This is about homeopathic medicine. They have a process called "potentizing", during which the "mother tincture" (the actual medicinal substance in alcohol) is diluted with water and then stirred or shaken so as to create vortices which are supposed to attract cosmic forces inside, increasing the curative effect of the mixture while from a mainstream scientific point of view there's hardly anything left but water to have an effect.
Anyway, here's What wikipedia says:
"[Founder of homeopathy] Hahnemann created the centesimal or "C scale", diluting a substance by a factor of 100 at each stage. [...] 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."
And de.wikipedia:
"Neben der bekanntesten D-Potenzierungsreihe (1:10) gibt es noch die C-Reihe (1:100) und die LM- oder Q-Reihe (1:50000)."

I haven't got into touch with homeopathy terribly often so others may judge better than I can, but as far as I can tell the "C" scale is the established one in the English speaking world (at least in India). So you might want to do the maths and use this scale instead of just providing the translation.


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Note added at 33 mins (2008-04-13 10:52:09 GMT)
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See especially the table in the paragraph "Potenzierung" in the German article.

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Note added at 1 hr (2008-04-13 11:28:56 GMT)
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You're welcome and you're right. Dil D 3 is 1:1000 dilution, i. e. the initial concentration divided by 10 to the power of 3 (10*10*10=1000). To express this on the Centesimal scale, you have to figure out which power of 100 equals 1000, i. e. the logarithm to the base 100 of 1000 which is indeed 1.5 (excel told me so).

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Note added at 2 hrs (2008-04-13 12:25:11 GMT)
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Actually, the idea of converting the scales mathematically may be somewhat unappropriate to the process described by scale and number. Practitioners of homeopathy may see a difference between potentizing a tincture once with a hundred times its volume of water or potentizing it twice with only a tenfold dilution at each step.
The .5 on the C scale at least seems a bit strange: I suspect they either stick with tenfold dilutions or hundredfold ones, but n.5C would mean a sequence of both or a different ratio altogether (in our case 10 followed by 100 or 100 followed by 10 or 1000 right away, which would be the "millenial" M scale).

"Homeopathic dilutions are either made on the C scale, where 99 parts of water are added to one part of the medicine for each dilution, or the X scale, where 9 parts of water are added to one part of medicine for each dilution"
http://homeopathy.inbaltimore.org/faq.html

"Depending on your condition, a doctor may prescribe a dilution of X (decimal), C (centesimal), or M (millennial). M is the strongest and an extension of the C scale"
http://hmedicine.com/homeopathy/information/faq.php

So at the end of the day, "X" seems to be the answer ("D" from Latin "decem"="ten", I suppose, and "X" is the Roman numeral for ten, with "X" appearing to be more widespread).
If indeed the "Dil D" scale is applied to a substance that has been potentized the decimal way. The fact that most instances of "Dil D" are even numbers makes me wonder whether they actually potentized using the centesimal scale and then just converted mathematically.