User:Filll/homeopathyscales

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"Hahnemann's idea at first was simply to reduce the "strength" or material mass of his drug, but his passion for accuracy led him to adopt a scale, that he might always be sure of the degree of reduction and establish a standard for comparison."[1]

Homeopathy potency scales are used to describe the "potency" of the remedies prescribed in homeopathy. Most homeopathic remedies are produced by diluting other substances in water or alcohol using a special technique.

The homeopathic remedies are not just diluted materials. The therapeutic substances are diluted by successive dilutions, and after each dilution the mixtures of water and the other substances are shaken vigorously, which is called "succussion". This procedure of successive dilutions alternating with succussion is called "potentization" or "dynamization".

Homeopaths believe that the more cycles of dilution and succussion a remedy goes through, the more potent it will be. The number of successive dilutions alternating with succussion and the amount of dilution is described by the potency scale of the homeopathic dose.

There are several different homeopathic potency scales; the most common are the X, D, C, M, LM and Q scales.[2] The potency of a remedy is given by a number (usually an integer) together with a letter, or pair of letters in the case of the LM scale). This potency can be associated with the concentration of the original substance which has been diluted to create the homepathic remedy, if one assumes modern atomic theory.

Crude dose[edit]

An undiluted substance is known in homeopathy as a crude dose, crude substance, natural substance or mother substance. For example, pure milk is a crude dose.[3] The remedies are usually made by diluting these crude substances with water, alcohol, or some other diluent.

Diluted materials can also be made from tinctures. A tincture in homeopathic terminology is a plant (or plant tissues) placed in 30% alcohol[4] and shaken every day for one month, then strained. This preparation is called the mother tincture, and is then used as a starting material to be diluted.

In addition, insoluble substances can be used to produce high potency remedies. Insoluble materials are mixed with soluble substances like lactose (milk sugar),[5] and ground up into pulverized material to create a low concentration powder, traditionally using a mortar and pestle. Some of this low concentration powder is then mixed with more of the soluble material and then the mixture is ground up again. This is done repeatedly, to create a very low concentration mass of fine particles, most of which are particles of the soluble substance. This product is then introduced into a liquid medium, and possibly diluted further afterwords.

Scales[edit]

Centesimal scale[edit]

The original and most important homeopathic potency scale is the "centesimal scale", which describes dilution by factors of 100. If 1 liter of pure milk is placed in a 100 liter container, and the remainder of the container filled with water, the concentration of the mixture is 1 part in 100, which is described as a 1% mixture.[6][7] That is, the original crude dose of milk is diluted by a factor of 100. After succussing, homeopaths call this 1% mixture a "1C dose".[8]

If 1 liter of this 1C dose is placed in a 100 liter container, and the remainder filled with water, the original crude dose of milk is diluted by a factor of 100 x 100 = 10,000 = 104. The concentration of this mixture is now 0.01%. After succussing, homeopaths call this 0.01% mixture a "2C dose".

One liter of this 2C dose placed in a 100 liter container, and then diluted with 99 liters of water creates a 0.0001% mixture, which after succussion is a "3C dose". The original crude dose of milk is diluted by a factor of 106 in a 3C dose. The crude dose of milk in 4C dose is diluted by a factor of 108. A 5C dose is diluted by a factor of 1010. A crude dose is described as a 0C dose.

Sometimes the potency notations CH and CK are used. These potency scales are identical to the C potencies, except slightly different methods of preparation are used. The K indicates that the Korsakovian Method[9] is used, and the H label means that the Hahnemann Method is used. The Hahnemann method requires a new vial at each succussion step but Korsakovian method does not.[10]

Decimal scales[edit]

Later, decimal scales emerged to describe the potency of homeopathic doses. If 1 liter of milk is placed in a 10 liter container, and the remainder of the container filled with 9 liters of water,[7] a 10% mixture is created,[6] and the concentration of the solution is now 1 part in 10. According to homeopaths, this preparation must be succussed to be potentized. After succussion, this is designated in homeopathy as a "1X dose".[11][12]

If 1 liter of this 1X dose, a 10% mixture, is placed in a 10 liter container, and the remainder filled with 9 liters of water, it forms a 1% preparation, having a concentration of 1 part in 100. After succussing, homeopaths designate the result as a 2X dose. Similarly, a 3X dose is diluted to 1 part in 1000, producing a 0.1% solution.

A similar notation used by homeopaths employs the letter "D" to designate dilution by factors of 10. A D1 dose is the same as a 1X dose, having a concentration of 10%. A D2 dose is the same as a 2X dose, or dilution to 1 part in 100. A D3 dose is the same as a 3X dose, or dilution to 1 part in 1000. The X and D notations are called "decimal scales".

Some doses with dilutions on the decimal scale have concentrations that can be compared to doses on the centesimal scale. Except for the putative effects of succussion, a 1C dose is the same as a 2X dose, or a D2 dose. Except for succussion, a 2C dose is the same as a 4X dose or a D4 dose. Similarly, the concentration of a 3C dose is the same as a 6X dose, or a D6 dose. A 5C dose on the centesimal scale has the same concentration as a 10X dose or a D10 dose on the decimal scale. According to homeopathic theory, although the concentrations are the same, the succussion patterns are different, so the doses might have different effects.

Sometimes, the designations DH and DK are used. DH and DK are digital scales, identical to the D scale, except that slightly different methods are used. The K indicates that the Korsakovian Method is used, and the H label means that the Hahnemann Method is used. The Hahnemann method requires a new vial at each succussion step of the dynamization procedure but Korsakovian method does not.

The "M" shorthand[edit]

A shorthand notation is used by homeopaths describes centesimal dilutions that are made sequentially thousands of times, alternating with succussion. One thousand dilutions by a factor of 100 is written as 1M.[13] That is, a 1M dose is diluted by a factor of 1001000, or a factor of 102000. A 1M dose is the same as a 1000C dose, which has the same concentration as a 2000X dose, or a D2000 dose.[14]

A 2M dose is created by diluting the crude dose by a factor of 100, and succussing the resulting solution, 2000 times. This corresponds to dilution by 1002000 = 104000. So a 2M dose is the same as a 2000C dose, and has the same concentration as a 4000X dose and a D4000 dose, although it has a different pattern of succussion. Similarly, a 3M dose is the same concentration as a 3000C dose, a 6000X dose and a D6000 dose, differing only by the effects of the different succussion patterns.

Quintamillesimal scale[edit]

Another scale used by homeopaths is the "quintamillesimal scale" (also known as the Q-potency scale, the quinquagentessimal scale or the 50 millesimal scale) , designated by the notation "Q" or "LM", which are equivalent. A dose that has been diluted to the level of LM1 (also designated as Q1) is commonly said to have been diluted by a factor of 50,000.

However, dilution by roughly a factor of 50,000 is only part of the preparation process of an LM dose. There are also some variations among the techniques designed to produce LM doses.

A dose that has been diluted to the level of LM2 (which is the same as Q2) has been diluted by a factor of (50,000)2. A dose that has been diluted to the level of LM3 has 1 part in (50,000)3 of the original crude dose.

Hahnemann used the notation 0/1 for LM1, 0/2 for LM2, 0/3 for LM3, etc. However, some homeopaths use the notation 1/0 for LM1, 2/0 for LM2, 3/0 for LM3, etc. Another common notation style is to denote LM1 as LM/1, LM2 as LM/2, LM3 as LM/3, etc. In India, homeopaths use the notation M/1 for LM1, M/2 for LM2, M/3 for LM3, etc.

100 Millesimal scale[edit]

The 100 millesimal scale is denoted by "CM". If one portion of the crude substance is diluted by a factor of 100,000, then the resulting dose has a potency of CM1 on the 100 millesimal scale. The concentration of a CM1 dose is 1 part in 100,000, or 10-3 percent.

Insoluble materials[edit]

The substances in homeopathic remedies need not only be soluble or miscible. Insoluble substances like flint, quartz, oyster shell or lycopodium pollen are ground up using a mortar and pestle in a procedure called trituration. To "dilute" these materials, a non-medicinal solid is ground up with the crude material.

For example, one grain of oyster shell might be placed in a mortar with nine grains of lactose (milk sugar) and ground into a powder. The resulting powder will be a "diluted" mixture of the oyster shell, diluted by a factor of 10, and therefore have a potency of 1X.[15] This procedure is usually repeated until the preparation has reached a potency of 3X or 6X, and then the preparation is transferred to a fluid. Soluble parts of the mixture will dissolve, and insoluble particles from the mixture will be held in suspension if they are ground sufficiently finely.

Scales, revised[edit]

Centesimal scale, revised[edit]

The earliest and most important homeopathic potency scale is the "centesimal scale", which describes dilution by factors of 101. If 1 liter of pure milk is placed in a 101 liter container, and the remainder of the container filled with 100 liters of water, the original crude dose of milk is diluted by a factor of 101. That is, the concentration of the crude dose is reduced to 1 part in 101, or 0.99%.[16] The concentration of this diluted milk is reduced by a factor of 1/101 or about 0.0099. After succussing, homeopaths call this 0.99% solution a 1C dose. A crude dose is described as a 0C dose on the centesimal scale.

If one liter of this 1C dose is placed in a 101 liter container, and the remainder of the container filled with 100 liters of water, a 2C dose is produced. A 2C dose is diluted by 101 x 101 = 10,201. That is, the concentration of the crude dose is reduced by a factor of (1/101) x (1/101), or by 1/10,201, and the resulting dose has a concentration of 1 part in 10,201, or about 0.98%. A 2C dose is more potent than a 1C dose, and is more diluted and has a lower concentration of the mother substance.

Similarly, if one liter of this 2C dose is placed in a 101 liter container, and the remainder of the container filled with 100 liters of water, a 3C dose is produced. The concentration of a 3C dose is 1 part in 1013 = 1030301 or 9.7 x 10-5 percent. The concentration of a 4C dose is 1 part in 1014 = 104,060,401, or about 9.6 x 10-7 percent.

Sometimes the potencies CH and CK are used. These potency scales are identical to the C potencies, except slightly different methods of preparation are used. The K indicates that the Korsakovian Method is used, and the H label means that the Hahnemann Method is used. The Hahnemann method requires a new vial at each succussion step but Korsakovian method does not.[17]

Decimal scales, revised[edit]

If 1 liter of milk is placed in a 11 liter container, and the container filled with 10 liters of water, a 9.1% solution is created,[18] and the concentration of the solution is now 1 part in 11. According to homeopaths, this solution must be succussed to be potentized. This is designated in homeopathy as a 1X dose. A crude dose is a 0X dose.

If 1 liter of this 9.1% solution (the 1X dose) is placed in a 11 liter container, and the remainder filled with 10 liters of water, it forms a 0.83% solution, with a concentration of 1 part in 112 = 121. After succussing, homeopaths designate this 0.83% solution as a 2X dose. Similarly, a 3X dose is diluted to 1 part in 113 = 1331. The concentration of the original natural material in a 3X dose is 0.075%.

A similar notation used by homeopaths uses the letter "D" to designate dilution by factors of 10. A D2 dose is the same as a 2X dose, or dilution to 1 part in 112 = 121. A D3 dose is the same as a 3X dose, or dilution to 1 part in 1331. The X and D notations are called "decimal scales". The X notation is used most often in the United States, and the D notation is more common in Europe.


Sometimes, the designations DH and DK are used. DH and DK are digital scales, identical to the D scale, except that slightly different methods are used. The K indicates that the Korsakovian Method is used, and the H label means that the Hahnemann Method is used. The Hahnemann method requires a new vial at each succussion step of the dynamization procedure but Korsakovian method does not.


The "M" shorthand, revised[edit]

A shorthand notation is used by homeopaths describes centesimal dilutions that are made sequentially, thousands of times (alternating with succussion). One thousand dilutions by a factor of 101 is written as 1M.

That is, a 1M dose is diluted by a factor of 1011000 = 2.0959 x 102004. Therefore, the concentration of the crude dose in a 1M remedy is 1 part in 2.0959 x 102004, or 4.77 x 10-2005 percent.

A 2M dose is created by diluting the crude dose by a factor of 101, and succussing the resulting solution, 2000 times. This corresponds to dilution by (101)2000 = 4.3 × 104008. That is, the resulting 2M remedy has a concentration of the crude dose of 1 part in 4.3 × 104008, or 2.3 x 10-4007 percent.

A 3M dose is created by diluting the crude dose by a factor of 101, and succussing the resulting solution, 3000 times. This corresponds to dilution by (101)3000 = 9.2 × 106012. The resulting 3M dose has a concentration of 1 part in 9.2 × 106012.

Quintamillesimal scale, revised[edit]

Another scale used by homeopaths is the quintamillesimal scale (also known as the LM scale, the Q-potency scale, the quinquagentessimal scale or the 50 millesimal scale) which uses the designations "Q" or "LM", which are equivalent. A dose that has been diluted to the level of LM1 (also designated as Q1) is created by placing 1 part of the crude substance in 50,000 parts of the diluent. Therefore, the crude substance in an LM1 dose is diluted by a factor of 50,001, and has a concentration of 1 part in 50,001, or 1.99996 × 10-3 percent.[19]

A dose that has been diluted to the level of LM2 (which is the same as Q2) has been diluted by a factor of 100,000. A dose that has been diluted to the level of LM3 has 1 part in 150,000 of the original crude dose.


Hahnemann used the notation 0/1 for LM1, 0/2 for LM2, 0/3 for LM3, etc. However, some homeopaths use the notation 1/0 for LM1, 2/0 for LM2, 3/0 for LM3, etc. Another common notation style is to denote LM1 as LM/1, LM2 as LM/2, LM3 as LM/3, etc. In India, homeopaths use the notation M/1 for LM1, M/2 for LM2, M/3 for LM3, etc.

100 Millesimal scale[edit]

The 100 millesimal scale is denoted by "CM". If one portion of the crude substance is diluted by 100,000 portions of water (or any other diluent), then the resulting dose has a potency of CM1 on the 100 millesimal scale. The concentration of a CM1 dose is 1 part in 100,001, or 9.9999 × 10-4 percent.


Comparisons with standard science[edit]

Avogadro's number calculations[edit]

Avogadro's number is 6.022 x 1023. This means that there are about 6.02 x 1023 molecules in one mole of a substance. A 15X solution has been diluted by a factor of 1015, so 1 mole of 15X solution would contain roughly 6.02 x 108 molecules of the original substance.

One mole of a 15C solution is about 0.6 US fluid ounces,[20] weighing about 18 grams if the diluent is water, and would be unlikely to contain a single molecule of the original substance. Assuming a water diluent, the probability that 0.6 US fluid ounces of a 15C dose contains one molecule of the original substance is roughly (1/10)30 x 6.02 x 1023 = 6.02 x 10-7, or roughly 1 chance in 1.66 million.[21] This is roughly the chance that either of two friends will be killed by lightning in the United States in a given year.

To get another perspective on these numbers, there are on the order of 1.39 x 108 moles of water in an Olympic size swimming pool, corresponding to 8.37 x 1031 water molecules.[22] If the pool were filled with a specific homeopathic remedy diluted to 15C, there would be only about 83 molecules of the original substance in the entire Olympic size swimming pool. Therefore, to have a 99% chance of consuming at least one of the original molecules of a 15C dose, one would need to consume about 4.6 x 1030 molecules of the remedy,[23] or about 5.5% of the volume of an Olympic swimming pool. Thus, the volume to be consumed would be about 137,000 litres with a mass of 137 tonnes, or 151 U. S. tons of fluid.[24][25]

Molecular dose[edit]

A molecular dose is a homeopathic remedy with a potency below the "Avogadro limit". That is, a molecular dose has a potency approximately between 0X (a crude dose, also described as 0C, D0, 0M or Q0) and about 12C (having a concentration of 10-24), which is a dose with the same concentration as a 24X dose, on the decimal scale.[26][27]

Therefore, a 'molecular dose' is a crude dose that probably contains at least one molecule of the original ingredient, which is not likely to be the case for potencies above 12C or 24X. Potencies above 12C or 24X are called submolecular, because the concentration is low enough that it is unlikely that a single molecule of the ingredient of interest remains in the dose after dilution.

Comparison table[edit]

Potassium dichromate, K2Cr2O7, is used as a anti-pain remedy by homeopaths, who call it kalium bichromicum.[28] For example, the headache remedy HeadOn contains potassium dichromate diluted to one part per million. Potassium dichromate has a molar mass of 294.19 grams/mole, a density of 2.676 grams/cm3, and a solubility in water of 4.9 gram/100 ml at 0°C. Therefore, the most potassium dichromate that can be dissolved in a liter of water is 49 grams at 0°C.

Potency molar units (mol/L) mg/mL volume-volume % Comment
crude dose 9.096 2676 100 Original material, denoted as 0C = 0X
1C 0.0127 3.74 1
2C 1.27 x 10-4 3.74 x 10-2 10-2
3C 1.27 x 10-6 3.74 x 10-4 10-4 Dilution used in HeadOn product.
12C 1.27 x 10-24 3.74 x 10-22 10-22 Approximate Avogadro limit
30C 1.27 x 10-60 3.74 x 10-58 10-58 Hahnemann's suggested potency
200C 1.27 x 10-400 3.74 x 10-398 10-398 High potency; potency of Oscillococcinum
1X 0.127 37.4 10
2X 1.27 x 10-2 3.74 1 Same as 1C except for succussion
3X 1.27 x 10-3 0.374 0.1
6X 1.27 x 10-6 3.74 x 10-4 10-4 Same as 3C except for succussion
M1 1.27 x 10-2000 3.74 x 10-1998 10-1998
LM1
LM2

Size of the universe[edit]

It is currently estimated by astronomers that the number of particles in the universe is somewhere between 1072 and 1087.[29] Therefore, any dose with a potency greater than D87 ( or 44C) is so dilute that if every single particle in the universe was in the dose, not a single particle of the active ingredient would be expected to remain in the dose. Doses with potencies of 200C are vastly more dilute than this.

Common potencies[edit]

The original dilutions used by the father of homeopathy, Samuel Hahnemann (1755–1843), correspond to dilutions by factors of 100, and are commonly represented on the centesimal scale, or C potency scale. In 1829, Hahnemann advocated 30C dilutions for most purposes, i.e. dilution by a factor of 10030 or 1060,[30] which is sometimes referred to as the "30th potency". In the last few years of his life, Hahnemann explored remedies with various potencies on the LM scale.

Around 1830, American homeopathic physician Constantine Hering introduced dilutions by factors of 10, alternating with succussion.[31] These dilutions are commonly represented on the decimal scales, that is, the X and D potency scales. They are particularly popular in Europe, where 3X and 6X potencies are common.

A common homeopathic remedy that is used by people suffering from influenza, Oscillococcinum, is a diluted and potentized solution of Barbary duck heart and liver with a potency of 200C.[32] That is, the duck heart and liver solution has been diluted by a factor of 100200=10400. Therefore, a single duck can be used to produce a very large amount of Oscillococcinum, leading to the following comment:

In a monetary sense, this single French duck may be the most valuable animal on the planet, as an extract of its heart and liver form the sole "active ingredient" in a flu remedy that is expected to generate sales of $20 million or more. (For duck parts, that easily beats out foie gras in terms of return on investment.)[33]

The term "high potency" commonly refers to potencies greater than 30C, or sometimes beyond 200C. The term "low potency" is a vague term that has several different definitions, such as a homeopathic remedy with a potency below 12C or below 6C. Often, a low potency homeopathic remedy has a potency of 12X, 6X or 3X.[34][35]

Summary[edit]

If n is any integer, then nX corresponds to a concentration of 1 part in 10n. And Dn is 1 in 10n. Also, nC is 1 in 100n=10(2 x n).[36] But although the symbol M usually refers to 1000, nM is not 1 in 1000n = 10 (3 x n), as might be expected, but 1 in 10(2000 x n). Also, Qn corresponds to a concentration of 1 in 50000n or 1 in 5n x 104n.

Higher potencies in homeopathy, which are more diluted, are considered to be stronger deep-acting remedies. Therefore, potency increases with increasing values of n.

References[edit]

  1. ^ Chapter XIV: Potentiation and the Infinitesimal Dose, Stuart M. Close, p. 216 of The Genius of Homeopathy Lectures and Essays on Homeopathic Philosophy, 1986 reprint, Homeopathic Minimum Price Books, Jain, India, (original, 1924)
  2. ^ The X and D scales are the same, as are the LM and Q scales.
  3. ^ According to modern science, milk is actually water with dissolved material, suspended solids, emulsified material, colloidal substances, and is partly a molecular solution (Milk chemistry—An introduction, International Livestock Research Institute).
  4. ^ A 30% alcohol mixture corresponds to a roughly 60 proof alcoholic liquid.
  5. ^ Milk sugar is known to homeopaths as saccharum lactis, and commonly referred to as "sac-lac" or "sac lac".
  6. ^ a b In analytical chemistry, this is called a volume-volume percentage for soluble materials. By obvious extension, a comparable measure can be made for other mixtures such as colloids and suspensions.
  7. ^ a b This assumes that the miscibility of water and milk is negligible.
  8. ^ An alternative and less common method of preparing a 1C dose starts by diluting 1 part of the active material in 100 parts of the diluent. This produces a mixture with slightly more than a 0.99% concentration, measured by volume-volume percentage.
  9. ^ The Korsakovian Method is named for Russian homeopath Semen Korsakov.
  10. ^ Single Remedy Guide - Singles, Homeopathic Medicine Store website
  11. ^ An alternate but less common method of producing a 1X dose is to dilute 1 part of the active ingredient in 10 parts of the diluent. In this case, the concentration of a 1X dose is slightly more than 9.091%, measured by the volume-volume percentage method.
  12. ^ A crude dose is a 0X dose.
  13. ^ Some sources claim that 1M is known as the millesimal scale, and that 1M corresponds to a dilution to 1 part in 1000 (for example, see [1] or [2]), but this is not standard nomenclature and usage. Some sources include not only this nonstandard M scale, but a nonstandard MM scale corresponding to dilution of 1 part in 1 million as well [3].
  14. ^ The patterns of succussion of a 1000C dose and a 2000X dose are different, so according to homeopathic theory, these doses are not equivalent.
  15. ^ What is homeopathy?, Gudjons; a video showing the trituration procedure.
  16. ^ In analytical chemistry, this is called a volume-volume percentage
  17. ^ Single Remedy Guide - Singles, Homeopathic Medicine Store website
  18. ^ In analytical chemistry, this is called a volume-volume percentage
  19. ^ Features Of LM Potency , Srikanta Choudhury
  20. ^ A 15 C solution has the same concentration as a 30X dose, and is identical except for the succussion.
  21. ^ If the diluent is pure ethanol, one mole is about 46.1 grams, and about 1.97 US fluid ounces. Assuming a pure ethanol diluent, the probability that 1.97 US fluid ounces of a 15C dose contains one molecule of the original substance is about 6.02 x 10-7.
  22. ^ An Olympic size swimming pool is at least 25 meters by 50 meters by 2 meters, or at least 2,500 cubic meters which is 2,500,000 liters. Each liter of water weighs about 1 kilogram, which is about 56 moles of water. Therefore, 2500 cubic meters of water is about 139 million moles of water.
  23. ^ 4.6 x 1030 molecules is about 7.64 x 106 moles
  24. ^ To consume at least 1 of n molecules of the original substance in a swimming pool containing N molecules, with probability P, one would have to consume k molecules, chosen independently, where k= log(1-P)/log(1-n/N).
  25. ^ Dynamization and Dilution, Alternative Medicine Division, Creighton University Medical Center website, accessdate=2008-03-12
  26. ^ A 12C dose corresponds to roughly one molecule of the treatment material in a mole of homeopathic remedy, or about 0.6 US fluid ounces.
  27. ^ It is most common to quote 24X or 12C as the Avogadro limit. However, really the Avogadro limit is a "fuzzy transition area ranging between 20X and 26X" depending on molecular weights of the solute, solvent and other factors (Book Review of "Homeopathy: Science or Myth" by Bill Gray, MD, Chris Kurz, Homeopathy Today, September 2001).
  28. ^ KALIUM BICHROMICUM, HOMÉOPATHE INTERNATIONAL website
  29. ^ The Biggest Numbers in the Universe, Bryan Clair, Strange Horizons, 2 April 2001
  30. ^ Samuel Hahnemann His Life and Work, Richard Haehl, Volume 1, p. 321-322, Jain, India, 1922.
  31. ^ High Dilution Effects: Physical and Biochemical Basis Nirmal C. Sukul, Anirban Sukul, Springer, 2004, ISBN 1402021550
  32. ^ British Homeopathy During Two Centuries, Peter Morrell, 2000
  33. ^ Flu Symptoms? Try Duck: Why sales of homeopathic products are soaring today, Dan McGraw, U.S. News & World Report, February 17, 1997.
  34. ^ The Faces Of Homeopathy - An Illustrated History Of The First 200 Years, Julian Winston, Great Auk, New Zealand, 1999, pp.87-102, ISBN 0-473-05607-0
  35. ^ GLOSSARY OF HOMEOPATHIC TERMS, Peter Morrell, in British Homeopathy During Two Centuries
  36. ^ Therefore, the decimal and centesimal scales are logarithmic scales, somewhat similar to the pH scale in chemistry for measuring the concentration of hydrogen ions in a solution, and therefore the acidity of the solution.


See also[edit]

[[Category:Scales]] [[Category:Homeopathy]]

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