Frequently it happens that the occupation of an objective, valid in a given situation, is not valid in an ensuing situation for the reasons: 1. That the object of the given line of movement is become unattainable, or, 2. Because it has become no longer worth attaining, or, 3. Because such belated attainment may be direct cause of disaster. PRINCIPLE _In order to select the decisive movement in a given situation it is necessary first to determine both the object and the objective, not merely of the required movement, but also of that series of movements, which collectively constitute the projected line of movement; together with the object and the objective of every movement contained therein._ The mathematician readily will perceive, and the student doubtless will permit himself to be informed, that: Before the true object and the true objective of any movement can be determined it first is necessary to deduce the common object of all movement. * * * * * As is well known, the combined movements of the Chess-pieces over the surface of the Chess-board during a game at Chess are infinite. These calculations are so complex that human perception accurately can forecast ultimate and even immediate results only in comparatively few and simple situations. Such calculable outcomes are limited to the earlier stages of the opening, to the concluding phases of a game; and to situations in the mid-game wherein the presence of but few adverse pieces minimizes the volume of effort possible to the opponent. Consequently, it is self-evident, that: PRINCIPLE _Situations on the Chess-board require for their demonstration a degree of skill which decreases as the hostile power of resistance decreases._ All power for resistance possessed by an army emanates from its ability to move. This faculty of Mobility is that inestimable quality without which nothing and by means of which everything, can be done. From this truth it is easy to deduce the common object of all movement, which obviously is: _To minimize the mobility of the opposing force._ The hostile army having the ability to move and consequently a power for resistance equal to that possessed by the kindred army; it becomes of the first importance to discover in what way the kindred army is superior to that adverse force, which in the Normal Situation on the Chess-board is its exact counterpart in material, position and formation. Such normal superiority of the White army over the Black army is found in the fact that: 1. _The former has the privilege of making the initial move of the game._ 2. _This privilege of first move is the absolute advantage in Time._ While no mathematical demonstration of the outcome of a game at Chess is possible, nevertheless there are rational grounds for assuming that with exact play, White should win.