Regarded as a Chessic Corps d’armee the Queen marches and attacks as infantry, cavalry and artillery. Either, neither, or both Queens may be present in any given Strategetic Horizon; and whenever present the effect of her co-operation mathematically is outlined, viz.: At her maximum of efficiency the Queen occupies the common vertex of one or more unequal triangles, whose aggregate area is from a minimum of 21 to a maximum of 27 points. Her offensive power is equally valid against all of these points; but her defensive power is valid for the support from a minimum of one point to a maximum of five points. THE ROOK. Regarded as a Chessic Corps d’armee the Rook marches and attacks as infantry, cavalry and artillery. From one to four Rooks may be present in any given Strategetic Horizon; and whenever present the effect of its co-operation mathematically is outlined, viz.: At her maximum of efficiency, the Rook occupies the common angle of four quadrilaterals, whose aggregate area always is 14 points. The Offensive Power of the Rook is equally valid against all these points, but his defensive power is valid for the support of only two points. THE BISHOP. Regarded as a Chessic Corps d’armee, the Bishop marches and attacks as infantry, cavalry and artillery. From one to four Bishops may be present in any Strategetic Horizon; and whenever present the effect of its co-operation mathematically is outlined, viz.: At its maximum of efficiency, the Bishop occupies the common vertex of four unequal triangles, having a maximum of 13 and a minimum of 9 points. His offensive power is valid against all of these points but his defensive power is valid only for the support of two points. KNIGHT. Regarded as a Chessic Corps d’armee the Knight marches and attacks as cavalry and artillery. From one to four Knights may be present in any given Strategetic Horizon; and whenever present the effect of its co-operation mathematically is outlined, viz.: At its maximum of efficiency, the Knight occupies the centre of an octagon of two points radius, having a minimum of two points and a maximum of eight points area. His offensive power is equally valid against all of these eight points, but his defensive power is valid for the support of only one point. THE PAWN. Regarded as a Chessic Corps d’armee, the Pawn at its normal post marches as infantry and cavalry. Should an adverse corps, however, take post within the kindred side of the Chessboard; that Pawn upon whose altitude the adverse Piece appears, at once loses its equestrian attributes and marches and attacks exclusively as infantry. Located at any other point than at its normal post, the Pawn is composed exclusively of infantry and never acts either as cavalry or artillery. From one to eight Pawns may be present in any Strategetic Horizon; and whenever present the effect of its co-operation mathematically is outlined as follows: