In the case of New Mexico v. Texas in 1927, the Supreme Court was asked to resolve a dispute between the two states over their shared border along the Rio Grande River. The controversy arose when changes in the river's course resulted in land that was once part of Texas becoming geographically located within New Mexico. The court had to determine which state held jurisdiction over this territory and its inhabitants. The Supreme Court ruled in favor of Texas, stating that despite shifts in geography due to natural causes like flooding or erosion, established boundaries between states remain fixed at their original location as determined by Congress upon each state’s admission into Union. Therefore, even though certain lands were now physically on New Mexico's side of Rio Grande due to river movement, they remained under legal jurisdiction and sovereignty of Texas because they were originally part of it when borders were set.

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 1850 federal statute rather than an 1891 survey. He believed that the Rio Grande River's shifting course did not alter the states' boundaries as established by Congress in this earlier law. The majority decision to uphold the validity of an inaccurate survey over a Congressional act was viewed as problematic by Holmes because it undermined federal authority and created unnecessary confusion about state borders. Furthermore, he expressed concern that this ruling could set a dangerous precedent for future cases involving interstate disputes or territorial claims.