In this case, the Supreme Court of the United States was asked to decide whether a state court had the authority to issue a writ of habeas corpus to a prisoner held in a federal prison. The prisoner, William H. H. Miller, had been convicted of a federal crime and was being held in a federal prison in the state of Ohio. The state court had issued a writ of habeas corpus to Miller, ordering him to be released from prison. The Supreme Court held that the state court did not have the authority to issue the writ of habeas corpus. The Court reasoned that the writ of habeas corpus is a federal remedy, and that the state court did not have the power to interfere with the federal government's authority to imprison a person convicted of a federal crime. The Court also noted that the writ of habeas corpus is a remedy that is available only to persons who are in custody in violation of the Constitution or laws of the United States. Since Miller was being held in a federal prison pursuant to a valid federal conviction, the state court did not have the authority to issue the writ of habeas corpus.

In the case of United States v. Realty Company, a majority opinion was issued by the Supreme Court that held that when an individual has been convicted of a crime and sentenced to pay a fine, they are not allowed to use their property as collateral for payment. The dissenting opinion argued that this decision would be detrimental to those who have limited financial means and could lead them into further debt or even bankruptcy if they were unable to pay off their fines in full. Furthermore, it was argued that allowing individuals with limited resources access to using their own property as security against fines would provide them with more options than simply being forced into poverty due to inability to pay off such debts. Ultimately, the dissent concluded that while there may be some potential risks associated with allowing people access these types of arrangements, it should still remain an option available for those who need it most in order ensure justice is served fairly across all economic classes.