The United States brought an appeal against the Mayor, Aldermen and Inhabitants of the Cities of Philadelphia and New Orleans. The case centered around a dispute over whether or not certain lands were subject to taxation by either party. The Supreme Court ruled that while Congress had exclusive jurisdiction over navigable waters within state boundaries, it did not have authority to tax those areas as they are owned by the states themselves. Furthermore, any taxes imposed on these areas must be done so with consent from both parties involved in order for them to be valid. This ruling established precedent for future cases involving disputes between federal and state governments regarding land ownership rights and taxation powers.

In this case, the United States argued that they had a right to build and maintain lighthouses in Philadelphia and New Orleans. The Mayor, Aldermen, and Inhabitants of those cities disagreed with the government's position. They argued that since these lighthouses would be built on land owned by them or their citizens, it was an unconstitutional taking of private property without just compensation. Chief Justice Taney wrote a dissenting opinion in which he agreed with the respondents' argument. He stated that if Congress could take away rights from individuals without providing adequate compensation for them then no one’s property was safe from being taken away at any time for any purpose deemed necessary by Congress. He further noted that while there may have been some benefit to society as a whole from having lighthouses in these two cities, it did not outweigh the individual rights of those affected by such action taken by Congress without due process or just compensation for their losses.