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.
Under the statutory provisions now in force, the Supreme Court consists of a chief justice and eight associate justices, and sits only at the national capital. By the constitution (Art. Ill, § 2, ¶ 2) the Supreme Court has both original and appellate jurisdiction; original "in all cases affecting ambassadors, other public ministers and consuls, and those in which a state shall be a party," and appellate in other cases as provided by law.
The original jurisdiction of this court cannot be extended by statute: but by statute it is made exclusive in some of those cases mentioned in the constitution, to wit, cases against ambassadors or public ministers or their domestics, and also cases to which a state is a party, except between a state and its citizens, or between a state and citizens of other states or aliens. It has already been explained (above, § 147) that, according to the rules of international law, ambassadors and public ministers are exempt from suit in the courts of the country to which they are accredited and by which they are received, so that the only practical effect of giving to the Supreme Court exclusive jurisdiction in such cases is to prevent any other court from entertaining jurisdiction. It is to be noticed, however, that this does not apply to consuls. But, on the other hand, the original jurisdiction of the Supreme Court in cases affecting consuls is not made exclusive, so that it is not necessary that suits against them be brought in the Supreme Court.
As to cases in which a state is a party, the effect of the statutory provision is to give the Supreme Court exclusive original jurisdiction where a suit is brought against a state, that is, where a suit is between states, or by the United States against a state, while, on the other hand, if the suit is by a state against citizens of another state or aliens, the suit need not be in the Supreme Court, but may be in some other federal court, if any such court has jurisdiction.
The appellate jurisdiction of the Supreme Court is extensive and complicated, but may briefly be described as follows: (1) It has jurisdiction of appeals from the district or circuit courts in prize cases, in cases of conviction of a capital or otherwise infamous crime, in cases involving the construction or application of the constitution of the United States, and in cases in which the constitutionality of any law of the United States, or the validity or construction of any treaty made under its authority is drawn in question; also in cases in which the constitution or a law of a state is claimed to be in contravention of the constitution of the United States. (2) It has jurisdiction of appeals from a circuit court of appeals in any case certified by that court to the Supreme Court, or removed from that court to the Supreme Court by direction of the latter, and in some other cases in which appeals to the circuit courts of appeals are not final. (3) It has jurisdiction of appeals from state courts of last resort in cases involving a federal question, where the decision of the state court is against the validity of a statute or treaty of or authority exercised under the United States, or in favor of the validity of a statute of or authority exercised under any state, where the validity of such statute or authority is called in question as being repugnant to the constitution, laws, or treaties of the United States, or where the decision is against any title, right, privilege, or immunity claimed under the constitution, statutes, treaties, or authority of the United States. (See above, § 158.) (4) It has jurisdiction of appeals from the Supreme Court of the District of Columbia, and from the supreme courts of the territories, with limitations as to amount in controversy which need not be here particularly specified. (5) It has jurisdiction of appeals from the court of claims, and from district or circuit courts in cases against the United States, with some limitation as to the amount in controversy. There are some other classes of cases in which the Supreme Court exercises an appellate jurisdiction which need not be here particularly enumerated.
 
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