Eldridge v. Hill was a United States Supreme Court case that addressed the issue of whether a state court could issue a writ of mandamus to compel a county court to issue a deed. The case was brought by the plaintiff, Eldridge, who sought to compel the defendant, Hill, to issue a deed for a tract of land that Eldridge had purchased from Hill. The Supreme Court held that the state court did not have the authority to issue a writ of mandamus to compel the county court to issue a deed. The Court reasoned that the writ of mandamus was a remedy of last resort and could not be used to compel a court to perform a ministerial act. The Court further held that the issuance of a deed was a ministerial act, and thus the state court did not have the authority to issue a writ of mandamus to compel the county court to issue a deed. The Court's decision in Eldridge v. Hill established that a state court does not have the authority to issue a writ of mandamus to compel a county court to issue a deed. This decision has been cited in numerous subsequent cases and has become an important precedent in the area of mandamus law.

Justice Field delivered the dissenting opinion in Eldridge v. Hill, arguing that the court should not have reversed the decision of the Supreme Court of California. He argued that under a long-standing rule established by prior cases, when a state court has decided an issue involving both federal and state law, it is binding on all other courts unless there is some clear error or misapplication of either federal or state law. In this case, he found no such error and therefore believed that the ruling from California's highest court should stand as final. Furthermore, Justice Field noted that even if there were errors in applying either federal or state laws to this case, they would be minor ones which could easily be corrected without reversing any decisions made by lower courts. Ultimately he concluded that since no substantial errors had been committed by any party involved in this dispute and since it was within California's jurisdiction to decide matters regarding its own citizens' property rights; then their decision should remain undisturbed at least until Congress chose to intervene with legislation specifically addressing these issues.