The Bancroft rule in colloidal chemistry states: "The phase in which an emulsifier is more soluble constitutes the continuous phase." This means that water-soluble surfactants tend to give oil-in-water emulsions and oil-soluble surfactants give water-in-oil emulsions. It is a general rule of thumb, still used, but regarded as inferior to HLD theory (Hydrophilic Lipophilic Difference), which takes many more factors into consideration.
It was named after Wilder Dwight Bancroft, an American physical chemist, who proposed the rule in the 1910s.