The weakness peculiar to the Topographical Horizon of the Rook lies in the fact that it never commands the origins of diagonals or obliques. Hence it is open to unopposed attack along the first from adverse Queen, King, Bishops and Pawns, and along the second from adverse Knights.
From the view-point of the _Bishop_, the surface of the Chess-board takes on a topographical aspect most forbidding.
To this Chess-piece at least one-half of the Topographical Zone is inaccessible, and under any circumstances his movements are limited to the thirty-two squares of his own color.
Thus, the Topographical Horizon of the Bishop takes the form of a broken country, dotted with high hills, deep lakes, impenetrable swamps, and thick woodlands. But between these obstacles thus set about by Nature, run level valleys, varied in extent and easy of access. This fact so modifies this harshest of all sensible horizons as to make the Bishop next in activity to the Rook.
Within its limited sphere of action, the Bishop may move in either one or four directions with a minimum of nine and a maximum of fourteen points open to his occupation. Unimpeded by other corps blocking his route of march, the Bishop may reach any desired point of his own color on the chess board in two moves.
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.
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.