This section is from the book "The Constitutional Law Of The United States", by Westel Woodbury Willoughby. Also available from Amazon: Constitutional Law.
In the most comprehensive sense of the term, Martial Law includes all law that has reference to, or is administered by, the military forces of the State. Thus it includes (1) Military Law Proper, that is, the body of administrative laws created by Congress for the government of the army and navy as an organized force; (2) the principles governing the conduct of military forces in time of war, and in the government of occupied territory; and, (3) Martial Law in sensu strictiore, or that law which has application when the military arm does not supersede civil authority but is called upon to aid it in the execution of its civil functions. This last form of Martial Law is to be sharply distinguished from those forms of Military Law which have been considered in the preceding chapters.1 l "There are under the Constitution three kinds of military jurisdiction: one to be exercised both in peace and war; another to be exercised in time of foreign war without the boundaries of the United States, or in time of rebellion and civil war within the States or districts occupied by rebels treated as belligerents; and a third to be exercised in time of invasion or insurrection within the limits of the United States, or during rebellion within the limits of States maintaining adhesion to the National Government, when the public danger requires its exercise. The first of these may be called jurisdiction under the military law, and is found in acts of Congress prescribing rules and articles of war, or otherwise providing for the government of the national forces; the second may be distinguished as military government, superseding, as far as may be deemed expedient, the local law, and exercised by the military commander, under the direction of the President, with the express or implied sanction of Congress; while the third may be denominated martial law proper, and is called into action by Congress, or temporarily, when the action of Congress cannot be invited, in the case of justifying or excusing peril, by the President, in times of insurrection or invasion, or of civil or foreign war, within districts or localities whose ordinary law no longer adequately secures public safety and private rights." Ex parte Milligan, 4 Wall. 2; 18 L. ed. 281.
It may be observed that down to the time of 1689, and indeed nearly a century later by Blackstone, when Martial Law is spoken of, reference is had to the first two of the above described forms of military jurisdiction.
 
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