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late 14c., "hounds placed along a line of chase," from Middle French relai "reserve pack of hounds or other animals" (13c.), from Old French relaier "to exchange tired animals for fresh," literally "leave behind," from re- "back" (see re-) + laier "to leave" (see delay (v.)). The etymological sense is "to leave (dogs) behind (in order to take fresh ones)." Of horses, 1650s. Electromagnetic sense first recorded 1860. As a type of foot-race, it is attested from 1898.
c.1400, "to set a pack of (fresh) hounds after a quarry;" also "change horses," from Old French relaiier, from relai (see relay (n.)). Related: Relayed; relaying.