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The highest use of Topography consists in reducing a superior adverse force to the inferior force, by minimizing the radius of action of the hostile Corps d’armee.

This is effected by so posting the kindred corps that in the resulting Strategetic Horizons, impassable natural barriers are presented to the march of hostile corps toward their respective objectives.

On the surface of the earth such natural barriers are formed by mountains, rivers, lakes, swamps, forests, deserts, the ocean, and the boundaries of neutral States.

On the Chess-board these topographical conditions are typified by peculiarities and limitations in the movements of the Chess-pieces, viz.:

• I. The sides of the Chess-board which terminate all movements of the chess pieces.
• II. That limitation of the movements of the Chesspieces which makes it impossible for them to move other than in straight lines.
• III. The inability of the Queen to move on obliques.
• IV. The inability of the Rook to move either on obliques or on diagonals.
• V. The inability of the Bishop to move either on obliques, verticals, or horizontals.
• VI. The inability of the Knight to move either on diagonals, verticals, or horizontals, and the limitation of its move to two squares distance.
• VII. The inability of the Pawn to move either on obliques or horizontals, and the limitation of its first move to two squares and of its subsequent moves to one square.
• VIII. The limitation of the King’s move to one square.

These limitations and impediments to the movements of the Chess-pieces, are equivalent in Chess-play to obstacles interposed by Nature to the march of troops over the surface of the earth.

Prefect Generalship, in its calculations, so combines these insurmountable barriers with the relative positions of the contending armies, that the kindred army becomes at every vital point the superior force.

This effect is produced by merely causing rivers and mountains to take the place of kindred Corps d’armee.

It is only by the study of Chessic topography that the tremendous problems solved by the chess player become manifest:

Instead of calculations limited to one visible and unchangeable Chess-board of sixty-four squares, the divinations of the Chess-master comprehend and harmonize as many invisible Chess-boards as there are Chess-pieces contained in the Topographical Zone.

Furthermore, all these surfaces differ to the extent and in conformity to that particular sensible horizon, appertaining to the Chess-piece from which it emanates.

The enormous difficulties of Chess-play, like those of warfare, arise from the necessity of combining in a single composite topographical horizon, all those differing, sensible horizons which appertain, not merely to the kindred, but also to the hostile corps; and to do this in such a manner, as to minimize the hostile powers for offence and defence, by debarring one or more of the hostile pieces from the true Strategetic Horizon.

To divide up the enemy’s force, by making natural barriers take the place of troops, is the basis of those processes which dominate Grand Manoeuvres.

Of all the deductions of Chess-play and of warfare, such combinations of Strategy and Topography are the most subtle and intangible. The highest talent is required in its interpretation, and mastery of it, more than of any other branch of Strategetics, proclaims the great Captain at war, or at chess.

TOPOGRAPHY OF THE KING

From the view-point of the King, the surface of the Chess-board takes on the topographical aspect of a vast expanse of open, level country.

This vista is void of insurmountable natural obstacles, other than the sides and extremities. The latter collectively may be regarded, for strategical purposes, either as the Ocean, or the boundaries of neutral States.

To the King, this vast territory is accessible in all directions. At his pleasure he may move to and occupy either of the sixty-four squares of the Chess-board, in a minimum of one and in a maximum of seven moves. The only obstacles to his march are distance and the opposition of an enemy.

The Strategical weakness of the Topographical Horizon peculiar to the King arises from its always taking on and maintaining the physical form of a plain. Consequently it is vulnerable to attack from all sides and what is far worse, it readily is commanded and from a superior topographical post, by every adverse piece, except the King and Pawn.

Thus, the hostile Queen, without being attacked in return, may enfilade the King along all verticals, horizontals and diagonals; the Rooks, along all verticals and horizontals; the Bishops, along all diagonals of like color; and the Knights along all obliques.

TOPOGRAPHY OF THE QUEEN

From the view-point of the Queen, the surface of the Chess-board takes on the topographical aspect of a series of wide, straight valleys separated by high, impassable mountain ranges, unfordable rivers, and impenetrable forests and morasses. These valleys, which number never less than three, nor more than eight, in the same group, are of varying length and always converge upon and unite with each other at the point occupied by the Queen.

These valleys contained in the Queen’s topographical horizon may be classified, viz.:

Class I, consists of those groups made up of three valleys.

Class II, of those groups made up of five valleys.

Class III, of those groups made up of eight valleys of lesser area; and

Class IV, of those groups made up of eight valleys of greater area.

Groups of the first class always have an area of twenty points; those of the second have an area of twenty-three points; those of the third have an area of twenty-five points, and those of the fourth have an area of twenty-seven points. Such areas always are exclusive of that point upon which the Queen is posted.

Although impassable natural barriers restrict the movement of the Queen to less than one-half of the Topographical Zone, these obstacles always are intersected by long stretches of open country formed by intervening valleys.

Hence, the march of this most mobile of the Chesspieces always is open either in three, five, or eight directions, and it always is possible for her, unless impeded by the interference of kindred or hostile corps, to reach any desired point on the Chess-board in two moves.

The weakness peculiar to the Topographical Horizon which appertains to the Queen, originates in the fact that it never commands the origins of obliques. Consequently, every post of the Queen, is open to unopposed attack by the hostile Knights.

TOPOGRAPHY OF THE ROOK

From the view-point of the Rook, the surface of the Chess-board takes on a topographical aspect which varies with the post occupied.

Placed at either R1 or R8 the Rook occupies the central point of a great valley, 15 points in length, which winds around the slope of an immense and inaccessible mountain range. This latter, in extent, includes the remainder of the Topographical Zone.

With the Rook placed at R2 or R7, this great mountain wall becomes pierced by a long valley running at right angles to the first, but the area open to the movement of the Rook is not increased.

Placed at Kt2, B3, K4, or Q4, the Rook becomes enclosed amid impassable natural barriers. But although in such cases it always occupies the point of union of four easily traversed although unequal valleys, its area of movement is neither increased nor diminished, remaining always at fourteen points open to occupation.

Unless impeded by the presence of kindred or adverse corps on its logistic radii, the Rook always may move either in two, three, or four directions, and it may reach any desired point on the Chess-board in two moves.

The weakness peculiar to the Topographical Horizon of the Rook lies in the fact that it never commands the origins of diagonals or obliques. Hence it is open to unopposed attack along the first from adverse Queen, King, Bishops and Pawns, and along the second from adverse Knights.

TOPOGRAPHY OF THE BISHOP

From the view-point of the Bishop, the surface of the Chess-board takes on a topographical aspect most forbidding.

To this Chess-piece at least one-half of the Topographical Zone is inaccessible, and under any circumstances his movements are limited to the thirty-two squares of his own color.

Thus, the Topographical Horizon of the Bishop takes the form of a broken country, dotted with high hills, deep lakes, impenetrable swamps, and thick woodlands. But between these obstacles thus set about by Nature, run level valleys, varied in extent and easy of access. This fact so modifies this harshest of all sensible horizons as to make the Bishop next in activity to the Rook.

Within its limited sphere of action, the Bishop may move in either one or four directions with a minimum of nine and a maximum of fourteen points open to his occupation. Unimpeded by other corps blocking his route of march, the Bishop may reach any desired point of his own color on the chess board in two moves.

The weakness peculiar to the topographical horizon of the Bishop is its liability to unopposed attack along verticals and horizontals by the hostile King, Queen and Rooks; and along obliques by the hostile Knights.

TOPOGRAPHY OF THE KNIGHT

From the view-point of the Knight, the surface of the Chess-board takes on the aspect of a densely wooded and entirely undeveloped country; made up of a profusion of ponds, rivulets, swamps, etc., none of which are impassable although sufficient to impede progress.

Unless interfered with by kindred or hostile corps, or the limitations of the Chess-board, the Knight always may move either in two, four, six, or eight directions. It may reach any desired point in a minimum of one and a maximum of six moves, and may occupy the sixty-four squares of the Chess-board in the same number of marches.

The weakness of the topographical horizon of the Knight lies in the fact that it never commands adjacent points, nor any of those distant, other than the termini of its own obliques. Hence it is open to unopposed attack along verticals and horizontals from the adverse King, Queen and Rooks, and along diagonals from the adverse King, Queen, Bishop and Pawns.

TOPOGRAPHY OF THE PAWN

From the point of view of the Pawn, the surface of the Chess-board takes on the topographical aspect of a country which as it is entered, constantly becomes wilder and more rugged.

The march of the Pawn always is along a valley situated between impracticable natural barriers, and the possible movements of the Pawn always decrease as the distance traveled increases.

Unhindered by either kindred or hostile corps, the Pawn may reach any point of junction in the kindred Logistic Horizon, which is contained within its altitude, in a minimum of five and in a maximum of six moves. It may march only in one direction, except in capturing, when it may acquire the option of acting in three directions.

The weakness of the topographical horizon of the Pawn originates in its inability to command the adjacent country. Therefore, it is exposed to unopposed attack along verticals and horizontals by the hostile King, Queen and Rooks; along diagonals by the adverse King, Queen and Bishops, and along obliques by the adverse Knights.

TOPOGRAPHY OF THE TOPOGRAPHICAL ZONE

That normal and visible surface of the Chess-board termed the Topographical Zone is bounded by four great natural barriers, impassable to any Chess-piece.

The two sides of the zone may be held to typify either the Ocean or the boundaries of neutral States. The two extremities of the Chess-board while holding the previously announced relation to Chess-pieces contained in the Topographical Zone, also holds another and radically different relation to those Chess-pieces not contained in the Topographical Zone, viz.:

In the latter case, the two extremities of the chessboard are to be regarded as two great mountain ranges, each of which is pierced by eight defiles, the latter being the sixteen points of junction contained in the kindred and adverse logistic horizons.

In the arena thus formed by these four great natural barriers, two hostile armies composed of the thirty-two Chess-pieces, are contending for the mastery.

Meanwhile, beyond these great mountain ranges, are advancing to the aid of the combatants, two other armies, represented by the power of promotion possessed by the Pawns. Each of these two hypothetical armies is assailing the outer slope of that range of mountains which lies in the rear of the hostile force. Its effort is to pass one of the eight defiles and by occupying a Point of Junction in the kindred Logistic Horizon, to gain entrance into the Topographical Zone. Then in the array of a Queen, or some other kindred piece, it purposes to attack decisively, the adverse Strategetic Rear.

To oppose the attack of this hypothetical hostile army, whose movements always are typified by the advance of the adverse Pawns, is the duty of the kindred column of manoeuvre.

Primarily this labor falls upon the kindred Pawns. Upon each Pawn devolves the duty of guarding that defile situated directly on its front, by maintaining itself as a Point of Impenetrability between the corresponding hostile pawn and the kindred Strategic Rear.

Conversely, a second duty devolves upon each Pawn; and as an integer of the Column of Support, it continually must threaten and whenever opportunity is presented it decisively must assault the defile on its front, for the purpose of penetrating to the kindred logistic horizon and becoming promoted to such kindred piece, as by attacking the adverse Determinate Force in flank, in rear, or in both, may decide the victory in favor of the kindred army.

Every variety of topography has peculiar requirements for its attack and its defence; and situations even though but little different from each other, nevertheless must be treated according to their particular nature.

In order to acquire the habit of selecting at a glance the correct posts for an army and of making proper dispositions of the kindred corps with rapidity and precision, topography should be studied with great attention, for most frequently it happens that circumstances do not allow time to do these things with deliberation.

PRINCIPLE

Acting either offensively or defensively, one never should proceed in such a way as to allow the enemy the advantage of ground;

That is to say: Kindred corps never should be exposed to unopposed adverse radii of offence, when the effect of such exposure is the loss of kindred material, or of time much better to be employed, than in making a necessary and servile retreat from an untenable post.

On the contrary, every kindred topographical advantage should unhesitatingly be availed of; and particular attention continually should be paid to advancing the kindred corps to points offensive where they cannot be successfully attacked.

Pains always must be taken to select advantageous ground. Indifferent posts must never be occupied from sheer indolence or from over-confidence in the strength of the kindred, or the weakness of the adverse army.

Particularly must one beware of permitting the enemy to retain advantages in topography; always and at once he should be dislodged from posts whose continued occupation may facilitate his giving an unforeseen and often a fatal blow.

The full importance of topography perhaps is best expressed in the following dictum by the great Frederic:

PRINCIPLE

“Whenever a general and decisive topographical advantage is presented, one has merely to avail of this, without troubling about anything further.”

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

RULE

1. If the principal adverse Corps of Position are situated upon points of a given color, and if the principal Kindred Corps of Position are situated upon points not of the given color, then:

That army which has the more Corps of Evolution able to act against points of the given color, and the equality in Corps of Evolution able to act against points of the opposite color, has the relative advantage in Topography.

2. To utilize the relative advantage in Topography, construct a position in which the kindred Corps of Position necessary to be defended shall occupy a point upon the sub-geometric symbol of a kindred Corps of Evolution; which point shall be a Tactical Key of a True Strategetic Horizon of which the kindred Corps of Evolution is the Corps of the Centre and of which either the adverse King or an undefendable adverse piece is the second Tactical Key.

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.

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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.

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MILITARY EXAMPLES

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.

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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.

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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.

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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.

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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.

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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.

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

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.”

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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.”

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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.

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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.

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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.

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

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

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

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

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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.

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

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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.

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

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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.

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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.

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

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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.

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

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