The U.S. Supreme Court case State of Arkansas v. State of Mississippi in 1919 revolved around a territorial dispute between the two states concerning their shared border along the Mississippi River. The conflict arose due to changes in the river's course over time, which led to uncertainty about where exactly the boundary lay. The court was asked to determine whether certain lands were part of Arkansas or Mississippi based on historical documents and evidence presented by both sides. Ultimately, it ruled that despite shifts in the river’s path, original boundaries established at statehood should be maintained unless there is clear proof that they intended for such alterations to affect borders; thus favoring Arkansas' claim.

In the dissenting opinion for the case of State of Arkansas v. State of Mississippi, Justice Holmes disagreed with the majority's decision to appoint a special master to determine boundary disputes between states. He argued that such matters should be resolved through negotiations and agreements between states rather than by federal intervention. Furthermore, he contended that historical claims and usage should play a significant role in determining state boundaries instead of relying solely on technical interpretations of geographical features or survey errors. In his view, this approach would better respect state sovereignty and promote harmonious relations among states.