The Columbia Mill Company v. Alcorn case in 1893 revolved around a dispute over water rights between the two parties. The Columbia Mill Company, located in South Carolina, claimed that Alcorn had unlawfully diverted water from a stream which they both used for their operations. This diversion allegedly caused significant damage to the company's mill operation and resulted in financial losses. The Supreme Court ruled against Columbia Mill Company stating that under common law principles of riparian rights (rights relating to water use), each party has an equal right to reasonable use of the waters as long as it does not cause unnecessary harm or significantly interfere with other users' rights. In this case, there was no evidence presented showing that Alcorn's actions were unreasonable or harmful enough to warrant legal action.

In the dissenting opinion for Columbia Mill Company v. Alcorn, it was argued that the majority's decision to uphold a state law imposing taxes on corporations based on their capital stock, including property located outside of the state, violated constitutional principles. The dissent contended that this taxation method unfairly burdened interstate commerce and infringed upon federal authority by effectively taxing property beyond state borders. It also pointed out inconsistencies in how different types of businesses were taxed under this law - while corporations were taxed based on total assets regardless of location, partnerships and individual business owners were only taxed on property within the state. This discrepancy was seen as discriminatory against corporations and thus unconstitutional according to equal protection principles.