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It is federal, because it is the government of States united in a political union, in contradistinction to a government of individuals, that is, by what is usually called, a social compact. To express it more concisely, it is federal and not national because it is the government of a community of States, and not the government of a single State or Nation.

JOHN C. CALHOUN (1854). “A DISQUISITION ON GOVERNMENT AND A DISCOURSE ON THE CONSTITUTIONA ND GOVERNMENT OF THE UNITED STATES”, p.113
It is federal, because it is the government of States united in a political union, in contradistinction to a government of individuals, that is, by what is usually called, a social compact. To express it more concisely,