Soaping is really just a big science (chemistry) experiment. Finding the combinations of ingredients that play well together to give the end result. Soap is really just a chemical reaction with the fats/oils.
Milk used as the liquid gives extra fats which most of us like (extra moisture). BTW- as Daisy can attest to, cow milk gives a much more moisture-rich soap because it is fattier. The name "goats milk" is trendy, but cow milk is where it's at.
Th tomato soap is made by puree tomatoes as the liquid. The tomato's sugar content with the cream/milk makes it creamy and lathery (made up word).
Thus concludes today's lesson
