The first and most extensive class of cases described as of federal cognizance, are those "in law and equity arising under this constitution, the laws of the United States, and treaties made, or which shall be made, under their authority." The distinction here recognized between cases in law and cases in equity is of no particular significance for present purposes. In the jurisprudence of England, there were at the time our Constitution was framed, and until recently, distinct courts of law and of equity. Law and equity in this sense are simply different divisions of jurisprudence; the distinction between them depends on the nature of the case, or the nature of the relief which the court may grant. Such distinction is still recognized in some of the states, although in many states the same courts administer both law and equity. By the use of these two terms in the federal constitution, it was only intended to indicate that both law and equity may be administered in the federal courts, if the case is one otherwise coming within the jurisdiction of those courts. (See below, § 168.)

The essential description of the cases within the class now under consideration is that they are cases arising under the constitution, laws, or treaties of the United States. Such a case may involve the construction of the federal constitution or a law or treaty of the United States, or it may involve the determination of some right, privilege, or immunity under such constitution, law, or treaty. In either event, it is a case as to which the federal judicial power may be exercised. For instance, if a person were being punished by state authority for violating some state statute, which statute was unconstitutional because in conflict with the provisions of the federal constitution, such person seeking relief as against the unlawful exercise of authority on the part of the state would have a case arising under the federal constitution. If one who has a patent from the United States entitling him to the exclusive use, manufacture, and sale of an invention should desire to bring suit against another who was infringing his right under such patent, the case would be one arising under the laws of the United States, for it is only under the United States laws that a patent may be granted and enjoyed, and the case would therefore be one within the possible jurisdiction of the federal courts. If the subject of a foreign state had the right by treaty between his government and the government of the United States to inherit property in the United States, and his right to thus inherit was denied to him or questioned under the laws of a state, his case would be one arising under a treaty, and therefore one as to which the federal courts might have jurisdiction.

It is to be noticed that it is not essential that cases of this class directly involve the interpretation of the federal constitution, statute, or treaty; it is enough if the right asserted be a right dependent upon such constitution, statute, or treaty. Thus, suits by or against federal corporations have been held to be cases arising under the laws of the United States, for a federal corporation can only exist by virtue of federal law (Osbom v. Bank of United States and Pacific Railroad Cases). However, national banks, although they are federal corporations, are by Congress prohibited from resorting to the federal courts on the ground that they are federal corporations, and must submit to the jurisdiction of the state courts in the same way as corporations organized under the authority of the states. But a detailed discussion of the cases which belong to this class is not practicable. It is enough to indicate their general characteristics.