"the middle of the afternoon," c. 1400, from mid (adj.) + afternoon. Earlier in the same sense was mid-overnoon (late 13c.).
Entries linking to mid-afternoon
mid adj.
"middle; being the middle part or midst; being between, intermediate," Old English mid, midd from Proto-Germanic *medja- (source also of Old Norse miðr, Old Saxon middi, Old Frisian midde, Middle Dutch mydde, Old High German mitti, German mitte, Gothic midjis "mid, middle"), from PIE root *medhyo- "middle."
By late Middle English probably felt as a prefix only, and now surviving in English only as a prefix (mid-air, midstream, etc.). Prefixed to months, seasons, etc. from late Old English. As a preposition, "in the middle of, amid" (c. 1400) it is from in midde or a shortened form of amid (compare midshipman) and sometimes is written 'mid.
afternoon n.
"part of the day from noon to evening," c. 1300, from after + noon. In 15c.-16c., the form was at afternoon; from c. 1600 it has been in the afternoon. As an adjective from 1570s. Middle English had also aftermete "afternoon, part of the day following the noon meal" (mid-14c.).