In the case of Last Chance Mining Company v. Tyler Mining Company, 1894, the U.S. Supreme Court was asked to resolve a dispute over mining rights in Montana. The two companies had overlapping claims on a rich vein of ore and both sought exclusive access to it. The lower court ruled in favor of Tyler Mining Company based on their earlier filing date for patent application with the General Land Office (GLO). However, Last Chance argued that they were entitled to mine because they discovered and developed the vein first. The Supreme Court upheld the decision by affirming priority right given by law to those who first discover valuable mineral deposits under public lands and comply with all legal requirements necessary for obtaining patents from government authorities such as GLO. It held that even though Last Chance may have been technically working on this particular vein before Tyler filed its claim, it did not follow proper procedure or meet statutory obligations required for securing mining rights which included making discovery known through an official record within reasonable time period after finding out about existence of minerals underneath land surface.

In the dissenting opinion for Last Chance Mining Company v. Tyler Mining Company, it was argued that the majority's decision failed to properly consider and apply established principles of mining law. The dissent asserted that the location notice filed by Tyler Mining Company did not meet statutory requirements, thus making their claim invalid from its inception. It also contended that even if there were ambiguities in these requirements, they should be resolved in favor of those who have performed labor and made improvements on a property - which in this case would be Last Chance Mining Company. Furthermore, it disagreed with the majority’s interpretation of “possession” under mining laws; arguing instead for an understanding based on actual occupancy or physical control over a property rather than mere legal title or right to possession. Lastly, it criticized what it saw as an undue emphasis placed by the majority on minor discrepancies between different versions of location notices while ignoring substantive issues related to rights and interests at stake.