I'm miserable with a cold, so I'm digging into this question tonight to distract myself from my runny nose and plugged up ears. Ugh....
Anyways, ammonia -- or ammonium hydroxide (NH4OH) -- is a base just like potassium hydroxide (KOH) and sodium hydroxide (NaOH). It will be happy to just politely react with fats to make ammonia-based soap. Unfortunately, no explosions are likely occur during the process, if you're looking for thrills and chills rather than soap.
Ammonium soaps are even more water soluble than potassium soaps, so this recipe should make an easy lathering bar, especially with the added sugar. The borax will neutralize excess lye, so including this ingredient makes the recipe somewhat similar to liquid soap recipes based on Catherine Failor's methods where borax is used to neutralize excess lye. The washing soda will act as a water softener.
Household cleaning ammonia is a solution of ammonia, water, and sometimes detergent. The MSDS I found for one product says this stuff contains about 5% ammonia, so only about 12 grams in every cup (236 g) of household ammonia is actually NH4OH -- not much.
So, okay, I ran this through my personal
soap calculator after modifying the calculations to handle these two lyes (NaOH and NH4OH).
I assumed the "grease" called for would be bacon fat (aka lard) with an NaOH saponification value of 0.140. A mix of lard and beef tallow or all tallow would also work fine, because tallow is pretty close to lard with a SV of 0.142. You're on your own if you want to substitute other fats, especially coconut, which has a much higher SV of 0.192.
Turns out the basic recipe is pretty well figured out -- 6 lb (2724 g) "grease", 1 cup 5% NH4OH solution (12 g NH4OH + 224 g water), and 13 oz (369 g) NaOH. The superfat is
about 4% (5/11/14 correction: I originally wrote 0% superfat, but later rechecked my numbers), but the borax will neutralize up to 32 g of excess NaOH, so that is your insurance against the soap being lye heavy.
The water called for in the OPs recipe -- 1/2 cup hot water, 2 pints cold water, and the water in the 1 cup of ammonia -- totals about 5 1/2 cups (1286 g). All that liquid makes a 22% solution of NaOH in water, which is low by today's standards. A "full water" recipe (28% NaOH solution) would need only about 4 cups (942 g) of water.
Bottom line -- the recipe could be tweaked a bit to reduce the water, but it should work fine as written. I don't know that I'd count on it being a luxurious bath and body bar -- what with the washing soda and all -- but it should lather nicely, clean well, and be safe for household use.
Edit: the ammonia won't smell after it's reacted into soap.
Another edit: These are "the numbers" from my recipe calculator (not SoapCalc) based on 100% lard as the fat in the recipe. Not too much bubbly lather, but the ammonia and sugar will help that issue. It otherwise looks like the soap would be mild and longlasting with lots of creamy lather.
Hardness (Lau-Myr-Palm-Ste) 42%
Cleansing, solubility (Lau-Myr) 1%
Long lasting (Palm-Ste) 41%
Conditioning (Oleic-Lino-Ric) 52%
Bubbly (Lau-Myr-Ric) 1%
Creamy (Palm-Ste-Ric) 41%
Saponification (INS) 139%
And yet another edit: The recipe comes from the days before stick blenders. The unusually large amount of water would have made it easier to make this soap with just hand stirring.
To explain -- Fat is immiscible (doesn't want mix) with plain water or lye solution -- fat just wants to float on top of the watery layer. If you didn't stir soap batter at all, the only place where soap would form is right at the interface where the fat touches the lye. Once enough soap forms at this interface, the two layers would be separated by a thin layer of soap and saponification would pretty much stop.
So there are two reasons for mixing soap batter -- (1) to break up the fat and lye into globs to create more surface area so the fat and lye can react better and (2) to keep the bits of newly forming soap from interfering with this happy union.
Stick blenders can break the fat into tiny globs that float around in the lye solution. This creates a LOT of surface area between the fat and lye solution so the fat and lye can saponify more easily. That's why saponification is so much faster when one uses a stick blender versus just stirring with a whisk, spoon, or spatula. A whisk mixes more efficiently than a spoon or spatula, but it's still not in the same league as a stick blender.
Getting back to why a watery lye solution works better for
hand mixing soap compared with a concentrated lye solution -- A concentrated lye solution is much denser (heavier) than the fat. If you mix soap by hand, a concentrated "heavy" lye will be much harder to mix with the much lighter fat due to the large density difference. If you really mix hard, you can get the two to temporarily blend together, but they won't stay mixed for long.
If the concentration of lye is less (more water for the same amount of alkali), the density of the lye will be more similar to the fat. That means the two will be easier to mix together into smaller bits and will stay mixed together for a bit longer. That means more saponification will happen and the faster the soap will emulsify. Once enough soap has formed, the mixture of the fat, lye, and soap will become stable. A soap maker could then add a more concentrated lye solution without problems.
