In Arrowsmith v. Harmonizing, Administratrix & Others, the Supreme Court of the United States was asked to decide whether a state court had the authority to issue a writ of mandamus to a federal court. The case arose when the plaintiff, Arrowsmith, sought to have a writ of mandamus issued by the state court to the federal court in order to compel the latter to hear a case that Arrowsmith had filed in the federal court. The state court had issued the writ, but the federal court refused to comply. The Supreme Court held that the state court did not have the authority to issue a writ of mandamus to a federal court. The Court reasoned that the state court lacked the power to issue a writ of mandamus to a federal court because the federal court was a court of exclusive jurisdiction, and the state court did not have the power to interfere with the federal court's jurisdiction. The Court also noted that the writ of mandamus was an extraordinary remedy, and that the state court should not be allowed to interfere with the federal court's jurisdiction by issuing such a writ. The Court's decision in this case established that state courts do not have the authority to issue a writ of mandamus to a federal court. This decision has been cited in numerous subsequent cases, and it remains an important precedent in the area of federal court jurisdiction.

Justice Field delivered the dissenting opinion in Arrowsmith v. Harmonizing, Administratrix & Others. He argued that the majority had erred in their interpretation of a will and its subsequent codicil, which was at issue in this case. The main point of contention was whether or not certain property should be distributed according to the terms of the will or if it should pass under intestacy laws as provided by state statute. Justice Field argued that since there were no ambiguities present within either document, they must be interpreted together and given effect according to their plain meaning; thus he concluded that all property should have been distributed according to the terms set forth within both documents rather than passing through intestacy laws as determined by state statutes.