Part 11

2. Express that superiority, equality, or inferiority in Numbers, which appertains to each of the opposing armies by the symbols +N, =N,-N, respectively; and such symbols will constitute the Second Term of the First Phase of the demonstration of any Prime Strategetic Proposition.

3. Express the objectives designated by the plus terms of the Strategic Syllogism, viz.:

(a) Objective of +A = Objective Plane, _i.e._, O. P.

(b) ” +S = Logistic Horizon, _i.e._, L. H.

(c) ” +M = Point of Junction, _i.e._, P. J.

and the symbols denoting such objectives will constitute the Third Term in the First Phase of the demonstration of any Prime Strategetic Proposition.

4. Combine those three terms which appertain to the advantage in Time, then combine those three terms which appertain to the disadvantage in Time, and the resulting equation when expanded will depict:

(a) The normal ability to move.

(b) The normal motif of movement.

(c) The normal directions of movement which appertain to each of the opposing armies.

EXAMPLE

White. (+T+N) + (+A+S+M) ----------------- Black. (-T-N) + (-A-S-M)

EXPANDED

First Term. +T = Normal ability to move.

Second Term. +N = Normal motif of movement, (a) Detachments, (b) Exchanges.

Third Term +O. P. = Normal objective of +A. +L. H. = ” ” ” +S. +P. J. = ” ” ” +M.

Hence, in the foregoing example the normal direction of movement for White may be either toward the Objective Plane with the Column of Attack, or toward the Logistic Horizon, or the Point of Junction with the Column of Support, or toward both objectives, with both columns simultaneously.

Meanwhile, the Black army having the disadvantage in Time is unable to move, and consequently is stationary.

Furthermore, White having the superiority in Numbers may move with an equal force against either objective designated by the Third Term of the equation, and with his excess force against one or more adverse vital points, simultaneously, against which latter movement, Black obviously has no adequate defence.

TACTICO-LOGISTIC INEQUALITY

The Tactico-Logistic Inequality is the algebraic expression of the relative advantages and disadvantages in Time and in Numbers appertaining to opposing Strategetic Entireties.

Such advantages and disadvantages are denoted by the terms, viz.:

+T. Signifies the absolute advantage in Time, _i.e._, the ability of an army, a grand column, a wing or a corps d’armee to move, while the opposing force must remain stationary.

-T. Signifies the absolute disadvantage in Time, _i.e._, the obligation of an army, a grand column, a wing, or a corps d’armee to remain stationary, while the opposing force is in motion.

+N. Signifies the absolute advantage in Numbers, _i.e._, the larger number of corps d’armee.

-N. Signifies the absolute disadvantage in Numbers, _i.e._, the smaller number of corps d’armee.

=N. Signifies the equality in Numbers, _i.e._, the same number of corps d’armee.

There are six forms of the Tactico-Logistic Inequality, viz.:

1. +T+N ------ -T-N

2. +T=N ------ -T=N

3. +T-N ------ -T+N

4. -T+N ------ +T-N

5. -T=N ------ +T=N

6. -T-N ------ +T+N

INITIAL STRATEGETIC EQUATION

The Initial Strategetic Equation is made up of those terms which compose the Strategic Syllogism and the Tactico-Logistic Inequality, viz.:

----------------- (+A+S+M) + (+T+N) - (-A-S-M) + (-T-N) = the Normal Motif and Direction of Effort.

RULE

1. _Set down in parenthesis those terms of the Strategic Syllogism which appertain to White._

_Set down in parenthesis those terms of the Tactico-Logistic Inequality which appertain to White._

_Connect the two kindred terms thus constructed, by the sign of addition, to show that each is to augment the other, and superscore all by the same vincula to show that all are to be taken together to form one side of the resulting equation._

* * * * *

2. _Repeat this process for the Black terms to construct the second side of the Initial Strategetic Equation, and separate the White from the Black terms by a minus sign._

STRATEGETIC VALUES

The Strategetic Values of the terms contained in the Strategic Syllogism and in the Tactico-Logistic Inequality are shown by the appended tables, viz.:

TABLE OF STRATEGIC VALUES.

_Term._ _Post._ _Direction._ _Motif._

1. +A Grand Vertex Tactical Key of To give checkmate Objective Plane

2. +M Point Proximity Point of Junction To queen a Pawn en command

3. +A Major Vertex 1. Grand Vertex To gain winning Position 2. Point Aligned with Column of Attack 3. Point en Potence

4. +M Point Proximity Point en Command To gain winning Position en Menace with Column of Support

5. +M Point Proximity Point en Menace To gain winning Position en Presence with Column of Support

6. +A Minor Vertex 1. Major Vertex To gain Superior Position 2. Point Aligned with Column of Attack

7. +S Point Proximity Point en Presence To gain Superior Position en Observation with Column of Support

8. +S Point Proximity Point en Observation To gain superior Position en Route with Column of Support

9. +S Point Proximity Point en Route To gain advantage with Remote Column of Support

TABLE OF LOGISTIC VALUES

_Term._

1. +T Unrestricted privilege to move any Piece.

2. +T Restricted to moving a Sustaining Piece en counter attack.

3. +T Restricted to moving an aggressive Covering Piece.

4. +T Restricted to moving a Passive Covering Piece.

5. +T Restricted to moving a Supporting Piece.

6. +T Restricted to moving the King out of check.

7. +T Restricted to moving the King from an untenable Objective Plane.

8. +T Restricted to moving a Piece to reduce the value of the Kindred King’s Logistic Radii.

TABLE OF TACTICAL VALUES

_Term._

1. +N Larger numbers of Grand Corps d’armee of Evolution.

2. +N Larger numbers of Major Corps d’armee of Evolution.

3. +N Larger numbers of Minor Corps d’armee of Evolution.

4. +N Larger numbers of Corps d’armee of Position.

PRIME STRATEGETIC PROPOSITION

SECTION TWO

PRIME STRATEGETIC PROPOSITION

SECTION TWO

THEOREM.

_Given any Strategetic Situation to determine the True Tactical Sequence._

DEMONSTRATION.

(_First Phase._)

Let the term +A in its degree represent the relative advantage in Position of the Column of Attack; +S in its degree the relative advantage in Position of the Column of Support, and +M in its degree the relative advantage in Position of the Column of Manoeuvre; let equality in Position of the several Columns be represented by the terms =A, =S, =M, and let inferiority in Positions of the several Columns be represented by the terms -A, -S, -M, and let those terms appertaining to the White Columns be written above a line and those terms appertaining to the Black Columns be written below the line, and let that collection of terms containing the plus and equal signs of greater Strategetic value be the Major Premise and that collection of terms containing the signs of lesser strategetic value be the Minor Premise of the _Strategic Syllogism_ thus constructed.

Let the ability to move while the opposing force must remain stationary be represented by the term +T, and let the converse be represented by the term -T, and let superiority in Numbers be represented by the term +N; the equality in Numbers by the term =N, and inferiority in Numbers by the term -N, and let the combining of any form of the terms T and N constitute a _Tactico-Logistic Inequality_.

Let any combination of that Strategic Syllogism which appertains to a given Strategetic Situation with the corresponding Tactico-Logistic Inequality, form the _Initial Strategetic Equation_.

Let the plus terms and the equality terms, which are contained in the Initial Strategetic Equation, be expanded into their highest forms according to the table of Strategetic Values, and annex to each of such terms that numeral which expresses the relative rank of such term in those calculations which appertain to the pending Prime Strategetic Proposition.

Compare the values so obtained and let the highest _Strategetically_ be regarded as the menace most immediately decisive, then:

If the term +T appertain to the Piece operating such menace, let such Piece be regarded as the Corps d’armee en Menace, and the Objective of such menace as the Prime Decisive Point; the occupation of such Point by such Piece as the Normal Motif of Offensive Effort, and the Logistic Radius connecting the Point of Departure occupied by such Piece and the Prime Decisive Point as the Normal Direction of Offensive Effort.

If the term +T does NOT apply to that menace which combined with the term +T would be most immediately decisive, then:

By further comparison of the terms of the Initial Strategetic Equation, select that Decisive Menace strategetically next in sequence to which the term +T does appertain; and let the Piece operating such Decisive Menace be regarded as the Corps d’armee en Menace; the Objective of such menace as the Prime Decisive Point; the occupation of such Point by such Piece as the Normal Motif of Offensive Effort, and the Logistic Radius connecting the Point of Departure occupied by such Piece and the Prime Decisive Points as the Normal direction of Offensive Effort.

Provided:

Whenever the term +T appertains to a Menace not so immediately decisive as another menace operated by an adverse army, column, wing or corps d’armee, but to which the term +T does _not_ appertain, then: the Normal motif of Effort is _defensive_, and the Normal direction of Defensive Effort is along the Logistic Radius between the Point of Departure of that Kindred Piece, which by the advantage of the term +A, is able to nullify the adverse most immediately Decisive Menace and that Point of Command which is the Objective of such Effort en Defence and from whence such adverse most immediately Decisive Menace may be nullified.

* * * * *

The second or Intermediate Phase of the Prime Strategetic Proposition appertains to Grand Manoeuvres; and the third, or Final Phase, appertains to Grand Operations.

_However vast one’s capabilities may be, there is no mind so comprehensive but that it has much to learn from other minds which have preceded it, and no talent is so potential but that its development is proportional to its exercise._

_For no matter how broad and exact one’s knowledge, the application of such knowledge alone constitutes Art, and the value of such knowledge always is commensurate to the degree of skill attained in the use of it._

_Hence, there is a training of the physical senses which gives quickness and strength to the eye, the ear and the hand; a training of the nervous organism which gives courage to the heart, clearness to the brain, and steadiness to the body; a training of the intellect which fructifies in originality, ingenuity, profundity and exactness of calculation._

_Such training is to be acquired only from systematic study of the best productions by Masters of the Art, and by incessant practice with the best proficients._