To Randall Halstead and other ­minority officers in the Boston Police Department, the story of Sergeant Horatio J. Homer serves as a beacon of hope and of the power of perseverance.

Homer, who in 1878 became the department’s first African-American officer, ushered in a new era in the city over a 40-year career. In the decade ­after his appointment, the force hired as many as a half-dozen additional black officers, in large part on his recommendation.