"pertaining to the system of weights and measures based on the meter," 1855, from French métrique, from mèter (see meter (n.2)). In this sense, metrical is attested from 1797. Metric system is attested by 1855.
"science of versification," 1760, from Latinized form of Greek he metrikē "prosody," plural of metron "meter, a verse; that by which anything is measured; measure, length, size, limit, proportion" (from PIE root *me- (2) "to measure"). Middle English had metrik "the branch of music which deals with measure or time" (late 15c.), from Medieval Latin metricus.