Calcium soaps are pretty much insoluble in water and would not be useful as a "soap", in the sense that you and I think of soap. There has to be a secondary reaction going on in this recipe to make a useful sodium soap, but I'll let you and Robert debate that issue.
The old makers didn't do lime saponification this way -- they did a multi-step process as I described earlier to make a lime soap, decompose the lime soap with a strong acid, and use the resulting fatty acids to make a sodium soap. Here is an excerpt from one soap making manual of the day:
"While by the term saponification as used in soap making it is inferred that this is the combination of caustic alkalis with the fatty acids to form soap, this term is by no means limited to this method of saponification, as there are various other methods of saponifying a fat. The chemical definition of saponification is the conversion of an ester, of which glycerides are merely a certain type, into an alcohol and an acid or a salt of this acid.
"Thus, if we use caustic alkali as our saponifying agent for a fat or oil, we obtain the sodium or potassium salt of the higher fatty acids or soap and the alcohol, glycerine. On the other hand, if we use a mineral acid as the saponifying agent, we obtain the fatty acids themselves in addition to glycerine....
[The author goes on to explain that soap making industry sometimes made its profit on the sale of the recovered glycerin, so making soap without recovering the glycerin was not a profitable venture. Lime saponification and other forms of saponification were developed to convert fats into fatty acids and glycerin. This was done, not so much because these processes made better soap, but because the glycerine could be more easily recovered and purified from the fatty acids than from the soap.]
"LIME SAPONIFICATION. The saponification in an autoclave is usually carried out by introducing the fats into the autoclave with a percentage of lime ... together with water. If the fats contain any great amount of impurities, it is first necessary to purify them either by a treatment with weak sulfuric acid ... or by boiling them up with brine and settling out the impurities from the hot fat.
"To charge the autoclave ... the required quantity of unslaked lime, 2 to 4 per cent. of the weight of the fat, is run in with the molten fat, together with 30 per cent. to 50 per cent. of water. While 8.7 per cent. lime is theoretically required, practice has shown that 2 per cent. to 4 per cent. is sufficient. The digestor, having been charged and adjusted, steam is turned on and a pressure of 8 to 10 atmospheres maintained thereon for a period of six to ten hours.
"When the saponification is completed the contents of the autoclave are removed... The mass discharged from the digestor separates into two layers, the upper consisting of a mixture of lime soap or "rock" and fatty acids, and the lower layer contains the glycerine or "sweet" water.
"The calculated amount of sulfuric acid to decompose the lime "rock" is then added, and the mass agitated until the fatty acids contained therein are entirely set free. Another small wash is then given...
"Due to the difficulties of working the autoclave saponification with lime, decomposing the large amount of lime soap obtained and dealing with much gypsum formed thereby which collects as a sediment and necessitates cleaning the tanks, other substances are used to replace lime. Magnesia, about 2 per cent. of the weight of the fat, is used and gives better results than lime. One-half to 1 per cent. of zinc oxide of the weight of the fat is even better adapted..."
Source: E. G. Thomssen. Soap-Making Manual: A practical handbook on the raw materials, their manipulation, analysis and control in the modern soap plant. 1922. From Project Gutenberg,
www.gutenberg.net.
