The U.S. Supreme Court case State of Arkansas v. State of Tennessee in 1917 revolved around a boundary dispute between the two states. The disagreement was over an area known as the "Island No. 37" on the Mississippi River, which had shifted course due to natural causes, causing confusion about state lines and jurisdictional boundaries. The court ruled that despite changes in the river's course, original boundaries set by treaties and agreements should be maintained unless explicitly changed by Congress or mutual agreement between states involved - thus upholding previous rulings regarding avulsion (sudden change in land caused by flood or channel movement). Therefore, even though Island No. 37 was physically located on Tennessee’s side after the shift, it remained under Arkansas’ jurisdiction because there hadn't been any legal alterations to state borders.

In the dissenting opinion for the case of State of Arkansas v. State of Tennessee, Justice Holmes disagreed with the majority's decision to use an avulsion theory in determining state boundaries. He argued that this approach was inconsistent with previous rulings and did not accurately reflect how rivers naturally change course over time. Instead, he believed that a gradual shift or accretion should be used as it better represents natural changes in river courses and would result in more stable state borders. Furthermore, he contended that using avulsion as a basis could lead to arbitrary results since it depends on sudden shifts which are unpredictable and can vary greatly in magnitude. Therefore, according to him, adopting such an approach would create uncertainty about where exactly state lines lie along rivers.