Yeah, wood ash and fat was the old way of making soap, and if you got the proportions wrong you'd have caustic soap. Ivory was different because they got a chemist to measure the alkalinity of the caustic they were buying so as to adjust the amount appropriately. Cincinnati was a big hog slaughtering place so hog fat was cheap. The story is that a worker went off for lunch and left the pot stirring too long and it whipped air into the soap, and people started asking for the soap that floats, confusing that with purity. The ad claim of 99 44/100ths was one of the early advertising efforts in the US.