In the United States v. Mills case of 1904, the Supreme Court examined whether a lower court had jurisdiction over a criminal case involving an American citizen who committed murder on an American ship in international waters. The defendant, Mr. Mills, was accused of killing another crew member while their vessel was sailing off the coast of Japan. He argued that because the crime occurred outside U.S territory, he should not be tried under U.S law but rather under international maritime law or Japanese law since they were closest to Japan at the time of incident. The Supreme Court ruled against this argument and upheld his conviction by stating that any crime committed aboard an American ship is subject to U.S laws regardless of its location at sea during commissioning such act. This decision reinforced America's legal authority over its citizens abroad and established precedent for future cases involving crimes committed by Americans in international waters.

The dissenting opinion in the United States v. Mills case argued that the government did not have sufficient evidence to convict Mr. Mills of conspiracy to defraud the United States by manipulating bids for mail contracts. The dissenters believed that while there was evidence of a relationship between Mills and other bidders, this alone could not prove beyond reasonable doubt that they conspired together with fraudulent intent against the U.S government. They also pointed out inconsistencies in witness testimonies used by prosecution, which further cast doubts on their credibility and reliability as substantial proof of guilt. Therefore, they concluded that Mr.Mills should be acquitted due to lack of concrete evidence proving his involvement in any criminal conspiracy.