The Rio Grande case was a dispute between the United States and Mexico over the Rio Grande River. The United States argued that the Rio Grande was the boundary between the two countries, while Mexico argued that the boundary was the Nueces River. The Supreme Court ultimately sided with the United States, ruling that the Rio Grande was the boundary between the two countries. The Court based its decision on the Treaty of Guadalupe Hidalgo, which was signed in 1848 and ended the Mexican-American War. The treaty stated that the boundary between the two countries was the Rio Grande River. The Court also noted that the United States had long recognized the Rio Grande as the boundary, and that Mexico had never objected to this interpretation. The Court also noted that the Rio Grande was a more natural boundary than the Nueces River, as it was more easily navigable and had been used as a boundary for centuries. The Court concluded that the Rio Grande was the boundary between the two countries, and that the United States had the right to use the river for navigation and other purposes.

The Rio Grande case was a dispute between the United States and Mexico over the boundary of Texas. The Supreme Court held that, based on an 1848 treaty between the two countries, the border should be set at the middle of the Rio Grande River. Justice Field dissented from this opinion, arguing that it would lead to serious consequences for both nations. He argued that setting such a definitive line could cause disputes in other areas where there were no clear boundaries or treaties in place. Furthermore, he noted that if one nation violated its obligations under this decision then it would have little recourse since any violation by either party would result in war with each other due to their inability to settle differences peacefully through diplomatic channels. Finally, Field asserted that Congress had not authorized such a definitive boundary and thus it was beyond what they had intended when ratifying said treaty back in 1848.