[2] Acheson was nominated by President Rutherford B. Hayes on January 6, 1880, to a seat on the United States District Court for the Western District of Pennsylvania vacated by Judge Winthrop Welles Ketcham.

He was confirmed by the United States Senate on January 14, 1880, and received his commission the same day.

His service terminated on February 9, 1891, due to his elevation to the Third Circuit.

[3] Acheson was nominated by President Benjamin Harrison on January 23, 1891, to a seat on the United States Circuit Courts for the Third Circuit vacated by Judge William McKennan.

Acheson was assigned by operation of law to additional and concurrent service on the United States Court of Appeals for the Third Circuit on June 16, 1891, to a new seat authorized by 26 Stat.