Chapter V: Preface: VII (3)

3. To neutralize the relative disadvantage in Topography, eliminate that adverse Corps d’armee which is able to act simultaneously by its geometric symbol against the principal Kindred Corps of Position upon a given color; and by its sub-geometric symbol against points of opposite color.

* * * * *

Perfection in Defensive Topography is attained whenever the ground occupied nullifies hostile advantages in Time, Organization, Mobility, Numbers and Position.

Perfection in Offensive Topography is attained whenever the ground occupied accentuates the kindred advantages in Time, Organization, Mobility, Numbers and Position.

MILITARY EXAMPLES

_“When you intend to engage in battle endeavor that your
CHIEF advantage shall arise from the ground occupied by your
army.”--Vegetius._

To cross the Granicus, Alexander the Great selected a fordable spot where the river made a long, narrow bend, and attacked the salient and both sides simultaneously. The Persians thus outflanked were easily and quickly routed; whereupon the Grecian army in line of Phalanxes, both flanks covered by the river and its retreat assured by the fords in rear, advanced to battle in harmony with all requirements of Strategetic Art.

* * * * *

At Issus, Alexander the Great so manoeuvred that the Persian army of more than a million men was confined in a long valley not over three miles in width, having the sea on the left hand and the Amanus Mountains on the right, thus the Grecians had a battlefield fitted to the size of their army, and fought in Phalanxes in line, both wings covered by impassable natural barriers and retreat assured, by open ground in rear.

* * * * *

At the Trebia, Hannibal by stratagems now undiscernible, induced the consul Sempronius to pass the river and following along the easterly bank to take position with his army upon the lowlands between an unfordable part of the stream and the Carthagenians.

Upon this, Hannibal detached his youngest brother Margo to cut off the retreat of the Romans from the ford by which they had crossed the Trebia; advanced his infantry by Phalanxes in line and overthrowing the few Roman horse, assailed the hostile left wing with 10,000 heavy cavalry. The destruction of the Roman army was completed by the simultaneous attack of their right wing by Margo and the impossibility of repassing the river in their rear.

* * * * *

By one of the most notable marches in surprise recorded in military annals, Hannibal crossed the seemingly impassible marshes of the river Po, and turned the left flank of the Roman army, commanded by the Consul C. Flaminius. Then the great Carthagenian advanced swiftly toward the city of Rome, devasting the country on either hand.

In headlong pursuit the Consul entered a long narrow valley, having Lake Trasymenus on the one hand and the mountains on the other.

Suddenly while entombed in this vast ravine, the Roman army was attacked by infantry from the high ground along its right flank; and in front and rear by the Carthagenian heavy cavalry, while the lake extending along its left flank made futile all attempts to escape.

* * * * *

At Cannae, Hannibal reproduced the evolutions of Alexander the Great at the passage of the Granicus. Selecting a long bend in the Aufidus, Hannibal forded the river and took position by Phalanxes in line, his flanks covered by unfordable parts of the stream and his retreat assured by the fords by which he had crossed, while as at Issus, the ground on his front though fitting his own army, was so confined as to prevent the Romans engaging a force greater than his own. Beyond Hannibal’s front, the hostile army was posted in a wide level plain, suited to the best use of the vastly superior Carthagenian heavy cavalry, both for the evolutions of the battle and the subsequent pursuit and massacre of the Romans.

* * * * *

At the River Arar (58 B.C.) Caesar achieved his first victory. Following leisurely but closely the marauding Helvetii, he permitted three-fourths of their army to cross to the westerly side of the river; then he fell upon the remainder with his whole army.

* * * * *

An eye-witness thus describes the famous passage of the Lech by Gustavus Adolphus:

“Resolved to view the situation of the enemy, his majesty went
out the 2nd of April (1632) with a strong body of horse, which
I had the honor to command. We marched as near as we could to
the bank of the river, not to be too much exposed to the enemy’s
cannon; and having gained a height where the whole course of
the river might be seen, we drew up and the king alighted and
examined every reach and turning of the river with his glass.
Toward the north, he found the river fetching a long reach and
doubling short upon itself. ‘There is the point will do our
business,’ says the king, ‘and if the ground be good, we will
pass there, though Tilly do his worst’.”

He immediately ordered a small party of horse to bring him word how high the bank was on each side and at the point, “and he shall have fifty dollars” says the king, “who will tell me how deep the water is.”

… The depth and breadths of the stream having been ascertained, and the bank on our side being ten to twelve feet higher than the other and of a hard gravel, the king resolved to cross there; and himself gave directions for such a bridge as I believe never army passed before nor since.

The bridge was loose plank placed upon large tressels as bricklayers raise a scaffold to build a wall. The tressels were made some higher and some lower to answer to the river as it grew deeper or shallower; and all was framed and fitted before any attempt was made to cross.

At night, April 4th the king posted about 2,000 men near the point and ordered them to throw up trenches on either side and quite around it; within which at each end the king placed a battery of six pieces and six cannon at the point, two guns in front and two at each side. By daylight, all the batteries were finished, the trenches filled with musketeers and all the bridge equipment at hand in readiness for use. To conceal this work the king had fired all night at other places along the river.

At daylight, the Imperialists discovered the king’s design, when it was too late to prevent it. The musketeers and the batteries made such continual fire that the other bank twelve feet below was too hot for the Imperialists; whereupon old Tilly to be ready for the king on his coming over on his bridge, fell to work and raised a twenty-gun battery right against the point and a breast-work as near the river as he could to cover his men; thinking that when the King should build his bridge, he might easily beat it down with his cannon.

But the King had doubly prevented him; first by laying his bridge so low that none of Tilly’s shot could hurt it, for the bridge lay not above half a foot above the water’s edge; and the angle of the river secured it against the batteries on the other side, while the continual fire beat the Imperialists from those places where they had no works to cover them.

Now, in the second place, the King sent over four hundred men who cast up a large ravelin on the other bank just where he planned to land; and while this was doing the King laid over his bridge.

Both sides wrought hard all the day and all the night as if the spade, not the sword, was to decide the controversy; meanwhile the musketry and cannon-balls flew like hail and both sides had enough to do to make the men stand to their work. The carnage was great; many officers were killed. Both the King and Tilly animated the troops by their presence.

About one o’clock about the time when the King had his bridge finished and in heading a charge of 3000 foot against our ravelin was brave old Tilly slain by a musket bullet in the thigh.

We knew nothing of this disaster befallen them, and the King, who looked for blows, the bridge and ravelin being finished, ordered to run a line of palisades to take in more ground and to cover the first troops he should send over. This work being finished the same night, the King sent over his Guards and six hundred Scots to man the new line.

Early in the morning a party of Scots under Capt. Forbes of Lord Rae’s regiment was sent abroad to learn something of the enemy and Sir John Hepburn with the Scots Brigade was ordered to pass the bridge, draw up outside the ravelin, and to advance in search of the enemy as soon as the horse were come over.

The King was by this time at the head of his army in full battle array, ready to follow his van-guard and expecting a hot day’s work of it. Sir John sent messenger after messenger entreating for permission to advance, but the King would not suffer it; for he was ever on his guard and would not risk a surprise. So the army continued on this side of the Lech all day and the next night.

In the morning the King ordered 300 horse, 600 horse and 800 dragoons to enter the wood by three ways, but sustaining each other; the Scots Brigade to follow to the edge of the wood in support of all, and a brigade of Swedish infantry to cover Sir John’s troops. So warily did this famous warrior proceed.

The next day the cavalry came up with us led by Gustavus Horn; and the King and the whole army followed, and we marched on through the heart of Bavaria. His Majesty when he saw the judgment with which old Tilly had prepared his works and the dangers we had run, would often say, “That day’s work is every way equal to the victory of Leipsic.”

* * * * *

With but 55,000 troops in hand and surrounded by the united Austrian and Russian armies aggregating a quarter of a million men; Frederic the Great availing of a swamp, a few hills, a rivulet and a fortified town, constructed a battlefield upon which his opponents dared not engage him.

This famous camp of Bunzlewitz is one of the wonders of the military art. It also is an illustration of the inability of the Anglo-Saxon to reason; for to this day many who wear epaulets, accepting the dictum of a skillfully hoodwinked French diplomat at the siege of Neisse, (Dec., 1740) commonly assert that “the great Frederic was a bad engineer.”

* * * * *

Washington compelled the British to evacuate Boston, merely by occupying with artillery Dorchester Heights, the tactical key of the theatre of action and thus preventing either ingress or egress from the harbor.

* * * * *

At Trenton the Hessian column was unable to escape from Washington’s accurate evolutions, on account of being imprisoned in an angle formed by the unfordable Delaware river.

* * * * *

At Yorktown, the British army under Lord Cornwallis was captured entire, being cut off from all retreat by the ocean on the right flank and the James river in rear.

* * * * *

Bonaparte made his reputation at Toulon (1793) merely by following the method employed by Washington in the siege of Boston.

* * * * *

Bonaparte gained his first success in Italy because the allied Piedmontese and Austrian armies, although thrice his numbers, were separated by the Apennine mountains.

* * * * *

Bonaparte’s success at Castiglione was due to the separation of the Austrian army into two great isolated columns by the Lake of Garda.

* * * * *

At Arcola, Bonaparte occupied a great swamp upon the hostile strategic center and the Austrian army was destroyed by its efforts to dislodge him.

* * * * *

At Rivoli, the Austrian army purposed to unite its five detached wings upon a plateau of which Bonaparte was already in possession. All were ruined in the effort to dislodge the French from this Tactical Center.

* * * * *

The Austrian army was unable to escape after Marengo on account of the Po river in its rear.

* * * * *

At Austerlitz the left wing of the Austro-Russian army was caught between the French army and a chain of lakes and rivulets and totally destroyed.

* * * * *

At Friedland the Russian army was caught between the French in front and the Vistula river in rear and totally destroyed.

* * * * *

At Krasnoe, the Russians under Kutosof, occupied the strategic center and were covered by the Dnieper. To force the passage of the river cost Napoleon 30,000 men.

* * * * *

At the Beresina, the Russians under Benningsen, occupied the Strategic Center and were covered by the unfordable river. To force the passage cost Napoleon 20,000 men.

* * * * *

At Leipsic, Napoleon was caught between the allied army and the Elbe. The retreat across the river cost the French 50,000 men.

* * * * *

At Waterloo, the high plateau sloping gradually to a plain, various hamlets on front and flank and the forest in rear, made a perfect topography for a defensive battle.

* * * * *

At Sedan, the Emperor, Napoleon III, and his army were enclosed between the Prussian army and the frontier of Belgium and captured.

* * * * *

_“Where the real general incessantly sees prepared by Nature means admirably adapted for his needs, the commander lacking such talents sees nothing.”--Hannibal._

MOBILITY

_“Success in an operation depends upon the secrecy and celerity
with which the movements are made.”--Napoleon._

* * * * *

_“An eye unskilled and a mind untutored can see but little where
a trained observer detects important movements.”--Von Moltke._

* * * * *

_“Caesar is a marvel of vigilance and rapidity, he finishes a war
in a march.”--Cicero._

MOBILITY

_“Victory lies in the legs of the soldier.”--Frederic the Great._

* * * * *

_“The principal part of the soldier’s efficiency depends upon his
legs._

_“The personal abilities required in all manoeuvres and in
battles are totally confined to them._

_“Whoever is of a different opinion is a dupe to ignorance and a
novice in the profession of arms.”--Count de Saxe._

_“It is easier to beat an enemy than commonly is supposed,” says Napoleon, “the great Art lies in making nothing but decisive movements.”_

To the proficient in Strategetics the truth of the foregoing dictum is self-evident. Nevertheless, it remains to instruct the student how to select from a multitude of possible movements, that particular movement or series of movements, which in a given situation are best calculated to achieve victory.

Whatever may be such series of movements, obviously, it must have an object, _i.e._, a specific and clearly defined purpose. Equally so, all movements made on such line of movement must each have an objective, _i.e._, a terminus. These objectives, like cogs in a gear, intimately are connected with other objectives or termini, so that the project thus formed constitutes always an exact and often a vast scheme.

Frequently it happens that the occupation of an objective, valid in a given situation, is not valid in an ensuing situation for the reasons:

1. That the object of the given line of movement is become
unattainable, or,

2. Because it has become no longer worth attaining, or,

3. Because such belated attainment may be direct cause of
disaster.

PRINCIPLE

_In order to select the decisive movement in a given situation it is necessary first to determine both the object and the objective, not merely of the required movement, but also of that series of movements, which collectively constitute the projected line of movement; together with the object and the objective of every movement contained therein._

The mathematician readily will perceive, and the student doubtless will permit himself to be informed, that:

Before the true object and the true objective of any movement can be determined it first is necessary to deduce the common object of all movement.

* * * * *

As is well known, the combined movements of the Chess-pieces over the surface of the Chess-board during a game at Chess are infinite.

These calculations are so complex that human perception accurately can forecast ultimate and even immediate results only in comparatively few and simple situations. Such calculable outcomes are limited to the earlier stages of the opening, to the concluding phases of a game; and to situations in the mid-game wherein the presence of but few adverse pieces minimizes the volume of effort possible to the opponent.

Consequently, it is self-evident, that:

PRINCIPLE

_Situations on the Chess-board require for their demonstration a degree of skill which decreases as the hostile power of resistance decreases._

All power for resistance possessed by an army emanates from its ability to move. This faculty of Mobility is that inestimable quality without which nothing and by means of which everything, can be done.

From this truth it is easy to deduce the common object of all movement, which obviously is:

_To minimize the mobility of the opposing force._

The hostile army having the ability to move and consequently a power for resistance equal to that possessed by the kindred army; it becomes of the first importance to discover in what way the kindred army is superior to that adverse force, which in the Normal Situation on the Chess-board is its exact counterpart in material, position and formation.

Such normal superiority of the White army over the Black army is found in the fact that:

1. _The former has the privilege of making the initial move of
the game._

2. _This privilege of first move is the absolute advantage in
Time._

While no mathematical demonstration of the outcome of a game at Chess is possible, nevertheless there are rational grounds for assuming that with exact play, White should win.

This decided and probably decisive advantage possessed by White can be minimized only by correcting a mathematical blemish in the game of Chess as at present constructed; which blemish, there is reason to believe, did not originally exist.

This imperfection seemingly is the result of unscientific modifications of the Italian method of Castling; which latter, from the standpoint of mathematics and of Strategetics, embodies the true spirit of that delicate and vital evolution.

To the mathematician and to the Strategist, it is clear that Chess as first devised was geometrically perfect. The abortions played during successive ages and in various parts of the Earth, merely are crude and unscientific deviations from the perfect original.

Thus, strategetically, the correct post of deployment for the Chess-King is at the extremity of a straight line drawn from the center of that Grand Strategic Front which appertains to the existing formation.

Hence, in the grand front by the right, the King in Castling K R, properly goes in one move to KKt1, his proper post. Conversely, in Castling Q R, he also should go in one move to QKt1, his proper post corresponding to the grand front by the left.

Again, whenever the formation logically points to the grand front by the right refused, the King should go in one move from K1 to KR1. When the formations indicate the grand front by the left refused, the King should go in one move from K1 to QR1.

In each and every case the co-operating Rook should be posted at the corresponding Bishop’s square, in order to support the alignment by P-B4, of the front adopted.

The faulty mode of castling today in vogue clearly is not the product either of the mathematic nor of the strategetic mind.

The infantile definition of “the books,” viz., “The King in Castling moves two squares either to the right or to the left,” displays all that mania for the commonplace, which characterizes the dilettante.

All that can be done is to call attention to this baleful excrescence on the great Game. Of course, it is useless to combat it. In the words of the Count de Saxe:

“The power of custom is absolute. To depart from it is a
crime, and the most inexcusable of all crimes is to introduce
innovations. For most people, it is sufficient that a thing is
so, to forever allow it to remain so.”

Says the great Frederic;

“Man hardly may eradicate in his short lifetime all the
prejudices that are imbibed with his mother’s milk; and it is
well nigh impossible to successfully wrestle with custom, that
chief argument of fools.”

Also bearing in mind the irony of Cicero, who regarded himself fortunate in that he had not fallen victim to services rendered his countrymen, it suffices to say:

The true Chessic dictum in regard to the double evolution of the King and Rook should read:

“_The King of Castling should deploy in one move to that
point where, as the Base of Operations, it mathematically
harmonizes with that Strategic Front, which is, or must become,
established._”

The change in the present form of Castling, herein suggested, should be made in the true interests of the Royal Game.

The instant effect of such change will be:

1. Largely to increase the defensive resources both of White and
Black;

2. To minimize the handicap on the second player, due to White’s
advantage of first move;

3. To permit open play on the Queen’s side of the board and thus
provide a broader and more resplendent field for Strategetic
genius.

* * * * *

In all our modern-day mis-interpretations of the ethics of Chess and our characteristic Twentieth Century looseness of practice as applied to Chess-play, perhaps there exists no greater absurdity, than that subversion of ordinary intelligence, daily evinced by permitting a piece which cannot move, to give check.

It is a well known and in many ways a deserved reproach, cast by the German erudite, that the mind of the Anglo-Saxon is not properly developed, that it is able to act correctly only when dealing with known quantities, and is inadequate for the elucidation of indeterminate things.

In consequence, they say, the argumentative attempts of the Anglo-Saxon are puerile; the natural result of a mental limitation which differs from that of monkeys and parrots, merely in ability to count beyond two.

Surely it would seem that a very young child readily would sense that:

A Chess-piece, which by law is debarred from movement, is, by the same law, necessarily debarred from capturing adverse material; inasmuch as in order to capture, a piece must move.

Nevertheless consensus of opinion today among children of every growth and whether Anglo-Saxon or German, universally countenance the paradox that:

A piece which is pinned on its own King, can give check _i.e._, threaten to move and capture the adverse King.

To argue this question correctly and to deduce the logical solution, it is necessary to revert to first principles and to note that:

It is a fundamental of Chess mathematics that the King cannot be exposed to capture.

Furthermore, it is to be noted as equally fundamental, that:

1. A piece exerts no force against that point upon which it is
posted;

2. That whatever power a piece exerts, always is exerted against
some other point than the point upon which it stands; and that;

3. In order to exert such power, it is an all-essential that the
piece move from the point which it occupies to the point at which
its power is to be exerted.

Hence, it is obvious and may be mathematically demonstrated, that,

1. A piece which cannot move, cannot capture.

2. A piece which cannot capture, does not exercise any threat of
capture; and

3. Consequently, a piece deprived of its right to move; which
cannot capture nor exercise any threat to capture, obviously and
by mathematical demonstration, cannot give check, inasmuch, as
“check” merely is the threat by a piece to move and capture the
adverse King.

Therefore, whatever may be the normal area of movement belonging to a piece, whenever from any cause such piece loses its power of movement, then,

It no longer can capture, nor exercise any threat of capture, upon the points contained within said area; and consequently such points so far as said immovable piece is concerned, may be occupied in safety by any adverse piece including the adverse King, for the reason that:

An immovable piece cannot move; and not being able to move it cannot capture, and not being able to capture, it does not exercise any threat of capture, and consequently it cannot give check.

This incongruity of permitting an immovable piece to give check constitutes the second mathematical blemish in the game of Chess, as at present constructed.

This fallacy, the correction of which any schoolboy may mathematically demonstrate, is defended, even by many who would know better, if they merely would take time for reflection; by the inane assumption, that:

A piece which admittedly is disqualified and rendered dormant by all the fundamentals of the science of Chess, and which therefore cannot legally move and consequently cannot legally capture anything; by some hocus-pocus may be made to move and to capture that _most_ valuable of _all_ prizes, the adverse King; and this at a time and under circumstances when, as is universally allowed, it cannot legally move against, nor legally capture _any other_ adverse piece.

The basis of this illogical, illegal, and untenable assumption is:

The pinned piece, belonging to that force which has the privilege of moving, can abandon its post, and capture the adverse King; this stroke ends the game and the game being ended, the pinning piece never can avail of the abandonment of the covering post by the pinned piece to capture the King thus exposed.

The insufficiency of this subterfuge is clear to the mathematical mind. Its subtlety lies in confounding together things which have no connection, viz.:

Admittedly the given body of Chess-pieces has the right to move, but it is of the utmost importance to note that this privilege of moving extends only to a single piece and from this privilege of moving the pinned piece is debarred by a specific and fundamental law of the game, which declares that:

“A piece shall not by removing itself uncover the kindred King to
the attack of a hostile piece.”

Thus, it is clear, that a pinned piece is a disqualified piece; its powers are dormant and by the laws of the game it is temporarily reduced to an inert mass, and deprived of every faculty normally appertaining to it as a Chess-piece. On the other hand, as is equally obvious, the pinning piece is in full possession of its normal powers and is qualified to perform every function.

To hold that a piece disqualified by the laws of the game can nullify the activities of a piece in full possession of its powers, is to assert that black is white, that the moon is made of green cheese, that the tail can wag the dog, or any other of those things which have led the German to promulgate his caustic formula on the Anglo-Saxon.

Hence, artificially to nullify the normal powers of an active and potential piece which is operating in conformity to the laws of the game, and artificially to revivify the dormant powers of a piece disqualified by the same laws; to debar the former from exercising its legitimate functions and to permit the latter to exercise functions from which by law, it specifically is debarred, is a self-evident incongruity and any argument whereby such procedure is upheld, necessarily and obviously, is sophistry.

* * * * *

No less interesting than instructive and conclusive, is reference of this question to those intellectual principles which give birth to the game of Chess, _per se_, viz.:

As a primary fundamental, with the power to give check, is associated concurrently the obligation upon the King thus checked, not to remain in check.

Secondly: The totality of powers assigned to the Chess-pieces is the ability to move, provided the King be free from check. This totality of powers may be denoted by the indefinite symbol, X.

The play thus has for its object:

The reduction to zero of the adverse X, by the operation of the kindred X.

This result is checkmate in its generalized form. In effect, it is the destruction of the power of the adverse pieces to move, by means of check made permanent.

By the law of continuity it is self-evident that:

The power to move appertaining either to White or to Black, runs from full power to move any piece (a power due to freedom from check), down to total inability to move any piece, due to his King being permanently checked, _i.e._, checkmated.

This series cannot be interrupted without obvious violation of the ethics of the game; because, so long as any part of X remains, the principle from which the series emanated still operates, and this without regard to quantity of X remaining unexpended.

Thus, a game of Chess is a procedure from total ability to total disability; _i.e._, from one logical whole to another; otherwise, from X to zero.

Checkmate, furnishes the limit to the series; the game and X vanish together.

This is in perfect keeping with the law of continuity, which acts and dominates from beginning to end of the series, and so long as any part of X remains.

Hence to permit either White or Black to move any piece, leaving his King in check, is an anomaly.

* * * * *

Denial to the Pawn of ability to move to the rear is an accurate interpretation of military ethics.

Of those puerile hypotheses common to the man who does not know, one of the most entrancing to the popular mind, is the notion that Corps d’armee properly are of equal numbers and of the same composition.

This supposition is due to ignorance of the fact that the multifarious duties of applied Strategetics, require for their execution like variety of instruments, which diversity of means is strikingly illustrated by the differing movements of the Chess-pieces.

The inability of the Pawn to move backward strategically harmonizes with its functions as a Corps of Position, in contradiction to the movements of the pieces, which latter are Corps of Evolution.

This restriction in the move of the Pawn is in exact harmony with the inability of the Queen to move on obliques, of the Rook to move on obliques or on diagonals, of the Bishop to move on obliques, verticals and horizontals, of the Knight to move on diagonals, verticals, and horizontals, and of the King to move like any other piece.

* * * * *

Possessed of the invaluable privilege of making the first move in the game, knowing that no move should be made without an object, understanding that the true object of every move is to minimize the adverse power for resistance and comprehending that all power for resistance is derived from facility of movement, the student easily deduces the true object of White’s initial move in every game of Chess, viz.:

PRINCIPLE

_To make the first of a series of movements, each of which shall increase the mobility of the kindred pieces and correspondingly decrease the mobility of the adverse pieces._

As the effect of such policy, the power for resistance appertaining to Black, ultimately must become so insufficient that he no longer will be able adequately to defend:

1. His base of operations.

2. The communications of his army with its base.

3. The communications of his corps d’armee with each other, or,

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,

1. Eight points in the base.

2. Eight points in the perpendicular.

3. Eight points in the hypothenuse.

Consequently the _three_ sides of this given right angled triangle are _equal_ to each other, which is a geometric _impossibility_.

Therefore, it is self-evident that there exists a mathematical incongruity in the surface of the Chess-board.

That is, what to the eye _seems_ a right angled triangle, is in its relations to the _movements_ of the Chess-pieces, an equilateral triangle. Hence, the Chess-board, in its relations to the pieces when the latter are at _rest_, properly may be regarded as a great _square_ sub-divided into sixty-four smaller squares; but on the contrary, in those calculations relating to the Chess-pieces in _motion_, the Chess-board must be regarded as the _quadrant_ of a circle of eight points radius. The demonstration follows, viz.:

Connect by a straight line the points KR8 and QR8. Connect by another straight line the points QR8 and QR1. Connect each of the fifteen points through which these lines pass with the point KR1, by means of lines passing through the least number of points intervening.

Then the line KR8 and QR8 will represent the segment of a circle of which latter the point KR1 is the center. The lines KR1-KR8 and KR1-QR1 will represent the sides of a quadrant contained in the given circle and bounded by the given segment, and the lines drawn from KR1 to the fifteen points contained in the given segment of the given circumference, will be found to be fifteen equal radii each eight points in length.

* * * * *

Having noted the form of the Static or positional surface of the Chess-board and its relations to the pieces at rest, and having established the configuration of the Dynamic surface upon which the pieces move, it is next in sequence to deduce that fundamental fact and to give it that geometric expression which shall mathematically harmonize these conflicting geometric figures in their relations to Chess-play.

As the basic fact of applied Chessic forces, it is to be noted, that:

PRINCIPLE

_The King is the SOURCE from whence the Chess-pieces derive all power of movement; and from his ability to move, emanates ALL power for attack and for defence possessed by a Chessic army._

This faculty of mobility, derived from the existence of the kindred King, is the all essential element in Chess-play, and to increase the mobility of the kindred pieces and to reduce that of the adverse pieces is the simple, sure and only scientific road to victory; and by comparison of the Static with the Dynamic surface of the Chess-board, the desired principle readily is discovered, viz.,

The Static surface of the Chess-board being a square, its least
division is into two great right angled triangles having a common
hypothenuse.

The Dynamic surface being the quadrant of a circle, its least
division also is into two great sections, one of which is a right
angled triangle and the other a semi-circle.

Comparing the two surfaces of the Chess-board thus divided, it will be seen that these three great right angled triangles are equal, each containing thirty-six points; and having for their common vertices, the points KR1, QR1 and R8.

Furthermore, it will be seen that the hypothenuse common to these triangles, also is the chord of that semi-circle which appertains to the Dynamic surface.

Again, it will be perceived that this semi-circle, like the three right angled triangles, is composed of thirty-six points, and consequently that all of the four sub-divisions of the Static and Dynamic surfaces of the Chess-board are equal.

Thus it obviously follows, that:

1. The great central diagonal, always is one side of each of
the four chief geometric figures into which the Chess board is
divided; that:

2. It mathematically perfects each of these figures and
harmonizes each to all, and that:

3. By means of it each figure becomes possessed of eight more
points than it otherwise would contain.

Hence, the following is self-evident:

PRINCIPLE

_That Chessic army which can possess itself of the great central diagonal, thereby acquires the larger number of points upon which to act and consequently greater facilities for movement; and conversely:_

_By the loss of the great central diagonal, the mobility of the opposing army is correspondingly decreased._

It therefore is clear that the object of any series of movements by a Chessic army acting otherwise than on Line of Operations, should be:

PRINCIPLE

_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:

PRINCIPLE

_Increased facilities for movement enhance the power of attacking pieces in a much greater degree than like facilities enhance the power of defending pieces._

Such increasing facilities for movement ultimately render an attacking force irresistible, for the reason that it finally becomes a physical impossibility for the opposing equal force to provide valid defences for the numerous tactical keys, which at a given time become simultaneously assailed. Hence:

PRINCIPLE

_Superior facilities for occupying any point at any time and with any force, always ensure the superior force at a given point, at a given time._

The relative advantage in mobility possessed by one army over an opposing army always can be determined by the following, viz.:

RULE

1. That army whose strategic front of operations is established upon the Strategetic Center has the relative advantage in Mobility.

2. To utilize the advantage in Mobility extend the Strategic Front in the direction of the objective plane.

3. To neutralize the relative disadvantage in Mobility eliminate that adverse Corps d’armee which tactically expresses such adverse advantage; or so post the Prime Strategetic Point as to vitiate the adverse Strategic front.

Advantage in Mobility is divided into two classes, viz.:

I. General Advantage in Mobility.

II. Special Advantage in Mobility.

A General Advantage in Mobility consists in the ability to act simultaneously against two or more vital points by means of interior logistic radii due to position between:--

1. The adverse army and its Base of Operations.

2. Two or more adverse Grand Columns.

3. The wings of a hostile Grand Column.

4. Two or more isolated adverse Corps d’armee.

Such position upon interior lines of movement is secured by occupying either of the Prime Offensive Origins, _i.e._:

1. Strategic Center _vs._ Adverse Formation in Mass.

2. Logistic Center _vs._ Adverse Formation by Grand Columns.

3. Tactical Center _vs._ Adverse Formation by Wings.

4. Logistic Triune _vs._ Adverse Formation by Corps.

Special Advantage in Mobility consists in the ability of a corps d’armee to traverse greater or equal distances in lesser times than opposing corps.

MILITARY EXAMPLES

_“Never interrupt your enemy when he is making a false
movement.”--Napoleon._

In the year (366 B.C.) the King of Sparta, with an army of 30,000 men marched to the aid of the Mantineans against Thebes. Epaminondas took up a post with his army from whence he equally threatened Mantinea and Sparta. Agesilaus incautiously moved too far towards the coast, whereupon Epaminondas, with 70,000 men precipitated himself upon Lacedaemonia, laying waste the country with fire and sword, all but taking by storm the city of Sparta and showing the women of Lacedaemonia the campfire of an enemy for the first time in six hundred years.

* * * * *

Flaminius advancing incautiously to oppose Hannibal, the latter took up a post with his army from whence he equally threatened the city of Rome and the army of the Consul. In the endeavor to rectify his error, the Roman general committed a worse and was destroyed with his entire army.

* * * * *

At Thapsus, April 6, 46 B.C., Caesar took up a post with his army from whence he equally threatened the Roman army under Scipio and the African army under Juba. Scipio having marched off with his troops to a better camp some miles distant, Caesar attacked and annihilated Juba’s army.

* * * * *

At Pirna, Frederic the Great, captured the Saxon army entire, and at Rossbach, Leuthern and Zorndorf destroyed successively a French, an Austrian and a Russian army merely by occupying a post from whence he equally threatened two or more vital points, awaiting the time when one would become inadequately defended.

* * * * *

Washington won the Revolutionary War merely by occupying a post from whence he equally threatened the British armies at New York and Philadelphia; refusing battle and building up an army of Continental regular troops enlisted for the war and trained by the Baron von Steuben in the system of Frederic the Great.

* * * * *

Bonaparte won at Montenotte, Castiglione, Arcola, Rivoli and Austerlitz his most perfect exhibitions of generalship, merely by passively threatening two vital points and in his own words: “By never interrupting an enemy when he is making a false movement.”

* * * * *

Perfection in Mobility is attained whenever the kindred army is able to act unrestrainedly in any and all directions, while the movements of the hostile army are restricted.

NUMBERS

_“In warfare the advantage in numbers never is to be
despised.”--Von Moltke._

* * * * *

_“Arguments avail but little against him whose opinion is voiced
by thirty legions.”--Roman Proverb._

* * * * *

_“That king who has the most iron is master of those who merely
have the more gold.”--Solon._

* * * * *

_“It never troubles the wolf how many sheep there
are.”--Agesilaus._

NUMBERS

_“A handful of troops inured to Warfare proceed to certain
victory; while on the contrary, numerous hordes of raw and
undisciplined men are but a multitude of victims dragged to
slaughter.”--Vegetius._

* * * * *

_“Turenne always was victorious with armies infinitely inferior
in numbers to those of his enemies; because he moved with
expedition, knew how to secure himself from being attacked in
every situation and always kept near his enemy.”--Count de Saxe._

* * * * *

_“Numbers are of no significance when troops are once thrown into
confusion.”--Prince Eugene._

Humanity is divisible into two groups, one of which relatively is small and the other, by comparison, very large.

The first of these groups is made up comparatively of but a few persons, who, by virtue of circumstances are possessed of everything except adequate physical strength; and the second group consists of those vast multitudes of mankind, which are destitute of everything except of incalculable prowess, due to their overwhelming numbers.

Hence, at every moment of its existence, organized Society is face to face with the possibility of collision into the Under World; and because of the knowledge that such encounter is inevitable, unforeseeable and perhaps immediately impending, Civilization, so-called, ever is beset by an unspeakable and all-corroding fear.

_To deter a multitude, destitute of everything except the power
to take, from despoiling by means of its irresistible physique,
those few who are possessed of everything except ability to
defend themselves, in all Ages has been the chiefest problem of
mankind; and to the solution of this problem has been devoted
every resource known to Education, Legislation, Ecclesiasticism
and Jurisprudence._

This condition further is complicated by a peculiar outgrowth of necessary expedients, always more or less unstable, due to that falsity of premise in which words do not agree with acts.

Of these expedients the most incongruous is the arming and training of the children of the mob for the protection of the upper stratum; and that peculiar mental insufficiency of hoi polloi, whereby it ever is induced to accept as its leaders the sons of the Patrician class.

That a social structure founded upon such anomalies should endure, constitutes in itself the real Nine Wonders of the World; and is proof of that marvellous ingenuity with which the House of Have profits by the chronic predeliction of the House of Want to fritter away time and opportunity, feeding on vain hope.

* * * * *

_The advantage in Numbers consists in having in the aggregate more Corps d’armee than has the adversary._

All benefit to be derived from the advantage in Numbers is limited to the active and scientific use of every corp d’armee; otherwise excess of Numbers, not only is of no avail, but easily may degenerate into fatal disadvantage by impeding the decisive action of other kindred corps. Says Napoleon: “It is only the troops brought into action, that avails in battles and campaigns--the rest does not count.”

A loss in Numbers at chess-play occurs only when two pieces are lost for one, or three for two, or one for none, and the like. No diminution in aggregate of force can take place on the Chess-board, so long as the number of the opposing pieces are equal.

This is true although all the pieces on one side are Queens and those of the other side all Pawns.

The reason for this is:

All the Chess-pieces are equal in strength, one to the other. The Pawn can overthrow and capture any piece--the Queen can do no more.

That is to say, at its turn to move, any piece can capture any adverse piece; and this is all that any piece can do.

It is true that the Queen, on its turn to move, has a maximum option of twenty-seven squares, while the Pawn’s maximum never is more than three. But as the power of the Queen can be exerted only upon one point, obviously, her observation of the remaining twenty-six points is merely a manifestation of mobility, and her display of force is limited to a single square. Hence, the result in each case is identical, and the display of force equal.

The relative advantage in Numbers possessed by one army over an opposing army always can be determined by the following, viz.:

RULE

_That army which contains more Corps d’armee than an opposing army has the relative advantage in Numbers._

_“With the inferiority in Numbers, one must depend more upon
conduct and contrivance than upon strength.”--Caesar._

MILITARY EXAMPLES

_“He who has the advantage in Numbers, if he be not a blockhead,
incessantly will distract his enemy by detachments, against all
of which it is impossible to provide a remedy.”--Frederic the
Great._

* * * * *

_“He that hath the advantage in Numbers usually should exchange
pieces freely, because the fewer that remain the more readily are
they oppressed by a superior force.”--Dal Rio._

At Thymbra, Cyrus the Great, king of the Medes and Persians, with 10,000 horse cuirassiers, 20,000 heavy infantry, 300 chariots and 166,000 light troops, conquered Croesus, King of Assyria whose army consisted of 360,000 infantry and 60,000 cavalry. This victory made Persia dominant in Asia.

* * * * *

At Marathon, 10,000 Athenian and 1,000 Plataean heavy infantry, routed 110,000 Medes and Persians. This victory averted the overthrow of Grecian civilization by Asiatic barbarism.

* * * * *

At Leuctra, Epaminondas, general of the Thebans, with 6000 heavy infantry and 400 heavy horse, routed the Lacedaemonean army, composed of 22,000 of the bravest and most skillful soldiers of the known world, and extinguished the military ascendency which for centuries Sparta had exercised over the Grecian commonwealths.

At Issus, Alexander the Great with 40,000 heavy infantry and 7,000 heavy cavalry destroyed the army of Darius Codomannus, King of Persia, which consisted of 1,000,000 infantry, 40,000 cavalry, 200 chariots and 15 elephants. This battle, in which white men encountered elephants for the first time, established the military supremacy of Europe over Asia.

* * * * *

Alexander the Great invaded Asia (May, 334 B.C.) whose armies aggregated 3,000,000 men trained to war; with 30,000 heavy infantry, 4000 heavy cavalry, $225,000 dollars in money and thirty days’ provisions.

At Arbela, Alexander the Great with 45,000 heavy infantry and 8,000 heavy horse, annihilated the last resources of Darius and reduced Persia to a Greek province. The Persian army consisted of about 600,000 infantry and cavalry, of whom 300,000 were killed.

* * * * *

Hannibal began his march from Spain (218 B.C.) to invade the Roman commonwealth, with 90,000 heavy infantry and 12,000 heavy cavalry. He arrived at Aosta in October (218 B.C.) with only 20,000 infantry and 6,000 cavalry to encounter a State that could put into the field 700,000 of the bravest and most skillful soldiers then alive.

* * * * *

At Cannae, Hannibal destroyed the finest army Rome ever put in the field. Out of 90,000 of the flower of the commonwealth only about 3,000 escaped. The Carthagenian army consisted of 40,000 heavy infantry and 10,000 heavy cavalry.

* * * * *

At Alesia, (51 B.C.) Caesar completed the subjugation of Gaul, by destroying in detail two hostile armies aggregating 470,000 men. The Roman army consisted of 43,000 heavy infantry, 10,000 heavy cavalry and 10,000 light cavalry.

* * * * *

At Pharsaleus, (48 B.C.) Caesar with 22,000 Roman veterans routed 45,000 soldiers under Pompey and acquired the chief place in the Roman state.

* * * * *

At Angora, (1402) Tamerlane, with 1,400,000 Asiatics, destroyed the Turkish army of 900,000 men, commanded by the Ottoman Sultan Bajazet, in the most stupendous battle of authentic record.