In the case of Montana Mining Company, Limited v. St. Louis Mining and Milling Company in 1906, the Supreme Court was asked to resolve a dispute over mining rights in Montana. The plaintiff, Montana Mining Co., claimed that it had acquired title to certain mineral lands through purchase from an individual who had obtained them under the U.S. mining laws before they were officially surveyed by government authorities. However, after official surveying took place, these lands were found to overlap with those already owned by defendant St.Louis Mining & Milling Co., which also claimed ownership based on prior possession and improvements made on its part of land. The main issue revolved around whether unsurveyed public mineral lands could be legally sold or transferred before being officially surveyed as per federal law requirements at that time. The court ruled against Montana Mining Co., stating that until such official surveys are completed and boundaries established for public domain lands (including mineral ones), no valid legal titles can be created or transferred for such properties - even if some form of possession or improvement has been done beforehand by private parties.

In the dissenting opinion for Montana Mining Company, Limited v. St. Louis Mining and Milling Company, Justice Harlan argued that the majority's decision was flawed in its interpretation of mining law and property rights. He contended that under established principles of mining law, a locator has exclusive right to all minerals within their claim boundaries - including those found beneath adjacent land if they extend from veins apexed within his claim. This principle is known as extralateral rights doctrine which allows miners to follow vein or lode even when it extends outside vertical planes bounding their claims on surface level into neighboring properties underground provided the vein apexes in their territory above ground level. Justice Harlan disagreed with majority’s view that this doctrine didn't apply here because both parties had valid overlapping claims over same mineral deposit but at different depths due to topography changes causing one party's claim boundary lines intersecting with other party's below surface level while remaining separate above ground. He believed such situations should be resolved by applying "apex rule" where ownership goes to whoever owns land directly above highest point (or 'apex') of mineral deposit regardless whether it descends into neighbor’s territory underneath since otherwise would lead absurd results like multiple people claiming ownership over same resources just based on depth differences rather than actual physical location leading potentially endless litigation disputes undermining stability necessary for encouraging investment in mining industry.