If that's a Bates square, they must have copied Starrett's design, right down to the nut.
I copied this from a Worthpoint page. Unfortunately, it doesn't have a photo of the square.
Vintage Bates Mfg. Co 12 Combo Square Tough Find is a very unusual find, a Bates Mfg. Co 12 Combo square in good + condition, no issues at all aside from light pitting on one end of rule on one side
www.worthpoint.com
"Vintage Bates Mfg. Co 12" Combo Square Tough Find is a very unusual find, a Bates Mfg. Co 12" Combo square in good + condition, no issues at all aside from light pitting on one end of rule on one side. Very good aside from that. offers this brief history on this company, which was not around for too long.... " Founded as the Union Caliper Company in 1908, the business had been organized by Emory E. Ellis at Fitchburg, Massachusetts, for the purpose of making calipers and dividers for machinists. In 1911, the Union Caliper Company acquired the Indiana-based Hill Standard Tool Company and was moved to a larger site in Orange , Massachusetts. The combined operations occupied four times the floor space that had been available in the old location, and the purchase of Hill Standard Tool added thickness gages, tapes, and feeler gages to the lineup. A second operation, the Bates Manufacturing Company, a producer of steel rules, combination squares and hacksaw frames located in Fitchburg, was sold to Union Caliper Company on Nov. 21, 1913, for $5,000. John Clayton Bates , the founder of Bates Manufacturing , continued to supervise the operation after the buyout. In 1915, J.C. Bates moved to Orange to become manager of the Union Caliper Company; the measuring tool and hacksaw operations moved with him. With the operation making center punches, dividers, machine vises, hack saws, measuring tools, nail sets, lathe and planer accessories and add-ons for automatic screw machines, the company's original name no longer reflected its product line. In 1916, Emory E. Ellis and the directors of the Union Caliper Company changed the name of the business to the Union Tool Company. When Ellis died at age fifty-four on November 11, 1924, he left behind a growing company that was doing nicely. (By 1930, the Union tool Company was capitalized at $400,000 and had one hundred employees on payroll.) J.C Bates continued as the firm's manager. With Bates at the helm, measuring tools became increasingly important part of the Union Tool operation, and t is evidence that the company was supplying combination squares to Millers Falls well before the 1957 buyout. John Clayton Bates died on November 15, 1956—a year before the Millers Falls Company acquired Union Tool. "