This section is from the book "Constitutional Law In The United States", by Emlin McClain. Also available from Amazon: Constitutional Law in the United States.
Congress has authority to provide for the punishment of four classes of crimes: (1) those specified in the federal constitution or which Congress is therein given express power to punish; (2) those committed within territory which is permanently subject to the exclusive jurisdiction of the United States, such as the District of Columbia, and forts, arsenals, navy yards, and public buildings, the sites of which have been ceded for public purposes by the state to the federal government; (3) those committed within territory subject to the jurisdiction of the United States, but not included within the limits of states admitted to the Union; (4) offences the punishment of which is provided for by Congress under implied power to carry out the express provisions of the constitution. Bearing in mind that the federal government is a government of delegated and not of general powers (see above, § 17), it is evident that any criminal legislation of Congress must be sustained under some one of these four heads; and that outside of these classes of cases, Congress has no authority to provide for the punishment of acts as crimes against the laws of the United States; and, of course, it has no authority to provide for the punishment of crimes against the laws of the states, for that is exclusively within the scope of state power.
 
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