2. It mathematically perfects each of these figures and harmonizes each to all, and that: 3. By means of it each figure becomes possessed of eight more points than it otherwise would contain. Hence, the following is self-evident: PRINCIPLE _That Chessic army which can possess itself of the great central diagonal, thereby acquires the larger number of points upon which to act and consequently greater facilities for movement; and conversely:_ _By the loss of the great central diagonal, the mobility of the opposing army is correspondingly decreased._ It therefore is clear that the object of any series of movements by a Chessic army acting otherwise than on Line of Operations, should be: PRINCIPLE _Form the kindred army upon the hypothenuse of the right angled triangle which is contained within the Dynamic surface of the Chess-board; and conversely,_ _Compel the adverse army to act exclusively within that semi-circle which appertains to the same surface._ Under these circumstances, the kindred corps will be possessed of facilities for movement represented by thirty-six squares; while the logistic area of the opposing army will be restricted to twenty-eight squares. There are, of course, two great central diagonals of the Chess-board; but as the student is fully informed that great central diagonal always is to be selected, which extends towards the Objective Plane. * * * * * Mobility, _per se_, increases or decreases with the number of squares open to occupation. But in all situations there will be points of no value, while other points are of value inestimable; for the reason that the occupation of the former will not favorably affect the play, or may even lose the game; while by the occupation of the latter, victory is at once secured. But it is not the province of Mobility to pass on the values of points; this latter is the duty of Strategy. It is sufficient for Mobility that it provide superior facilities for movement; it is for Strategy to define the Line of Movement; for Logistics, by means of this Line of Movement, to bring into action in proper times and sequence, the required force, and for Tactics, with this force, to execute the proper evolutions. Mobility derives its importance from three things which may occur severally or in combination, viz.: 1. All power for offense or for defense is eliminated from a Chess-piece the instant it loses its ability to move. 2. The superiority possessed by corps acting offensively over adverse corps acting defensively, resides in that the attack of a piece is valid at every point which it menaces; while the defensive effort of a piece, as a rule, is valid only at a single point. Consequently: PRINCIPLE _Increased facilities for movement enhance the power of attacking pieces in a much greater degree than like facilities enhance the power of defending pieces._