A quarter of a mile race.
1792. His time is employed in quarter races, cock-fights.Description of Kentucky, p. 12. (N.E.D.)
1795. The whole to conclude with the Poney Races; and Quarter Race.Advt., Gazette of the U.S., Nov. 23.
1836. In this year A Quarter Race in Kentucky, appeared in the N.Y. Spirit of the Times.
1853. Got a smart chunk of a pony thar. Yes, sir, hes some pumkins sure; offered ten cows and calves for him; hes death on a quarter [i.e., a quarter race.]S. A. Hammett (Philip Paxton), A Stray Yankee in Texas, p. 44.
1885. In North Carolina and the up-country of Virginia quarter-races were much esteemed . Quarter-courses usually consisted of two parallel paths, and were run by two horses at a time.E. Eggleston, Social Life in the Colonies, Century Mag., xxx. 397/2 (July). (N.E.D.)