reciprocation (n.)

1570s, "existing on both sides, exclusive or interchangeable" (of duties, etc.), with -al (1) + stem of Latin reciprocus "returning the same way, alternating," from pre-Latin *reco-proco-, from *recus (from re- "back;" see re-, + -cus, adjective formation) + *procus (from pro- "forward," see pro-, + -cus). Related: Reciprocally.

From 1590s as "given, felt, or shown in return;" c. 1600 as "corresponding or answering to each other, mutually equivalent." The sense of "moving backward and forward, having an alternating back and forth motion" (c. 1600) is obsolete. The noun meaning "that which is reciprocal" (to another) is from 1560s. In scientific and mechanical uses, reciprocating, reciprocative (1804), and reciprocatory (1826) have been tried.

1610s, "to give and return mutually," a back-formation from reciprocation, or else from Latin reciprocatus, past participle of reciprocare "rise and fall, move back and forth; reverse the motion of," from reciprocus "returning the same way, alternating" (see reciprocal). Sense of "cause to move back and forth" is from 1650s; intransitive sense of "move backward and forward" is from 1670s. Meaning "to give or do in response, act in return or response" is from 1820. Related: Reciprocated; reciprocating.