To the King, this vast territory is accessible in all directions. At his pleasure he may move to and occupy either of the sixty-four squares of the Chess-board, in a minimum of one and in a maximum of seven moves. The only obstacles to his march are distance and the opposition of an enemy. The Strategical weakness of the Topographical Horizon peculiar to the King arises from its always taking on and maintaining the physical form of a plain. Consequently it is vulnerable to attack from all sides and what is far worse, it readily is commanded and from a superior topographical post, by every adverse piece, except the King and Pawn. Thus, the hostile Queen, without being attacked in return, may enfilade the King along all verticals, horizontals and diagonals; the Rooks, along all verticals and horizontals; the Bishops, along all diagonals of like color; and the Knights along all obliques. TOPOGRAPHY OF THE QUEEN From the view-point of the _Queen_, the surface of the Chess-board takes on the topographical aspect of a series of wide, straight valleys separated by high, impassable mountain ranges, unfordable rivers, and impenetrable forests and morasses. These valleys, which number never less than three, nor more than eight, in the same group, are of varying length and always converge upon and unite with each other at the point occupied by the Queen. These valleys contained in the Queen’s topographical horizon may be classified, viz.: Class I, consists of those groups made up of three valleys. Class II, of those groups made up of five valleys. Class III, of those groups made up of eight valleys of lesser area; and Class IV, of those groups made up of eight valleys of greater area. Groups of the first class always have an area of twenty points; those of the second have an area of twenty-three points; those of the third have an area of twenty-five points, and those of the fourth have an area of twenty-seven points. Such areas always are exclusive of that point upon which the Queen is posted. Although impassable natural barriers restrict the movement of the Queen to less than one-half of the Topographical Zone, these obstacles always are intersected by long stretches of open country formed by intervening valleys. Hence, the march of this most mobile of the Chesspieces always is open either in three, five, or eight directions, and it always is possible for her, unless impeded by the interference of kindred or hostile corps, to reach any desired point on the Chess-board in two moves. The weakness peculiar to the Topographical Horizon which appertains to the Queen, originates in the fact that it never commands the origins of obliques. Consequently, every post of the Queen, is open to unopposed attack by the hostile Knights. TOPOGRAPHY OF THE ROOK From the view-point of the _Rook_, the surface of the Chess-board takes on a topographical aspect which varies with the post occupied.