_The chief requisite for success when acting offensively against an adverse Grand Column, or Wing, or Corps d’armee, in Contact, is the advantage in NUMBERS._ The primary process is that of a Grand Battle in which the kindred army has an overwhelming superiority in Numbers in contact, and at least the equality in all other Prime Strategetic Means. In this circumstance, the object of such Grand Battle always is: 1. To attack the hostile Formation in Mass frontally at the center, and upon both wings obliquely; all three attacks being made simultaneously and the evolutions so executed that the hostile army never is able to penetrate between either kindred wing and the kindred center, nor to outflank that kindred wing which may be in the air. 2. In case the kindred army has the equality or inferiority in all other Prime Strategetic Means, then the object of a Grand Battle on the Offensive is to attack the hostile Formation in Mass obliquely with the whole kindred army, and preferably upon that wing which covers the route of communication of the adverse army with its Base of Operations, but always upon that wing which contains the Tactical Key of the actual Battlefield. Obviously, the concentration of the entire kindred army against a single adverse wing always will constitute an overwhelming superiority in Numbers. In making such attack obliquely against a single adverse wing, the center and remaining wing of the kindred army must not engage until the kindred Van and Corps of Position of the attacking wing first have formed the _center_ of three sides of an octagon; of which the Kindred Corps of Evolution will form the _farthest_ side and the Kindred Center and left wing Corps d’armee will form the _nearest_ and latest constructed side. * * * * * _The chief requisite for success when acting defensively against a Grand Column, or Wing, or Corps d’armee is the advantage in TOPOGRAPHY._ The primary process is that of a Grand Battle in which the kindred army, decidedly inferior in Numbers in the aggregate, has the advantage in Topography and equality in all other Prime Strategetic Means. In this case the object is to support both flanks of the inferior army upon impassable natural barriers, strengthening both wings at the expense of the center, both in quantity and in quality of troops. If the Tactical Defensive be selected, the center should retire before the oncoming of the hostile army in order to enclose it between the Kindred Wings, which will then overwhelm it by superior Numbers, while the natural barriers on the flanks being impassable will prevent the remaining hostile corps from participating in the battle otherwise than as spectators. Should the Tactical Offensive be selected, that kindred wing best adapted for attack should engage supported by all kindred Corps of Evolution, while advancing the Kindred Center in reserve and holding the remaining wing refused and in observation.