D.C. Police Sgt. Joseph A. Smith, 52, a veteran of 22 years on the force and an instructor at the department's police academy for nine years, died in a Columbia, S.C., hospital following a stroke. He was vacationing at the time.

He became an instructor at the academy in 1965, and taught classes in community relations, report writing, jvenile delinquency, and a specialty of his, a course dealing with the history and basic geography of the city of Washington.

Fellow officers remember him as an instructor who was a great favorite of the rookies. He took an interest in the problems and careers of his students and gained a reputation for communicating on a very human level with his charges.

Sgt. Smith had served as administrative sergeant in the police department's court liaison office in D.C. Superior Court since 1974.

He was a native of Fort Pierce, Fla., and moved to Washington in 1951. He was a resident of Seat Pleasant.

Sgt. Smith began his police career at the old second precinct in 1956. He became a sergeant in 1968.

He had attended Howard University and American University.

He was a lieutenant colonel in the Army Reserves.

Survivors include a sister, Bertha Smith, of Florence, S.C., and two brothers, Calvin J. and Edwin B., both of Fort Pierce.