The U.S. Supreme Court case State of Arkansas v. State of Tennessee in 1917 was a boundary dispute between the two states over an area known as the "Island No. 37" on Mississippi River, which had shifted its course due to natural causes and moved this island from Tennessee's side to Arkansas'. The court ruled that when a river forming a boundary between states changes its course gradually through erosion and deposit (accretion), the boundary follows the changing course of the river; however, if it shifts abruptly by cutting across land (avulsion), then original boundaries remain intact despite any geographical relocation. In this case, since evidence showed that Island No. 37 was separated from Tennessee by avulsion rather than accretion, it remained part of Tennessee even though geographically it appeared closer to Arkansas after shift in river’s path.

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 event as a determinant for state boundaries. He argued that such a sudden change in river course should not be used to determine jurisdictional lines between states because it is unpredictable and arbitrary. Instead, he suggested that these borders should remain constant over time regardless of natural changes in geography. This would ensure stability and predictability in legal matters concerning interstate disputes about territory or resources. Furthermore, he contended that using avulsion events could potentially lead to unnecessary conflicts between states if they were forced to constantly renegotiate their boundaries following every significant shift in river courses.