"...The finer soaps are perfumed by the cold [process] method; the soap is shaved down to thin slices, and the essential oil kneaded into and mixed with it by special machinery, after which it is formed into cakes by pressure in suitable moulds. The greater quantity of high-class toilet soaps are now made by a milling process. A high class soap, which after framing contains about 30% of water, is brought down to a water content of 11-14% by drying in chambers through which warm air is circulated. The soap is now milled in the form of ribbons with the perfume and colouring matter, and the resulting strips are welded into bars by forcing through a heated nozzle. The bars are then cut or moulded into tablets, according to the practice of the manufacturer...."
Source:
https://web.archive.org/web/20130123080239/http://www.1911encyclopedia.org/Soap
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"...A milled soap is a dried, grained soap reduced to laminae [thin sheets] and made compact by pressure. Such a soap may be greatly improved by the application of perfume and color.
Soap intended to be milled may be made by either the cold or semi-boiled process...
"The early manufacture of milled soap was naturally very primitive, the dried shavings being reduced and mixed with perfume by means of a mortar and pestle and the agglomerated mass moulded into bars by the pressure of the hands. Subsequent mechanical devices have not departed from this simple procedure.
"Milled soap was first made in the United States in Philadelphia in 1844 by Jules Haul, a Frenchman, who in that day kept a shop for the sale of imported soaps and perfumes. He began making toilet-soaps in a small way in the rear part of his store with a double iron roll sugar-mill and an old screw-press, both worked by hand. The dried chipped soap was passed between the rolls a number of times until homogeneous. It was then shaped by hand with a wooden paddle to as near the dimensions of the die as possible, after which the bars were laid away on racks for two or three weeks until well dried. They were then pressed by means of the screw-press into a plain die without lettering, after which they were again dried for two or three weeks, and were finally pressed in a die with lettering. It required a period of four or five weeks before the soap was ready for sale.
"This method of manufacture continued until 1847, at which time A. W. Harrison, of Philadelphia, imported from France a set of toilet-soap machinery which consisted of a two-roll granite mill and a plodder....
"In the drying of milled-soap base, the amount of water is reduced almost one-half, viz., to 15 to 18 per cent. This proportion varies according to the stock used and the quality of soap desired, being determined to a large degree by the way in which the soap behaves under the subsequent mechanical treatment in the mill and plodder. Initial drying is to prepare the soap for chipping, after which with the large extent of drying surface proper conditions for milling are readily obtained....
"With the soap in proper condition to mill it may be mixed with perfume and coloring-matter... The toilet-soap mill consists essentially of a substantial iron frame with bearings in which are mounted shafts carrying polished and non-absorbent cylindrical granite-crushing rolls... The purpose of milling is to reduce the dried chips with perfume and coloring-matter, or talc if used, to a perfectly homogeneous mass. The chips may be passed through the mill once and then mixed with perfume and coloring-matter, or they may be mixed before milling... The soap is removed from the last roll [of the mill] in thin ribbons by means of serrated knife-edges adjusted against the roll.... The number of millings usually given the soap depends upon its quality, ease of incorporating the ingredients, and number of the rolls; for cheaper grades 3 to 4 millings suffice, while for the finest grade 7 to 8 millings are common....
"[T]he soap as it comes from the mill [is] in long translucent ribbons of the thinness of paper. [It] is transferred directly to the hopper of the plodder [a piece of equipment that functions as a combination mixer and auger], from which, under the action of the compressive force of the screw, it is discharged in a compact, continuous bar which is cut into sections and which is again reduced to cakes of the dimensions required by pressing...."
Source: Modern Soaps, Candles, and Glycerin. L.L. Lamborn. 1920. This book is available through the Internet Archive or Google Books.
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"...In 1904, at the St. Louis World's Fair, a plodder and a new soap mill from France were exhibited. Both machines were purchased by Colgate, and Cashmere Bouquet became a milled soap. But it was not known until May 1926, when an advertisements for Cashmere Bouquet appeared in the Ladies Home Journal. The heading stated, “Now this ‘hard milled’ soap, used every day, keeps skin young and lovely.” In the text, “hard milling” was explained in great detail: “It is ‘hard milled’ which means that it is put through special pressing and drying processes that give each cake an almost marble firmness. It is not the least bit squadgy. This special hardness is what makes it safe.”
"Roll mills are used to refine and homogenize soaps.... There is no “soft” or “hard milling”. Consumers do not really know the meaning of “hard milled”, “French milled”, or “triple milled”, but these claims connote quality and long lasting soap, so they are still used....
"Soap is not only mixed/ milled and refined in order to evenly distribute perfumes, colour etc. It is mixed/ milled and refined in order to change the crystal phase structure and to give soap with better user properties...."
Source: Soap Manufacturing Technology. Luis Spitz, editor. 2009.
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Words in brackets [ ] are mine.
These sources, both old and modern, make it pretty clear that a "real" milled soap is
not made by raising the water content and melting the soap, as is commonly done with rebatching.