Homeopathic Caesar Urine

Julius Caesar (100-44 B.C) lived 55 years, and assuming he urinated two liters every day, there should be approximately 40 cubic meters of water from his urine. Calculations I omit from here suggest that photosynthesis, the most likely method of breaking water molecules down in nature, has had a modest affect on this amount. Therefore we can approximate all that water has survived to this day and dispersed evenly on our planet during the past two millenia.

Dividing the 40 cubic meters with the total volume of all oceans we obtain that one molecule in every 3.6 * 10^15 today is genuine "chez Caesar". The strongest homeopathic medicines have been diluted up to 10^30, but 10^15 should already have a clear effect. Unfortunately I can't quite figure out what it should cure - megalomania, or perhaps laurel rash?

Another way of looking at this is to say that the Coca-Cola company has sold half a millilitre of Caesar's urine world-wide during its entire operation. I guess that's the "secret ingredient".