_Form the kindred army upon the hypothenuse of the right angled triangle
which is contained within the Dynamic surface of the Chess-board; and
conversely,_
_Compel the adverse army to act exclusively within that semi-circle which
appertains to the same surface._
Under these circumstances, the kindred corps will be possessed of
facilities for movement represented by thirty-six squares; while the
logistic area of the opposing army will be restricted to twenty-eight
squares.
There are, of course, two great central diagonals of the Chess-board; but
as the student is fully informed that great central diagonal always is to
be selected, which extends towards the Objective Plane.
* * * * *
Mobility, _per se_, increases or decreases with the number of squares
open to occupation.
But in all situations there will be points of no value, while other
points are of value inestimable; for the reason that the occupation of
the former will not favorably affect the play, or may even lose the game;
while by the occupation of the latter, victory is at once secured.
But it is not the province of Mobility to pass on the values of points;
this latter is the duty of Strategy. It is sufficient for Mobility that
it provide superior facilities for movement; it is for Strategy to define
the Line of Movement; for Logistics, by means of this Line of Movement,
to bring into action in proper times and sequence, the required force,
and for Tactics, with this force, to execute the proper evolutions.
Mobility derives its importance from three things which may occur
severally or in combination, viz.:
1. All power for offense or for defense is eliminated from a
Chess-piece the instant it loses its ability to move.
2. The superiority possessed by corps acting offensively over
adverse corps acting defensively, resides in that the attack of
a piece is valid at every point which it menaces; while the
defensive effort of a piece, as a rule, is valid only at a single
point. Consequently: