4. To prevent the White hypothetical force penetrating to its
Logistic Horizon.
To produce this fatal weakness in the Black position by the advantage of
the first move is much easier for White than commonly is supposed.
The process consists in making only those movements by means of which the
kindred corps d’armee, progressively occupying specified objectives, are
advanced, viz.:
I. _To the Strategetic Objective, when acting against the
communications of the adverse Determinate Force and its Base of
Operations._
II. _To the Logistic Horizon, when acting against the
communications between the adverse Determinate and the adverse
Hypothetical Forces._
III. _To the Strategic Vertices, when acting against the
communications of the hostile corps d’armee with each other._
To bring about either of these results against an opponent equally
equipped and capable, of course is a much more difficult task than to
checkmate an enemy incapable of movement.
Yet such achievement is possible to White and with exact play it
seemingly is a certainty that he succeeds in one or the other, owing to
his inestimable privilege of first move.
For the normal advantage that attaches to the first move in a game of
Chess is vastly enhanced by a peculiarity in the mathematical make-up of
the surface of the Chess-board, whereby, he who makes the first move may
secure to himself the advantage in mobility, and conversely may inflict
upon the second player a corresponding disadvantage in mobility.
This peculiar property emanates from this fact:
_The sixty-four points, i.e., the sixty-four centres of the
squares into which the surface of the Chess-board is divided,
constitute, when taken collectively, the quadrant of a circle,
whose radius is eight points in length._
Hence, in Chessic mathematics, the sides of the Chessboard do not form a
square, but the segment of a circumference.
To prove the truth of this, one has but to count the points contained
in the verticals and horizontals and in the hypothenuse of each
corresponding angle, and in every instance it will be found that the
number of points contained in the base, perpendicular, and hypothenuse,
is the same.
For example:
Let the eight points of the King’s Rook’s file form the perpendicular of
a right angle triangle, of which the kindred first horizontal forms the
base; then, the hypothenuse of the given angle, will be that diagonal
which extends from QR1 to KR8. Now, merely by the processes of simple
arithmetic, it may be shown that there are,