The Rio Grande case was a dispute between the United States and Mexico over the boundary between the two countries. The case was heard by the United States Supreme Court in 1876. The dispute centered around the Rio Grande River, which was the boundary between the two countries. The United States argued that the boundary should be the middle of the river, while Mexico argued that the boundary should be the southern bank of the river. The Supreme Court ultimately sided with the United States, ruling that the boundary should be the middle of the river. The Court reasoned that the Rio Grande had been the boundary between the two countries since the Treaty of Guadalupe Hidalgo in 1848, and that the boundary should remain the same. The Court also noted that the middle of the river was the most practical boundary, as it would be easier to maintain and enforce. The Court's decision was a major victory for the United States, as it established the boundary between the two countries and prevented any future disputes. The decision also established a precedent for future boundary disputes between the United States and other countries.

In the dissenting opinion of The Rio Grande, Justice Field argued that Congress had no authority to grant a right-of-way for a railroad across public lands. He noted that the Constitution did not give Congress any power to dispose of public lands and thus it could not authorize such an action. Furthermore, he stated that even if Congress had some implied power in this area, it was limited by the terms of its grants which must be strictly construed. In his view, granting a right-of-way would amount to disposing of public land and therefore exceeded Congressional authority under both express and implied powers. As such, Justice Field concluded that the lower court's decision should have been reversed as there was no legal basis for granting a right-of way across public land without congressional authorization or approval from other relevant authorities.