I was curious what the old fellas had to say (or not say) about the use of potato in soap and found this tidbit. I get the strong impression from this excerpt that the potato flour actually consumes some lye. The comments in brackets [] and the bolding are mine. Here goes:
Potato-flour is to a considerable extent used for filling soft soaps [soap made with mostly or all KOH]. It does not swell much either in cold water or in an alkaline solution, but when caustic lye is added it is at once converted into a smooth, stiff paste. It possesses also the property of fixing much moisture and making soap filled with it more compact and durable. As, however, the resulting product is more turbid [cloudy], only inferior qualities of soap are filled with potato-flour.
Filling with this material is effected as follows: A large vat of soft wood is placed near the kettle for the reception of the filling material. Pour into the vat 1 part of water or potash solution of 5° to 8° B., stir in 1 part of potato-flour and finally crutch in 1 part of silicate of soda. The latter may be omitted using in place of it 1 part of potato-flour stirred into 2 parts of potash solution of 10° to 12° B., or into potassium chloride solution.
[B. stands for Baume. It is a measure of the density (heaviness) of a solution. In this context, a higher degree Baume means the lye solution is stronger or more concentrated.]
Add to the filling material thus prepared, whilst stirring vigorously, a sufficient quantity of the finished soap from the kettle to form a dissolved creamy mass and then thoroughly crutch it into the soap in the kettle. The soap, after the filling has been added becomes soft, viscid [thick] and long [superfatted], and has again to be fitted or shortened, this being effected with caustic lye of 27° to 30° B.
[To "fit" the soap or to make it "sharp" to the tongue or "short" means to make the soap slightly lye heavy. This was a way to ensure the soap was fully saponified using the soapmaking methods of the day. If the soap was to be a toilet soap, it would be finished at the end to make a more neutral soap. Otherwise most soap was finished and sold slightly lye heavy. This helped prevent rancidity.]
Add of this lye, whilst crutching [mixing] vigorously, a sufficient quantity to impart the shortness [slight lye excess] required and a sample upon the glass appears full and round as well as firm and shows the required sharpness [zap]; for 1 part potato-flour about 1 part of caustic potash [KOH] lye is generally allowed for fitting.
The operation of filling is frequently, also carried on as follows: About the quantity of lye required for fitting is crutched into the finished soap previous to adding the filling material, the soap acquiring thereby an almost torn appearance. The filling, however is more readily and better absorbed, and the soap presents a more uniformly smooth appearance.
The soapmaker's handbook, Carl Diete, 1912.