The weakness peculiar to the topographical horizon of the Bishop is its liability to unopposed attack along verticals and horizontals by the hostile King, Queen and Rooks; and along obliques by the hostile Knights.
TOPOGRAPHY OF THE KNIGHT
From the view-point of the Knight, the surface of the Chess-board takes on the aspect of a densely wooded and entirely undeveloped country; made up of a profusion of ponds, rivulets, swamps, etc., none of which are impassable although sufficient to impede progress.
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.