In the case of New Mexico v. Texas in 1927, the U.S Supreme Court was tasked with resolving a dispute over territorial boundaries between these two states. The disagreement arose from differing interpretations of an 1850 Congressional Act which established Texas's western and northern borders when it was admitted to the Union. The boundary line had been defined as running along the course of Rio Grande River, but changes in its channel caused confusion about where exactly this border lay. New Mexico claimed that gradual shifts in river’s course did not alter their shared boundary while Texas argued that any change should be reflected in adjusted state lines. The court ruled against New Mexico by applying principles from international law regarding riparian boundaries (those formed by rivers). It held that if a river serving as a boundary changed gradually through natural processes (accretion), then the political border would move accordingly; however, if such alteration happened suddenly due to events like floods or avulsion, then original boundary would remain unchanged despite physical relocation of riverbeds. This decision clarified how geographical changes could impact state borders and set precedent for future cases involving similar disputes.

In the dissenting opinion for New Mexico v. Texas, Justice Holmes argued that the boundary between Texas and New Mexico should be determined by a river's course at the time of Texas' admission to the Union in 1845, not its current location. He believed that changes in a river’s course due to natural causes such as erosion or flooding did not alter state boundaries established by Congress. Furthermore, he contended that if any adjustments were necessary due to significant shifts in geography over time, they should be made through legislation rather than judicial decisions. This perspective was rooted in his belief that courts should avoid making political decisions whenever possible and leave them instead to legislative bodies more equipped for such tasks.