The U.S. Supreme Court case State of Arkansas v. State of Mississippi in 1920 revolved around a territorial dispute between the two states concerning the boundary line along their shared portion of the Mississippi River. The controversy arose due to changes in the river's course over time, which led to confusion about where exactly the border was located according to an 1836 act admitting Arkansas into Union as a state and defining its boundaries. The court ruled that despite shifts in geography, historical borders should be maintained unless there is clear evidence that both parties intended for them to change with alterations in physical landmarks like rivers. Therefore, it upheld Arkansas' claim on disputed territory based on original boundaries defined by Congress at its admission into Union rather than current geographical realities shaped by natural forces.

In the dissenting opinion for the case of State of Arkansas v. State of Mississippi, Justice Holmes disagreed with the majority's decision to deny Arkansas' claim over a disputed territory along their shared border. He argued that historical evidence and past legal precedents supported Arkansas' claim to this land, which had been altered by changes in the course of the Mississippi River. According to Holmes, these shifts should not affect state boundaries established at earlier times when rivers served as natural demarcations between states. He believed that such an interpretation was consistent with international law principles and would ensure stability in interstate relations by preventing frequent boundary disputes caused by river movements. Furthermore, he contended that denying Arkansas’ claim could potentially encourage other states to make similar territorial claims whenever rivers change their courses naturally or due to human intervention.