In the 1932 case Vermont v. New Hampshire, the Supreme Court was asked to resolve a border dispute between these two states. The disagreement arose from differing interpretations of a decree issued by King George III in 1764 that established New Hampshire's western boundary as the west bank of the Connecticut River. However, over time, changes in river flow caused confusion about where exactly this boundary lay. Vermont claimed ownership of islands and land on both sides of the river while New Hampshire argued for its jurisdiction up to low-water mark on Vermont’s side based on historical usage rights and practices. The Supreme Court ruled in favor of New Hampshire stating that it had jurisdiction up to ordinary low-water mark along Vermont's shore except where otherwise agreed upon or prescribed by existing treaties or statutes; thus confirming that all islands within Connecticut River belong to New Hampshire unless specifically allocated to Vermont through previous agreements.

In the dissenting opinion for Vermont v. New Hampshire, Justice Stone disagreed with the majority's decision to grant New Hampshire jurisdiction over the Connecticut River up to its west bank, effectively giving it control of all islands within that river. He argued that historical evidence and past legal decisions did not support this ruling. Instead, he believed they indicated a shared jurisdiction between Vermont and New Hampshire over these waters and islands. He pointed out that both states had exercised concurrent authority in this area without dispute for many years prior to this case being brought before the court. Furthermore, he contended that there was no compelling reason or necessity presented by either state which would justify altering their long-standing arrangement regarding control of these lands and waters.