The Ship Potomac case was a dispute between Simpson, the claimant and Baker, the libellant. The Supreme Court had to decide whether or not Simpson was entitled to compensation for his services as master of the ship. In order to make this determination, they looked at both parties’ claims and evidence presented in court. They found that while there were some discrepancies in what each party claimed regarding their respective roles on board the vessel, ultimately it was determined that Simpson did indeed provide valuable service as master of The Ship Potomac and should be compensated accordingly. Furthermore, since he had been hired by an agent acting on behalf of Baker (the libellant), it was ruled that any payments due would come from him rather than from Simpson himself. This ruling set a precedent for future cases involving disputes over payment for services rendered aboard vessels owned by private individuals or companies.

In the case of The Ship Potomac, Simpson, Claimant; Baker, Libellant (1862), Justice Nelson delivered a dissenting opinion. He argued that the court should have accepted the testimony of witnesses who testified that they had seen Simpson in possession and control of the vessel prior to its seizure by Baker. Furthermore, he contended that there was no evidence presented to prove any agreement between Simpson and another party for use or possession of the ship at any time before it was seized by Baker. In addition, Justice Nelson noted that even if such an agreement existed between them prior to seizure it would not be sufficient grounds for denying Simpson's claim as owner since his title had already been established through legal documents which were produced in court. Finally, he concluded with a statement affirming his belief that "the claimant is entitled to recover."