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.