to a "pinch of salt in both the North and South Atlantic Oceans", which is approximately correct. One-third of a drop of some original substance diluted into all the water on earth would produce a remedy with a concentration of about 13C. A popular homeopathic treatment for the flu is a 200C dilution of duck liver, marketed under the name oscillococcinum. As there are only about 1080 atoms in the entire observable universe, a dilution of one molecule in the observable universe would be about 40C. Oscillococcinum would thus require 10320 more universes to simply have one molecule in the final substance. The high dilutions characteristically used are often considered to be the most controversial and implausible aspect of homeopathy.