Unless interfered with by kindred or hostile corps, or the limitations of the Chess-board, the Knight always may move either in two, four, six, or eight directions. It may reach any desired point in a minimum of one and a maximum of six moves, and may occupy the sixty-four squares of the Chess-board in the same number of marches. The weakness of the topographical horizon of the Knight lies in the fact that it never commands adjacent points, nor any of those distant, other than the termini of its own obliques. Hence it is open to unopposed attack along verticals and horizontals from the adverse King, Queen and Rooks, and along diagonals from the adverse King, Queen, Bishop and Pawns. TOPOGRAPHY OF THE PAWN From the point of view of the _Pawn_, the surface of the Chess-board takes on the topographical aspect of a country which as it is entered, constantly becomes wilder and more rugged. The march of the Pawn always is along a valley situated between impracticable natural barriers, and the possible movements of the Pawn always decrease as the distance traveled increases. Unhindered by either kindred or hostile corps, the Pawn may reach any point of junction in the kindred Logistic Horizon, which is contained within its altitude, in a minimum of five and in a maximum of six moves. It may march only in one direction, except in capturing, when it may acquire the option of acting in three directions. The weakness of the topographical horizon of the Pawn originates in its inability to command the adjacent country. Therefore, it is exposed to unopposed attack along verticals and horizontals by the hostile King, Queen and Rooks; along diagonals by the adverse King, Queen and Bishops, and along obliques by the adverse Knights. TOPOGRAPHY OF THE TOPOGRAPHICAL ZONE That normal and visible surface of the _Chess-board_ termed the Topographical Zone is bounded by four great natural barriers, impassable to any Chess-piece. The two sides of the zone may be held to typify either the Ocean or the boundaries of neutral States. The two extremities of the Chess-board while holding the previously announced relation to Chess-pieces contained in the Topographical Zone, also holds another and radically different relation to those Chess-pieces _not_ contained in the Topographical Zone, viz.: In the latter case, the two extremities of the chessboard are to be regarded as two great mountain ranges, each of which is pierced by eight defiles, the latter being the sixteen points of junction contained in the kindred and adverse logistic horizons. In the arena thus formed by these four great natural barriers, two hostile armies composed of the thirty-two Chess-pieces, are contending for the mastery.