“THE GREATER FORCE ALWAYS OVERCOMES THE LESSER.”—Napoleon.
Hence, unless more immediately vital considerations prevent, superiority in Numbers, of itself, is decisive of victory; and thus it readily is to be deduced that all else being equal, the advantage in Time plus the advantage in Numbers constitutes the easiest and simplest winning combination known to Strategetic Art.
But it so happens that the advantage in Time may be combined not only with the greater force, but also with an equal, or even with the lesser force, and from this it is self-evident that Strategetic Situations are divided into three classes, viz.:
There are two primary methods for availing of superiority in Numbers to destroy the opposing lesser force, viz.:
From the foregoing it is obvious that conversely there are two principal considerations, which all else being equal, must dominate the procedure of the Numerically inferior force, viz.:
The second consideration in the making of a Grand Reconnaissance by the commander-in-chief of an army having the advantage in Time, is the element of Position; for the reason that by unscientific posting of Corps d’armee, relative advantages in Time, or in Numbers or in both, may be rendered nugatory, on account of inability of the kindred Columns of Attack, of Support and of Manoeuvre to perform their functions.
In case the Corps are scientifically posted and are in positions to avail of advantage in Time and Numbers, those adverse vital points whose occupation may be effected by superior force, always will be the objectives of the movements of the latter.
Hence, the following:
As the advantage in Time gives the right to MOVE and the advantage in Numbers indicates the MOTIF of movement; so does the advantage in Position, as expressed by the Strategic Syllogism, specify the DIRECTION of that movement which normally appertains to the army having the advantage in Time.
The proper direction of that movement which normally appertains to the advantage in Time always is indicated by the plus signs in the Strategic Syllogism, viz.:
The First Phase in the demonstration of every Strategetic Proposition is determined by the following:
Given the Normal ability to move, to determine the Normal motif and direction of movement.
1. Designate that army having the advantage in Time and express such advantage by the symbol +T, express the corresponding disadvantage in Time which appertains to the opposing army, by the symbol -T, and such symbols will constitute the First Term of the First Phase of the demonstration of any Prime Strategetic Proposition.
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:
| White. | (+T+N) | + | (+A+S+M) |
| Black. | (-T-N) | + | (-A-S-M) |
| 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.
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 |
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. |
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.
The Strategetic Values of the terms contained in the Strategic Syllogism and in the Tactico-Logistic Inequality are shown by the appended tables, viz.:
| Term. | Post. | Direction. | Motif. | |
| 1. | +A | Grand Vertex | Tactical Key of Objective Plane | To give checkmate |
| 2. | +M | Point Proximity en command | Point of Junction | To queen a Pawn |
| 3. | +A | Major Vertex | 1. Grand Vertex 2. Point Aligned 3. Point en Potence |
To gain winning Position with Column of Attack |
| 4. | +M | Point Proximity en Menace | Point en Command | To gain winning Position with Column of Support |
| 5. | +M | Point Proximity en Presence | Point en Menace | To gain winning Position with Column of Support |
| 6. | +A | Minor Vertex | 1. Major Vertex 2. Point Aligned |
To gain Superior Position with Column of Attack |
| 7. | +S | Point Proximity en Observation | Point en Presence | To gain Superior Position with Column of Support |
| 8. | +S | Point Proximity en Route | Point en Observation | To gain superior Position with Column of Support |
| 9. | +S | Point Proximity Remote | Point en Route | To gain advantage with Column of Support |
| 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. |
| 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. |
Given any Strategetic Situation to determine the True Tactical Sequence.
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.