A number of observed cases are reported of doubly logarithmic rectilinearity with least square fits (1) in the phenomenon of brand-names (including trade- names) of manufacturers and distributors in the United States (1946) in reference to (a) the varying number of concerns that use the same brand-name, (b) the varying number of brand-names in cities of origin of different population sizes, (c) the varying preferences of families for different brands of like commodities, (d) the varying number of different items under like brands; and (2) in the closely related phenomenon of (a) the varying number of different manufacturers of like goods, (b) the varying number of factories in cities of different population size, and (c) the varying number of manufacturers with different numbers of warehouses and other subsidiary organizations.