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.

Meanwhile, beyond these great mountain ranges, are advancing to the aid of the combatants, two other armies, represented by the power of promotion possessed by the Pawns. Each of these two hypothetical armies is assailing the outer slope of that range of mountains which lies in the rear of the hostile force. Its effort is to pass one of the eight defiles and by occupying a Point of Junction in the kindred Logistic Horizon, to gain entrance into the Topographical Zone. Then in the array of a Queen, or some other kindred piece, it purposes to attack decisively, the adverse Strategetic Rear.

To oppose the attack of this hypothetical hostile army, whose movements always are typified by the advance of the adverse Pawns, is the duty of the kindred column of manoeuvre.

Primarily this labor falls upon the kindred Pawns. Upon each Pawn devolves the duty of guarding that defile situated directly on its front, by maintaining itself as a Point of Impenetrability between the corresponding hostile pawn and the kindred Strategic Rear.

Conversely, a second duty devolves upon each Pawn; and as an integer of the Column of Support, it continually must threaten and whenever opportunity is presented it decisively must assault the defile on its front, for the purpose of penetrating to the kindred logistic horizon and becoming promoted to such kindred piece, as by attacking the adverse Determinate Force in flank, in rear, or in both, may decide the victory in favor of the kindred army.