MOBILITY

“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 hisinfantry 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 levelplain, 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 ofSwedish 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

“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.

“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.

“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 theproject 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:

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 thepresence of but few adverse pieces minimizes the volume of effort possible to the opponent.

Consequently, it is self-evident, that:

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:

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:

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 checki.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:

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

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 thatmostvaluable ofallprizes, the adverse King; and this at a time and under circumstances when, as is universally allowed, it cannot legally move against, nor legally captureany otheradverse 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 befree 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 whodoes 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.:

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:

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.:

To bring about either of these results against an opponent equally equipped and capable, of course is amuch 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 processesof simple arithmetic, it may be shown that there are,

Consequently thethreesides of this given right angled triangle areequalto each other, which is a geometricimpossibility.

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

That is, what to the eyeseemsa right angled triangle, is in its relations to themovementsof the Chess-pieces, an equilateral triangle. Hence, the Chess-board, in its relations to the pieces when the latter are atrest, properly may be regarded as a greatsquaresub-divided into sixty-four smaller squares; but on the contrary, in those calculations relating to the Chess-pieces inmotion, the Chess-board must be regarded as thequadrantof 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 atrest, 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:

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.

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 hypothenusecommon 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:

Hence, the following is self-evident:

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:

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.:

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:

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.:

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.:

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:—

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

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.

Back to Index Next