The Central Lumber Company v. State of South Dakota case in 1912 revolved around the issue of whether a state could impose taxes on an out-of-state corporation for business conducted within its borders. The Central Lumber Company, based in Minnesota, had lumber yards and conducted business in South Dakota but argued that it should not be subject to taxation because it was incorporated outside the state. However, the Supreme Court ruled against this argument stating that if a foreign corporation conducts continuous and systematic part of its general business within another state, it is liable to pay tax imposed by such states irrespective of where they are incorporated. This ruling established precedent for future cases involving interstate commerce and taxation issues.

In the dissenting opinion for Central Lumber Company v. State of South Dakota, Justice Holmes disagreed with the majority's decision that a state could impose taxes on an out-of-state corporation based solely on its business transactions within the state. He argued that this interpretation violated principles of interstate commerce and due process. According to him, a company should not be subject to taxation in every jurisdiction where it conducts business unless it has established a permanent presence or domicile there. The mere act of conducting occasional transactions does not constitute sufficient grounds for imposing tax obligations under constitutional law as per his understanding. Therefore, he believed that Central Lumber Company was unfairly taxed by South Dakota since they did not have any physical presence or property in the state but only conducted sporadic lumber sales there.