^ *o;o' o,^ % ^°-n^ r..--. i CHESS STRATEGETICS ILLUSTRATED WORKS ON CHESS BY FRANKLIN K. YOUNG THE MINOR TACTICS OF CHESS THE MAJOR TACTICS OF CHESS THE GRAND TACTICS OF CHESS CHESS STRATEGETICS SELF-TEACHING CHESSBOARDS Black. i ri ri T i i i r iT|-r| ?«^ m iffli' 'e of ^Ianceutre 191 Geometrically Expressed 191 PROCESSES OF GREATER LOGISTICS (Grand) .... 195 Crucial phase of chessic art and science 195 The irrepressible conflict between theory and practice . . . . 195 The theorist a worshipper of abstract propositions, the tactician enamoured of tangible and material detail 195 The theorist and the tactician contrasted 196 Both people also have the utmost contempt for the methods of the other 196 The theorist despises the lack of system in the tactician, and the latter mocks at what he calls the egotistical pedantry of the other 196 Reason why the tactician outranks the theorist in every walk of life . .' 196 The theorist is handicapped by a world-wide fallacy which ren- ders his knowledge of little use to himself or to anybody else 196 The great secret which governs the application of knowledge to practical uses 196 This secret unknown to the theorist but understood by the tactician 196 CONTENTS. xvii fAGK PROCESSES OF GREATER LOGISTICS (Grand)— conimuec/. Morphy and Napoleon combined in themselves both the educa- tion of the theorist and the skill of the tactician 197 Moreover, they knew the secret whereby is bridged tlie seem- ingly impassable gulf between science and art 197 This secret is a method of calculation whereby the principles of the science and the laws of the art are harmonized and made to co-operate to produce the desired end 198 " A Genius " is one who comprehends that method of calcula- tion whereby are harmonized the principles of the science and the processes of the art 199 That calculation whereby the true Strategetic Horizon can be detected is the connecting link between the science of chess and the art of chessplay 201 Basic Proposition of Greater Logistics 202 THE TACTICAL SEQUENCE 204 Fourteenth Law of the Art of Chessplay 204 First Tactical Sequence 205 Illustration of the order of marches contained therein .... 205 Second Tactical Sequence 212 Illustration of the order of marches contained therein . . . 212 Third Tactical Sequence 217 Illustration of the order of marches contained therein . . .217 CORPS DEFENSIVE 222 Sustaining corps 223 Supporting corps 224 Covering corps 225 Surprised 226 Surrounded 227 Isolated 228 Commanded 229 Outflanked 230 Outfronted 231 CORPS DETACHED 232 Fifteenth Law of the Art of Chessplay 233 PLANS OF CAMPAIGN 234 Factors subordinate 234 Sixteenth Law of the Art of Chessplay 234 Rules for making a Reconnoissance on the Chessboard . 235 The strategetic offensive 235 The strategetic defensive 236 XVlli CONTENTS. PAGE PRIME LOGISTIC OPERATIONS 237 ORDERS OF BATTLE 240 Offensive 241 Defensive 242 The Tactician's Rule 243 THE INITIATIVE 245 Seventeenth Law of the Art of Chessplat 248 GRAND LAW OF THE ART OF CHESSPLAY .... 249 APPENDIX. The Battle of Waterloo historicallt and technically illustrated on the chessboard 253 Capture of Souhaiu 258 " Papelotte 260 " La Haye Sainte 261 " " the Park of Hougoumont . .' 262 Rout of the Dutch Belgians 264 Biilovp- attacking at Planchenoit 266 " turns the French right 267 Reille attacking Hougoumont 269 Grand assault on Mont St. Jean 272 French army changes front 275 Arrival of Bliicher 277 Napoleon's Last Battle-Line 279 Destruction of the " Old Guard " 282 Flight of the French 284 INTRODUCTORY. IN placing before the public this fourth and final vol- ume of the " Chess Strategetics Series," the author completes a work — undertaken merely as a relief from more arduous labors — which has been accorded rec- ognition in technical literature far exceeding his expec- tations ; a recognition which commands his deepest and sincere appreciation. The synthetic method of chessplay — which for the first time is formulated and put into language in these volumes — early received the indorsement of Emmanuel Lasker, who, in a personal letter to Mr. Edwin C. Howell, collaborator in " Minor Tactics," stated that the new method of chessplay " was replete with logic and com- mon sense." This distinguished stamp of approval, placed upon the new synthetic method by the Chess Champion of the World, was supplemented a few months later by recog- nition, high and flattering, in another sphere. The " London (Eng.) Spectator," in its issue of June 1, 1895, devoted a page and a half to an intelligent and compli- mentary review of the " Minor Tactics of Chess," and stated : — " The book is clearly written, but an effort is required to master the theory — and it needs to be mastered entire — before the light dawns. The reviewer, a poor player, XX INTRODUCTORY. played for many years with a friend from whom he usually received odds and a beating. After acquiring (by six months' study) the new theory, he has played a series of games with the same friend (to whom this theory was un- known) without taking odds, and has not only won the majority of the games, but made a much better fight in those which he lost than he had been able to make before becoming acquainted with the theory." On this side of the Atlantic the reception accorded the new method was equally cordial, and that high authority, R. F. Foster, in his " Complete Hoyle " said : — ^'Of all the standard works on the game, 'The Minor Tactics of Chess ' will be found most useful to beginners." The appearance of " The Grand Tactics of Chess," the second volume of the series to be published, " marks an epoch in the literature of the game ; and is," said "The Green Bag," "a revelation of the possibilities of chess." " The Providence Journal " treated the volume editorially, viz. : — " He (Mr. Young) is brief in his explanations, clear in his definitions, and with the aid of diagrams, exemplary in his instructions. His plan of treating the materials is syste- matic from beginning to end. He leads the reader up from general principles and laws by a logical course of procedure, and he actually shows how a good game of chess should be played ; how, indeed, it always is played by a great player." It was at this point in his chess writings that the author first came to believe that his work would be un- derstood and appreciated in his own lifetime. This was a consummation hardly to be hoped for, — it is difficult to teach old dogs new tricks ; the chess-players of the day were wedded to their books of analysis, and it was too much to expect that the new synthetic method would INTRODUCTORY. xxi find converts outside of a rising generation, whose mind was free from the effect of prior teachings and of estab- lished habit. But the simple system of " logic and common-sense " found supporters, and particularly did it attract to itself those who are in the daily habit of using their intellects, — men who buy books and who study them, — the pro- fessional class. Lawyers, doctors, the clergy, and grad- uates of army and navy colleges eagerly perused the new argumentative treatises on a game which they all admire and practise, — treatises which went to the root of things, which gave the whys and wherefores, and fitted the reader to evolve for himself better analysis than he can buy ready-made. But, more surprising still, the obvious merit of the new synthetic method carried by storm the very citadel of the established order of things Caissic in America ; and that high conservator of things that are — " The American Chess Magazine" — in its issue for Sei)tember, 1898, says : — "For the student who desires to enter the broader chan- nels of chess, the best books are by Franklin K. Young ; his ' Minor Tactics of Chess ' and his more elaborate ' Grand Tactics ' are the most important productions of modern chess literature." Backed by such high indorsements as these, the growth of the new system of chessplay naturally was rapid and most satisfying to the author. But that highest authority whose approval he most desired still was silent. By his writings it was the object of the author to show that the mathematics of the science of war and the mathematics of the science of chess are identical, and that the high tactics of warfare and of XXll INTROD UCTOR Y. chessplaj are the same ; and most of all did the author desire public recognition of his labors in this regard from an admitted military authority. It was not until the publication of " The Major Tactics of Chess " in December, 1898, that the accuracy of the author's treatment of chessic art and science was placed beyond dispute. The " New York Clipper " pronounced the third volume a book which " deserves nothing but commendation." The " New York Sun " said : " It is really the higher mathematics of chess, — the combination that, to a mind quick at geometrical evolution, will be a means of con- founding the adversary ; the insight into it a surprise and delight, and the outcome having the unexpectedness of a happy piece of wit." On Dec. 23, 1899, that sphinx, for which the author so long had waited, opened its mouth, and with the great voice of military authority, " The Army and Navy Reg- ister" (Washington, D. C), said : — ^'This additional contribution to chess literature from the able pen of Mr. Young will be received with even more delight than were his former scientific treatises, as it is a more complete development of his unique system. It forms the second volume of the Chess Strategetics Series, and, as the author confesses, may not improperly be termed a book of chess tricks. In the words of the text, 'Major Tactics is that branch of the science of chess strategetics which treats of the evolutions appertaining to any given integer of chess force when acting either alone, or in co-operation with a kindred integer, against any adverse integer of chess force ; the latter acting alone, or in com- bination with any of its kindred integers.' This definition is a little discouraging to the student, but he should take heart, and, if he can handle simple equations, he luill not INTRODUCTORY. ^^^H find the book difficult The secret of Major Tactics in chess is to attack an adverse piece at a time when it cannot move, at a point where it is defenceless, and with a force that is irresistible. The hook is to the student of chess what Clausewitz and Von Hohenlohe are to the soldier at arms. It is not intended for the beginner any more than is a treatise on ballistics recommended for the recruit. In it one finds the 2^^'inci2?les of grand strategy and logistics ajp'plied to chess in a unique and scientific way. The treat- ment is so clear and masterful a,s to win for the author the gratitude of all devotees of the royal game. Every move is given its place in the plan of attack and defence, and is discussed in the light of examples from the historic contests of the great generals of the game. In print, paper, and general presentment the book leaves no room for adverse comment.'' CHESS STRATEGETICS ILLUSTRATED. CHESS STRATEGETICS ILLUSTRATED, TOPOGRAPHICAL HORIZON. THE principles which underlie the science of war and those which underlie the science of chess are one and the same ; those processes whereby these principles are applied in actual warfare and in actual chessplay are nothing more nor less than processes in daily and common use in the various branches of the mathematics. The science of mathematics is founded upon the proposition that one and one make two ; the science of war is founded upon the proposition that two men, all else being equal, can whip one man. The art of warfare consists in those processes whereby two men are made simultaneously to attack one man, and the art of chessplay consists in these processes whereby two kindred chesspieces are made simultaneously to attack a single adverse piece. In the elaboration of these processes the individual properly may become a collection of individuals, as, for example, armies and covpB d'armee^ and whether posted on the battlefield or on the chessboard ; but in either case the law remains the same, — a law promulgated by one whose authority few will dispute : — "The fundamental law of war," says Napoleon, "is this, — the greater force always overcomes the lesser." 4 CHESS STRATEGETICS. The reader will observe that the master of military science does not qualify his statement ; he does not say that the greater force usually overcomes the lesser ; nor that it almost always overcomes the lesser ; he says " ALWAYS overcomes the lesser." There are men who up to this moment have held a different opinion. The mind of average humanity is illogical ; it does not think, — it merely receives impres- sions through the senses. Thus its conclusions neces- sarily are based upon results, — i. 6?., upon things which can be seen, heard, and felt, — and hence it readily is de- ceived and imposed upon through the defects and limita- tions of the bodily organism. Consequently, many men are of the opinion that it is possible for the weak to overcome the powerful, for grapes to grow on thorns, for the tail to wag the dog, and who would be astounded to know that the race is to the swift and the battle to the strong, the Scriptures to the contrary, notwithstanding. Furthermore, there are men who even after reading the law as laid down by the illustrious Corsican will continue to hold to their different opinion. Of such, this is all that need be said : he who is not endowed with an understanding of mathematics sufficient to sense by mere instinct, as it were, the grand mechani- cal fact underlying Napoleon's dictum, should not waste his time in the perusal of these volumes ; Nature has not equipped him for the study of strategetics, — whetlier the latter relate to war or to chess. In the terse sen- tences of Frederick the Great : — " Nothing can serve to enlighten stupidity and stub- bornness; a mule would not improve in his tactics, though he made twenty campaigns with Prince Eugene." TOPOGRAPHICAL HORIZON. 5 But those who approach this subject with the desire to learn, readily will detect the peculiar wording of the law. They will note that the great captain uses the term, "/orce," that he does not say "bodies of men," neither does he say " greater number of men ; " and that, in short, he does not say anything whatsoever about men, either individually or collectively but he says — " FORCE." Now it is essential that the student of this theory, once and for all, comprehend that this " force " which the great master of military science is talking about has no relation to inert masses of men, but is a pure mechanical power. li\ war, this force is the weight multiplied by the square of the velocity of flying pro- jectiles from small arms and artillery, and of the bodily impact of charging men and horses, whereby hostile troops and material are put hors du combat ; in chess it is the power inherent in kindred chessmen to elimi- nate adverse pieces from the surface of the chessboard. Hence, the first corollary of the fundamental law of Strategetics obviously is : — A mass of troops or of chessmen does not achieve vic- tory merely because it numerically is superior to the opponent, — the mass that wins may be in the aggregate either larger or smaller than the enemy, all that is matter of indifference, — the winning is effected in each and every case by operating against a vital point a ''force ; " i. e., a power to destroy greater than the power to defend which at the given time and place is operated by the enemy. Says Napoleon : — "It "is only the force brought into action which avails in battles and campaigns, — the rest does not count." Of this force, as applied to the chesspieces, a most b CHESS STRATEGETICS. erroneous idea commonly is held. The Queen, for in- stance, is termed the " strongest," or the " most power- ful " of the chesspieces ; the Rook, the " next strongest," and so on. As a matter of fact, the chesspieces are of equal strength: none is either more or less powerful than the other. The Pawn can capture — i. e., destroy — any adverse chesspiece by eliminating the latter from the surface of the chessboard ; so can the Rook, the Bishop, the Knight, and the King — the Queen can do no more. Hence, obviously, the force for destruction exerted by one piece is equal to that possessed by any other chesspiece. The fact that the Queen can attack at eight different points at one and the same time, and that she can traverse the length of the chessboard in a single move, are in no sense manifestations of " force " (for she can capture and destroy at only one point in a single move, and any other of the pieces is able to do likewise), but of superiority in mobility ; i. e., in freedom of movement. This superiority of the Queen over the other pieces in mobility is a tremendous advantage in special positions, and greatly enhances her value in the abstract ; but this advantage does not take the form of "force," but of extraordinary facilities for bringing force into action. It is as if, of two equal forces, one, the Queen, by virtue of good roads, could reach the battlefield in an hour ; while the other, the Pawn, en route through a broken country, might require two, three, four, five, or even more hours, to reach the scene of action. In this connection the student will observe that the fact of one piece not being able to move on a diagonal, while another cannot move on a vertical or a horizontal, and still yet another cannot move on an oblique, is typi- cal merely of those topographical conditions which pre- TOPOGRAPHICAL HORIZON. 7 vent a body of troops from crossing an unfordable river, an impassable morass, an impenetrable forest, or an in- accessible range of heights ; and that the swifter march of one piece as compared with the slower march of an- other piece merely typifies favorable and unfavorable physical conditions of ground and of troops, which accel- lerate the one army and impede the other. Thus, the student readily will see instead of the chessboard having but a single surface common to all the pieces, that in any given situation there necessarily are as many different surfaces as there are different pieces, and that while the material or visible chessboard is a simple matter of one big square, subdivided into sixty-four smaller squares, alternately colored light and dark, that the invisible or mathematical chessboard is a composite of all the topographical horizons which ap- pertain to the chesspieces contained in the given situa- tion. The student should thoroughly comprehend the appended diagrams illustrative of the topographical horizons of the various chesspieces, before proceeding further. CHESS STRATEGETICS. TOPOGEAPHICAL HORIZON OF THE PAWN. FlGUKB 1. Black. i White. Note. — This diagram shows the points possible for the Pawn to reach in a single move. TOPOGRAPHICAL HORIZON. TOPOGRAPHICAL HORIZON OF THE KNIGHT. Figure 2. Blach. H H B B ^ B ^» H H W^i'te. Note. — This diagram shows the points possible for the Knight to reach in a single move. 10 CHESS STRATEGETICS. TOPOGRAPHICAL HORIZON OF THE BISHOP. FiGUEE 3. Black. m White. Note. — This diagram shows the points possible for the Bishop to reach in a single move. TOPOGRAPHICAL HORIZON. 11 TOPOGRAPHICAL HORIZON OF THE ROOK. Figure 4. Black. m White. Note. — This diagram shows the points possible for the Rook to reach in a single move. 12 CHESS STRATEGETICS. TOPOGRAPHICAL HORIZON OF THE QUEEN. Figure 5. Black. iHi White. Note. — This diagram shows the points possible for the Queen to reach in a single move. TOPOGRAPHICAL HORIZON. 13 TOPOGRAPHICAL HORIZON OF THE KING. Figure 6. Black. i White. Note. — This diagram shows the points possible for the King to reach in a single move. 14 CHESS STRATEGETICS, TOPOGRAPHICAL HORIZON COMPOSITE. {a) Figure 7. Black. y///M ^Si y:^//////^. '/-> o -tJ m ^ ^ fl cS o ,^ © '^. tH 05 t> O § ^ 5 CH a ^ t|_J T-S C c5 ^ ^ a - S «4-l -c ° B '^ •; ^ , XI > o ^ 1^2 e ^ g^ ^ G Sh < .5 flH % 2 o rJ3 -(J ^ -^ o ^ bC c; C g ? t^ S o vA o n ^ s C) ^ c^ ■4^ -t^ i-i := o o &- pG & if ^ S ^ <^— 1 '^ O O rt - § •r s l^-o o s ^ 1 "^ 1 =« H H pG o -^ ;zi ^ CS © n^ White. 34 CHESS STRATEGETICS. Btach m i» m f "•i" l f i ^ w c5 .2 o ■5 i ^ X! w >^ > c3 O ^ -^J p c t£ J^ c; ^ < ^ •n ^ ^ o ^ X o s^ • V :z; cT CN ;:3 > c o o s o o CO 1—^ trH o -i-3 O s _ ^" ri -4-3 ^ o c 2 ,^ > '^ ^ rt ;_ o o -1^ „^ 1 C5 E ;:; H • p— 1 O >-, 12; s ■g ir/u-^e. A -J'. PRIME STRATEGETIC FACTORS. 35 Black. i=l a o o f^ !> s 8 ::^ i=i aj a a B '■+3 o O ^ o C3 o il J_, <^-i o o .2^ XI 5=1 Ph o t^ t-l Ci^ ri n o ^ O) bo a C ^ c ;h o 0") o rg s ^ •V O) c o s &. 13 o OS r^ t4H o o a s ~M ^ 8 ^ 9 o ri o -M >■ n-i 1? C3 :-i o 0) r^ -*J -M ,__, H 'c^ -(-3 1 O 1 TU m rj H • rH ^ s <4-3 W O) r^ TFAiYe. 36 CHESS STRATEGETICS. Black. ■ ^]^^ ^^ ^^■. :#:#!# ^ 9 1 m i« m m ]Vh>tf: PRIME STRATEGETIC FACTORS. 37 Note. — Either with or without the move, the numer- ically inferior column of manoeuvre can destroy in detail the adverse column of support composed of two promot- able factors, and without the move, it can destroy in detail the adverse column of support composed of three promotable factors ; according to Prop. XL of " Major Tactics." COLUMN OF SUPPORT. The principle which governs the processes incident to the column of support is derived from the fact that, in the absence of a point of iyni^eyietr ability on its vertical, it is possible for a Pawn to penetrate to the kindred logistic horizon. Hence : — PRIXCIPLE. A Point of Junction is open to occupation whenever the number of Pawns advancing against the given logistic hori- zon exceeds the number of adverse points of iinpenetrability. There are four basic positions which underlie all situations in which the column of support penetrates through the adverse column of manoeuvre and gains possession of a point of junction on the logistic horizon, viz. : — (rt) A position in which there is no point of impene- trability. (5) In which an adverse point of impenetrability is overlapped by two adjacent kindred supporting elements. (c) In which the point of impenetrability is over- lapped by two separated kindred supporting elements. (f?) In which three points of impenetrability are opposed by three supporting elements, the latter having the move. These four basic positions are shown in the following diao-ram : — 38 CHESS STRATEGETICS. Black. White. PRIME STRATEGETIC FACTORS. 39 Note. — These basic situations are founded on the fact that all the points of impenetrability and of resist- ance being eliminated from the attitude of the given Pawn the latter will queen without capture, according to Props, v., VI., VIII., IX., X., and XL (see " The Major Tactics of Chess," pp. 110-121). The student readily will see that the White Queen on the extreme left of the hypothetical zone has an unim- peded route of march to White's Q R 8 ; that the White Queens on the centre of the same zone will easily remove the point of impenetrability on their front, by attacking it with one Queen supported by the other Queen, and that if the Black Pawn captures the attack- ing Queen, the supporting Queen, by capturing in turn the Black Pawn, or by merely advancing along its logistic radius, will remain with an unimpeded route of march to its lo2:istic horizon. Again, if in the example on the extreme right, either White Queen attacks the Black Pawn, the result is that one of the White Queens will remain with an unimpeded route of march to its logistic horizon, for whether the Black Pawn captures the attacking White Queen or ad- vances or remains stationary, the point of impenetrabil- ity will be eliminated from the vertical of one, at least, of the White symbols of promotion, and it will be ob- served that either with or without the move, the White Queens may penetrate to their logistic horizon with equal jfertainty and facility. In the case of the three Black Queens, the student will observe that it is imperative that they have the move ; otherwise the white column of manoeuvre will securely cover the white strategetic rear by advancing the centre pawn one square towards the black symbols of promo- \ 40 CHESS STRATEGETICS. tion. This is the only move to maintain the integrity of the White defence, for if either of the other White Pawns advance, Black wins by attacking with one of the Black Queens the supporting White Pawn ; whereupon one of the Black Queens will find itself in one of the three situations just described^ and accordingly will be able to penetrate to its logistic horizon. This same situation results if Black has the first move and he wins by advancing the centre black symbol of promotion one step. See " Grand Tactics," page 59. COLUMN OF SUPPORT. Figure 23. Adolph Anderssen. Paul Morphy. PRIME STRATEGETIC FACTORS. 41 This position occuiTed in the first game of the match between these masters. THE PLAY. X [ll. MORPHY. Herr Anderssen. 50. Kt - B 6. 50. P X Kt. 51. Q X P (ck). 51. K-Ktl. 52. Q - Kt 6 (ck). 52. K - B 1. 53. Q X P (ck). 53. K-Kl. 54. Q - Kt 6 (ck). 54. K-Q2. 55. P - E 6. 55. Q - Q 4. 56. P - E 7. 56. Q X P (ck) 57. K - Kt 1. 57. Kt-Kt4 ^B>. P — K E 8 (Queen). b^. Q X 2ndQ. 59. Q X Kt. COLUMN OF ATTACK. The principle which governs the processes. incident to the Column of Attack is derived from the fact that the possession of that central diagonal ivhich extends toward the objective j^lane gives such an advantage in mobility that the consequent facility wdth which the kindred pieces may act in co-operation both for attack and for defence must ultimately lead to the checkmate of the adverse king. Hence : — PRINCIPLE. - All else being equal, a properly constructed minor stra- tegic front establishes an equality in position ; a properly constructed major strategic front establishes the superiority in position ; and a p>roperly constructed grand strategic front establishes a ivinning advantage in position. 42 CRESS STRATEGETICS. MIXOR EIGHT OBLIQUE {White). MIlsOR LEFT OBLIQUE REFUSED [Black). Figure 24. Adolph Anderssen. Pi i pl^H i PI ^X^ X ^1 ill i% ^y//////////. WY/z/yy/A WWM p ^AkM -mm p 1^1 ^ ^» Paul Morpht. This position occurred at move 14 in the fifth game of the Morphy-Anderssen match. The student will observe that the White pieces are posted in strict accord with this theory of chessplay, and that collectively they constitute the formation termed in " Minor Tactics^' p. 149, the 0PB2C. If the student will study carefully these fourteen opening moves and will compare them with the moves PRIME STRATEGETIC FACTORS. 43 given by the so-called " analytical authorities," he readily will see that Morphy made no pretence of con- forming to their dicta, but merely played to establish the best available primary base, on a strategic front directed by the right, and so manoeuvring as to prevent Black advancing his K P to K 4. MINOR LEFT OBLIQUE ALIGNED ( White). Figure 25. m. bornemann. i I ^, Wy///////., m ^ m fm m Hi* y/Tm//. W/A ^.. g^ Paul Morpht. This position occurred on the 18th move at Table No. 3 in the great blindfold match played at the Caf^ de la R^gence, Paris, September, 1858. 44 CHESS STRATEGETICS. The student will observe that the Black K is castled on the Queen's side, and that the White position is depicted in " Grand Tactics," Formula No. 17, page 136. MINOR LEFT OBLIQUE [White). Figure 26. Herr Harrwitz. {'/A 4m W//. '///. m 'mm,. ^^..-M-..-.^^,, .w//////^.^ -0/////////.. fm g pi! Paul Morphy. This position occurred in the eighth game of the match between these nxasters. PRIME STRATEGETIC FACTORS. 45 MAJOR RIGHT OBLIQUE (White). Figure 27. Adolph Anderssen. k « mi i y^/////y/7 ^^^^^^^ ffif W/, %y////A f Si . IS ill- « iMi m ^ « <^ — ^^^<^ i«l Paul Morpht. This position occurred in the eleventh game of tlie match between these masters. 46 CHESS STRATEGETICS. MAJOR RIGHT OBLIQUE {Black). FiGUEE 28. Paul Moephy. H. E. B] This position occurred at the 10th move in the cele- brated Philidor's Defence between these masters. The student will observe that Black has wrested from White the advantage of the initial move of the game, and has established a formation which properly should belong to the first player. PRIME STRATEGETIC FACTORS. 47 MAJOR LEFT OBLIQUE {White). (Objective Plane, Left.) Figure 29. m. bornemann. k i 81 m'fmm'm m 1 m mwM m.....^„^ W^y,,^ iS, Paul Morpht. This situation occurred on the 29th move at Table No. 3 in the great blindfold exhibition at Paris, 1858. 48 CHESS STRATEGETICI MAJOR LEFT OBLIQUE {^yhite). (Objective Plane, Centre.) ElGUKE 30. Paul Moephy. m mi 4 ■ i '//A . ■//. Adolph Axderssen. This position occurred at the 13th move in the third and last game won from Morphy by the great German master. 4 PRIME STRATEGETIC FACTORS, 49 THE PLAY. Here Anderssen. Mr. Morphy. 13. B - K Kt 5. 14. Q-K4. 14. Q X Q. 15. Kt X Q. 15. B xR. 16. Kt X K B. 16. B-R4. 17. BxP. 17. P X P. 18. Kt X Kt P (ck). 18. K - K 2. 19. B - Q Kt 5. 19. Ex P. 20. R- Kl (ck). 20. K-B3. 21. R-K8. 21. B - Kt a 22. Kt - Q 6. White won. 50 CHESS STRATEGETICS. MAJOR LEFT OBLIQUE {White). (When Black Q P cannot occupy Q 3.) Figure 3L Paul Mokphy. ///y///^//A 11 iBi «. %. ^_„-„__„i III i \.\..^m ^B M ''m>m. " 'MM. ^ ii ^ ■ m km Adolph Anderssen. This situation occurred in the ninth game of the match between these masters. PRIME STRATEGETIC FACTORS. 51 THE PLAY. Me. Morphy. Herr Andeessen. 5. Kt-Kt5. 5. P-Q3. 6. B-KB4. 6. P - K 4. To B - K 3. 7. P-B4. 8. QKt-B3. 8. P - B 5. 9. Kt-Q5. 9. P X B. 10. K Kt - B 7 (ck). 10. K-B2. 11. Q - B 3 (ck). 11. Kt - B 3. 12. B-B4. 12. Kt - Q 5. 13. Kt X Kt (dis ck). 13. P-Q4. 14. B X P (ck). 14. K - Kt 3. 15. Q - K E 5 (ck). 15. K X Kt. 16. P X P. 16. Kt X P (ck), 17. K-K2. White won. 52 CHESS STRATEGETICS GRAND RIGHT OBLIQUE EN APPUI {White). MAJOR LEFT OBLIQUE REFUSED (Black). Figure 32. Judge A. B. Meek. i 11 ^H II. ■ ^„ w/////^. YA y/777777/y^. _ — m ^^ '"" IP '^y//////m 'mm,, m I ©I e i s Paul Morphy, This position occurred in the eleventh game of the match between these masters. It shows the Strategetic Objective occupied by a piece. 54. CHESS STRATEGETICS. GEAND LEFT OBLIQUE EN APPUI WITH MINOR CROCHET {White). ElGUEE 34, S. S. BODEX. m is. .'V//////y/. '//^//tM wy////^. 'Zy/////M. i Ill i 'mm. m Paul Morpht. This position occurred on the 39th move of a Two Knights Defence. f PRIME STRATEGETIC FACTORS. 55 MINOR RIGHT OBLIQUE REFUSED AND ALIGNED {Black). Figure 35. Paul Morphy. II iwM. »////////.. m m Hi '^ « k 4m. i ■ I W', W///////A Hi/ MONGREDIEN. This position occurred at the 14th move of the seventh game in the match between these masters. 66 CHESS STRATEGETICS. MINOR LEFT OBLIQUE REFUSED {Black). Figure 36. Paul Morpht. mmi 11 ii i ■-iM i ill i Wi m„ jZv/////^. Mm.. m i ^^ Judge McConnell. This situation occurred at the 11th mo^e of a French Defence. Black's position is the model of this form of defence against the Major Right Oblique En Potence. PRIME STRATEGETIC FACTORS. 57 THE PLAY. Judge McConnell. Mk. Morpht. 11. B X P (ck) 12. P X B. 12. Kt X Kt P. 13. Q-Q2. 13. E-B7. 14. Q-Ql. 14 Kt - K 6. Black won. 58 CHESS STRATEGETICS. MINOE LEFT OBLIQUE EEFUSED AND ALIGNED {White). FlGUEE 37. Paul Morpht. iWi m m mm^.. ■^mm/''''''^% ^/S^..^ mm^y, ^/ ■'^mi li 1! i ■ y^^/^. \w WW HI 4m 4k Adolph Andeessen. This position occurred in the tenth game of the match between these masters. It shows the defence of the K Kt at K B 3 by K B-K 2 against the Fianchetto of the adverse Q B. THE PLAY. Hekk Anderssen. Mr. Morphy. 24. B-QKt2. 25. Q - B 2 24. Q-KB2, 25. B-K2. PRIME STRATEGETIC FACTORS. 59 MAJOR RIGHT OBLIQUE REFUSED EN POTENCE {Black). Figure 38. Paul Morphy. 1 /■"" 4m 7//////%'. i i #Si i% W//////A v//////y ■ J^ 7////////. i m #////^, i^„ _, W^^^y. Jacob Lowenthal. This position occurred at the 40th move of the ninth game in the match between these players. 60 CHESS STRATEGETICS. MAJOR CROCHET ( White). Figure 39. Mr. Barnes. ■ il fifj i ^11 i m 'mm""'/% ''- 4^A 'mmA...'^.'mm, m m. M «. -„% SI Paul Morpht. This position occurred at the 24th move in a King's Bishop's opening. White won by P-Q Kt 5. PRIME STRATEGETIC FACTORS. 61 THE ECHELOX ( White). Figure 40. Adolph Axderssen. m w Mi...^,..W//////A .. . . ^S^y. II i ■ i ■ u W///MM. '/^////////!',-f^zJ,f^^^^'.. m^m. mAm Paul Moephy. This situation occurred in the fifth game of the match between these masters. It shows the construction of tlie Echelon, the En Appui, and the En Potence in the Right Oblique by White. / 5f r ^ 62 CHESS STRATEGETICS. THE PLAY. Mr. MOEPHY. Here Andeessen. 15. P - K R 3. 15. Q - B 1. 16. K-E2. 16. K-Rl. 17. E - K Kt 1. 17. E-KKtl. 18. P - K Kt 4. 18. P-KKt4. 19. P - K B 4, etc. PRIME STRATEGETIC FACTORS. 63 THE EN POTENCE {White). Figure 41, Stauntox and Owen. m ww.^ ^^,„.%.^^^. w/////^. y^//////M:, 'Z^//////yZi V. '^////////y'' '/y/^^//',. MoRPHY and Barnes. This position occurred at the 21st move in the second game of the famous consultation contest played at Bir- mingham, England, 1858. White won. 64 CHESS STRATEGETICS. THE FIANCHETTO [Black), ElGURE 42. Paul Morpht. m i m WHfM Wm m 4M fm.. m, * » Wa ^» ^Si ^^ Mr. Mongredien. This position occurred at the 43d move in the third jame between these players. m PRIME STRATEGETIC FACTORS. Qb CROCHET ALIGNED IN DOUBLE FRONT BY THE RIGHT ( White). Figure 43. Jacob Lowenthal. i ill i M I ■ * iii * ^^.^^^^...^^^^p. .^ M^4M ™ i W///////A rv^ $5^$?2^^ i ^ 1^1 Paul Morpht. This situation occurred on the 20th move in the twelfth game of the match between these masters. 66 CHESS STRATEGETICS. CROCHET ALIGXED IN DOUBLE FRONT BY THE LEFT {White). Figure 44. Theodore Lichtexhein. ^ 11 ^ mm,.^^f;;;;^J^^M, 4^11 i ■ m^lM. ^ 1^1 i i %#i~ Paul Morpht. This position occurred at the 20th move of a Petroff Defence. White won. PRIME STRATEGETIC FACTORS. 67 MINOR FRONT DOUBLY ALIGNED {White). Figure 45. Jacob Lowexthal. ^i v/z/zz/yZ'. 'Z^zzzzz///'.^ Wz t^i,.„^,^a ^ Isl * 1 il i VZ///////Z/ WM. if i Pi vy//ZZZy VZy/y/yZZZy m. ■, i mi A fSi y/zzz/vzzz '^'' vzzzzzzzzzz ^^^^^^^^^ IS4 ™ ^ I MB 'M yZZ/rtV/Z "%>... ^....."yZZZZZZy^. Paul Moephy. This situation occurred in the fourth game of the match between these masters. 68 CHESS STRATEGETICS. The student perceives that the column of attack is composed of a force represented by the combined action of all those kindred pawns and pieces which at *any given time are contained within the Topographical Zone, and that the movements and operations of the column of attack always are restricted to the limits of the visible, or material chessboard. It also is equally evident that the column of support is composed of a force represented by the combined action of all those kindred pawns and pieces which at any given time are contained within the Topographical Zone ; whose operations always are exclusively directed against the logistic horizon with the object of occupy- ing one or more points of junction with a kindred pawn ; but whose movements technically are restricted to the limits of the kindred Hypothetical Zone, z*. e., to that part of the mathematical or invisible chessboard wliich appertains to the kindred body of chesspieces. Lastly, it easily is seen that the column of manoeuvre is composed of a force represented by the combined action of all those kindred pawns and pieces which at any given time are contained within the Topographical Zone ; whose operations are exclusively directed against the adverse column of support and for the defence of the kindred strategetic rear, with the sole object of preventing any hostile pawn from penetrating to its logistic horizon and occupying a point of junction; but whose movements technically are restricted to the limits of the adverse Hypothetical Zone, i. e., to that part of the mathematical or invisible chessboard which apper- tains to the adverse body of chesspieces. As the student already has been taught, whenever a line of operations exists, all principles may be violated, all formations disrupted, which are not germane to the PRIME STRATEGETIC FACTORS. 69 immediate calculation ; i. e.^ in all cases wherein the winning of the game can be mathematically demon- strated, either by the checkmate of the adverse king, by the queening of a kindred pawn, or by the gain of adverse material ; then, that analytical calculation whereby such determinate result is obtained is supreme. For all the elements being known, the situation may be depicted accurately, and consequently the process is exact and is merely one of simple arithmetic. But in all other cases, i. e., wherein no line of operations can be demonstrated, then, as the student likewise has been taught, the situation properly is one of manoeuvre, i. e., one in wliich a systematic attempt is being made to bring about the position termed a line of operations. In this case, one or more of the elements are not known, the situation, therefore, cannot be exactly de- picted ; it is first necessary out of the midst of the differences which exist to extract harmony ; conse- quently, the process is one of the differential calculus. Hence, as the student already has been taught in such situations, no principle of strategy nor of tactics, nor of logistics, should be violated ; no sacrifice of material should be made, and no formation constructed in ac- cordance with this theory should be disintegrated. The student thus will easily perceive, that in compli- ance to the requirements of these principles, and to the basic law of the Science of Chess Strategetics of which these principles are but the corollaries, at every move the column of attach., the column of support^ and the column of manoeuvre must act together as a unit for the defence of the kindred and for the attack of the adverse position. It equally is obvious that the three- fold duties which respectively appertain to these columns, 70 , CHESS STRATEGETICS. taken collectively, are devolved, in the execution, upon the sixteen corps d\irmi^e which originally constitute the chessic army, ^. e., that these sixteen kindred chesspieces are required, as it were, to multiply themselves threefold, and to perform the labors of forty-eight corps cVarmce ; and that, instead of contemplating the movements of thirty-two men on a chessboard of sixty-four squares, the calculations of the chessplayer comprehend the deployments, developments, manoeuvres, and operations of combined kindred and adverse determinate and hy- pothetical forces represented by ninety-six pawns and pieces, over the surface of a mathematical chessboard composed of one hundred and seventy-six squares : tico- thirds of the chesspieces and two-thirds of the chessboard being invisible. The student of strategetics, whether of war or of chess, readily sees the mathematical exactness of this vast chessic proposition, and equally so, that in compre- hensiveness and in profundity it easily is equal to any proposition known to military art and science. Hence, to the soldier and to the chessplayer alike, it is obvious that the following is true and valid : SECOND LAW OF THE ART OF CHESSPLAY. At every turn to play and no line of operations existing, ahuays act simultaneously u'ith the Column of Attack in the Topographical Zone, icith the Column of Support in the Kindred Hypothetical Zone, and ivith the Column of Manoeuvre in the Adverse Hypothetical Zone, and always reject every move ichich violates those principles governing the processes incident to these Prime Strategetic Factors. The student furthermore will see that whenever the kindred force is insufficient to give checkmate it cannot PRIME STRATEGETIC FACTORS. 71 win the game ; that whenever no kindred pawns remain on the board, no further reinforcement of the original kindred force is possible, and that whenever no adverse pawns remain on tlie board, there is no longer any necessity for guarding the strategetic rear. Hence, it is obvious that the following is true and valid : — THIRD LAW OF THE ART OF CHESSPLAY. I. The Column of Attach ceases to exist whenever the net value of the Kindred Determinate Force is less than the mobility/ of the Objective Plane. II. The Column of Support ceases to exist whenever the last hiyidred promotable factor is eliminated, III. The Column of Manoeuvre ceases to exist whenever the last kindred point of imp eyietr ability is eliminated. In the position shown in the diagram following, Black has a column of support, but no column of attack nor column of manoeuvre ; while White has columns of attack and of manoeuvre, but no column of support. Note. — The student readily perceives that the com- bined White Rook and Knight constitute a column of attack movements, as they jointly are able to command the Objective Plane ; that the three Black Pawns are a column of support, and that the White King is a column^ of manoeuvre, inasmuch as it can defend the white strat- egetic rear against the Black Pawns. FOURTH LAW OF THE ART OF CHESSPLAY. In every situation and at every turn to move., always manoeuvre either with that kindred Prime Strategetic Factor which has the advantage; or with any Kindred Factor to make subordinate a dominant adverse Prime Strategetic Factor. 72 CHESS STRATEGETICS. Black. m White. PROCESSES OF GEEATER LOGISTICS (JIAJOK). PROCESSES OF GREATER LOGISTICS (MAJOR). The student who attempts to master this volume with- out having thoroughly familiarized himself with " Minor Tactics," "Major Tactics," and "Grand Tactics," will have his labor for his pains. Before he can comprehend the art of chessplay, he must first have thoroughly educated himself in the sci- ence of chess ; it is not possible that one may under- stand the processes of Greater Logistics and the complexities of Lines of Manoeuvre and of Operation, until he first has fathomed the preparatory intricacies of Lesser Logistics, as interpreted in Lines of Mobiliza- tion and of Development. In fact, it is now necessary to assume that the student has the whole chessic theory, as laid down in the three preceding volumes of this series, at his fingers' ends, so to speak; and that, in actual play over the board, he is not at loss to know the proper construction of any given primary base, to know how to mobilize and how to develop any desired strategic front, and how to avoid those errors in tactics whereby he may fall victim to a superior knowledge of routine evolutions on the part of his opponent. In other words, there is no " climbing in through the cabin window," as the sailors say ; the road to chessic excellence is steep and rugged, and even the directness 76 CHESS STRATEGETICS. and clearness of this synthetic method of chessplay can be of no avail to one who is ignorant of its simplest processes. As the student already has been taught, all calcula- tions having but a single point of command belong ex- clusively to the domain of Major Tactics ; they are determinate propositions, and are solved by simple arithmetic ; and until the student has thoroughly mas- tered them, he should confine his studies to the second volume of this series. For a similar reason, if the stu- dent is not entirely familiar with the proper construction of the several strategic fronts and of the direction which should be given to each ; and if he does not comprehend the utility of the various supplementary formations which appertain to these strategic fronts, — he should continue the study of "Grand Tactics" until he has acquired the knowledge which fits him to approach this volume with some slight idea of its import. In case he is ignorant even of the construction of primary bases, and the reasons therefor, then the " Minor Tactics of Chess " is the book he needs, — not this one. As before has been laid down, both the science of war and the science of chess are based upon the axiom that, all else being equal, two men can whip one. The art of warfare and the art of chessplay consist in getting the two men simultaneously upon the other man's hack. So simple and so indisputable are the principles and the processes appertaining to the science of war in the ab- stract, that even savages utilize them with vigor and accuracy, and every civilized man, whatever his condi- tion, feels himself competent to sit in solemn and final judgment on the profoundest military propositions, re- gardless of the fact that since the dawn of history only eleven men, out of many billions, have evinced a thor- PROCESSES OF GREATER LOGISTICS. 77 ough understanding of the concrete processes of the art of warfare. In chess it is much the same. The practitioner, as a rule, and whatever may be his rank in the chess world, usually overestimates his weight in the chessic scale, — a fact upon which the famous master Mackenzie once commented, " We are none of us so strong as we think we are." The reason of this is that the minds of ordinary hu- manity seldom rise above the processes of simple arith- metic. So long as the proposition is exact, and all of the elements are known, even the tyro, whether at war or at chess, gets along fairly well ; his operations in the field or on the chessboard are successful, and his judg- ments, whether in military or in chessic councils, are just and conclusive. This condition, whether on the chessboard or on the battlefield, is the triumph of mediocrity, and is due to the fact that the theorist pure and simple is the most pitiably helpless and useless of all human beings. On the other hand, the man with but little education, yet possessed of the faculty of making full use of what knowledge he has, is the man more properly equipped for success, whether in chessplay, in warfare, or, for that matter, in anything else. But let a man arise who combines the thorough un- derstanding of theory with the thorough understanding of those processes whereby theory is correctly applied, whether in chessplay or in warfare, and you have Morphy and Napoleon. Those processes, whereby theory properly is applied in actual warfare or in chessplay, are not the processes of simple arithmetic. This is the reason why there is but one Morphy in the annals of Chess and but one Napoleon in the annals of War. Any- 78 CHESS STRATEGETICS. body can simultaneously attack one man with two men, either on the chessboard or on the battlefield, — if he is given time enough, and no resistance is made by the single man. But the moment that the unknown ele- ments of the single man's resistance and of time and distance enter into the calculation, then the proposition beco'mes indeterminate ; it is no longer a sum in simple arithmetic, but a problem in the differential calculus. It is now that the theorist, pure and simple, although utterly impotent, inasmuch as his comprehension of the science is offset by his lack of understanding of the art, nevertheless rubs his hands and howls with glee at the sight of so-called " practical " chessplayers or soldiers — mere arithmeticians, rather — ignominiously overthrown, horse, foot, and dragoons, as the old saying is, by a " genius," a " prodigy," a " supernatural intelligence," which last, being interpreted, simply means that a man has come to the top who thoroughly comprehends both the theory and the art of applying it. Thus the student will observe that there is nothing miraculous in the fact of a boy of twenty-one, in the per- son of Morphy, defeating with ease and in the most bril- liant manner the greatest chessmasters of his day ; nor in a boy of twenty-six defeating the greatest generals of his day with equal ease and in an equally brilliant man- ner. Both of these prodigies are dead and gone, and both are by posterity admitted to stand at the head of their respective professions. The success of the one was due to the fact that he had a theory in regard to chess, and thoroughly understood the art of applying this theory in actual chessplay, for the overcoming of time, of distance, and of the resistance of the opponent ; the success of the other was due to the fact that he had a theory in regard to war, and thoroughly understood the PROCESSES OF GREATER LOGISTTCS. 79 art of applying this theory in actual warfare for the overcoming of time, of distance, and of the resistance of the opponent. The reason why the generality of men are neither Morphys nor Napoleons is because the generality of men base their conclusions upon results ; because they are ignorant of the causes which bring about these results ; and because they are oblivious to the fact that causes and not results are the prime essentials for suc- cess, and that in comparison with these causes, mere results are matters of insignificance, being at most nothing but necessary sequences. Consequently, the generality of men never look deeper than mere results, and, sillily accepting these latter as primary elements, they project a horizon lacking in exactness and con\prehensiveness. Then by a simple process of addition and subtraction — in which all their mental energy not infrequently is expended — they gain what success they do gain, not as the logical outcome of profound and accurate calculations, but as the direct out- come of blunders on the part of the opponent, and because these blunders happen to be more numerous and more egregious than those which they themselves commit. That is to say, the processes of ordinary chessplayers and of ordinary generals at best are no more than the processes of Major Tactics, — processes which are simple and exact ; whose results are determinate, and whose validity depends upon the commission of a blunder by the opponent and not infrequently upon the commission of such a blunder as logically only the tyro in chessplay or in warfare should be guilty of. On the other hand, the processes of Napoleon and of Morphy are based upon logical deductions as to the relative values of causes^ whereby harmony of theory is 80 CHESS STRATEGETICS. established in the midst of tactical and strategic differ- ences created by lack of time, topographical obstacles, and the resistance of the enemy. These processes of the differential calculus, infinitely superior to the methods of the average chessplayer and of the average general, are thus defined by Napoleon : — "Questions of high tactics are indeterminate physico- mathematical problems, which admit of several solutions, and cannot be determined by the formulas of elementary geometry." Every school-boy is familiar with the fact that Napo- leon won his victories before his battles were fought by sticking his inap of Europe full of pins surmounted by divers-colored balls of sealing-wax. This perform- ance is thus described by the distinguished military writer. Baron de Jomini : — "Napoleon knew how to collect together, with admirable precision, upon the decisive point of the zone of operations, his corps d'armee which previously had departed from the most divergent posts. The choice of this decisive point was a skilful strategic combination, and the calculation of the movements of the corj^s (Tarmee was a logistic oj)era- tion which emanated from his closet. Eurnished with a compass opened at a scale of from seven to eight leagues in a right line, leaning over and sometimes lying down upon his map, where the positions of his corps cVarmee and the presumed position of the enemj^ were marked by pins of different colors, he ordered the movements of his army ivith an assurance of ivhich it icould he difficidt to give a just idea. Moving the compass with vivacity upon the map, he judged, in the twinMing of an eye, of the number of marches necessary to each of his corps for arriving at the point ichere he luished to have it at a given day ; then placing his pins in these new positions and PROCESSES OF GREATER LOGISTICS. 81 combining the rapidity of the march which it would be necessary to assign to each of their columns with the possible epoch of their departure, he dictated those in- stimctions which of themselves alone would be a title to glory." This extract is quoted for more than one reason, and among others to show how easy it is for a man to wTite interestingly, even upon a subject of which he is totally ignorant. The Baron de Jomini is the most conspicuous example afforded by military annals of a theorist pure and simple, — i. e., a man devoid of the least understanding of the art. He was educated in the regular service ; was personally present in many campaigns, and for nine years served under Napoleon, who never would intrust him even with the command of a battalion in the field. Had Jomini possessed military ability equal to his enthusiasm and his industry, he obviously not only would have been the greatest of Napoleon's marshals, but he must have become even the rival of the illustrious Corsican. The student who attentively reads the above extract from Jomini's " Art of War," p. 271, will at once notice an incongruity. Of course, there are a number of incon- gruities, but, in particular, the student will observe that Jomini, while seeming to explain Napoleon's calculation, utterly fails, — 1. To state the rule by which this decisive point is to be determined ; 2. To describe the " logistic operation^^^ whereby the corps d''armee were made to concentrate at this decisive point; or, 3. To formulate that grand law of the art of war- fare, whereby Napoleon was enabled to solve " in the tivinkling of an eye " propositions which on page 305 of 82 CHESS STRATEGETICS. his Memoirs the great captain describes as " problems of transcendant geometry which would have turned Lagrange and Laplace pale ; " and of which he further opines, " they [Lagrange and Laplace] would have studied many nights before they could free them from unknown quantities and have brought them to a solution." As a matter of fact, the Baron de Jomini had no idea of what Napoleon was doing as the latter lay prone upon his map of Europe, — whisking his dividers about over its surface, and sticking a red pin here, a blue pin there, and a yellow pin at some other place. There is a free- masonry among the great ; it is not well for the upper stratum that the lower billions, however well these may theorize, should comprehend the art of warfare, the art of government, or the art of finance, not to men- tion, incidentally, a few other arts intimately connected with the foregoing. Neither Epaminondas, Alexander, Hannibal, Caesar, Gustave Adolphus, Turenne, Prince Eugene, Frederic, Washington, nor Napoleon saw fit to put on paper, for the guide and enlightenment of the future man on horseback, the laws and processes of a complete and specific system of warfare ; neither did Morphy, Anderssen, McDonnell, De la Bourdonnais, Deschapelles, Philidor, Petroff, Der Laza, Ghulam Kas- sim, Greco, Lolli, Salvio, Stamma, Buy Lopez, Staunton, Buckle, Lowenthal, Harrwitz, nor any whose genius has illumined the literature of chess, see fit to put on paper the laws and processes of a complete and specific system of play. But although these prodigies in chess and in war suc- ceeded during their entire lifetimes in not divulging the secrets of their respective trades, and, dying, could take their vast knowledge with them out of the world, it was beyond the power even of Morphy to conceal the move- PROCESSES OF GREATER LOGISTICS. 83 ments made by the pieces under his guidance over the surface of the chessboard ; and beyond the power even of the greatest captain to obliteratej the imprint made by his armies in march and in battle from the surface of the earth. Hence, he who intelligently can contemplate the processes of Morphy and the greater masters in chess, and the processes of Napoleon and the greater captains in war, may readily detect a similarity in their courses of procedure, and these processes, properly classified and arranged, obviously may be reduced to a system which latter may become available as the basis, not only of a theory, but of the true theory of chess and of war. Although the Baron de Jomini understood nothing of the art of warfare, and but little of the science of war, on the other hand, his veracity as to facts which came under his personal observation is beyond question. Therefore the following statement by the Baron de Jomini is of the highest value to the layman : — " In my presence the Emperor (Napoleon I.) once remarked, ' I know of but one way of making war, and that is — to act against the enemy's communications.'" This, of course, is the positive, the aggressive, the strategetic-offensive phase of that "way of making war" which is common to all great captains, from Epaminon- das to Yon Moltke. For the negative, the finessing, the defensive phase of scientific warfare, we must look to the words of the ablest of them all : — " The art of the great captain," said Frederic the Great, " consists in dividing up the enemy's force." Both of these great soldiers meant the same thing, but each clothed the idea in words which reflected that method for applying this idea in warfare which was dis- tinctively his own. In the first is seen a vast generali- zation, a contempt of detail characteristic of one whose 84 CBESS STRATEGETICS. processes were nothing if not spectacular ; and in the second is seen the exact, definite conclusion of the greatest organizer of victory on the battlefield that the world has ever seen. Each meant to say that to seize upon and to occupy with your army the central space between two or more sections of a hostile army ; or, to seize upon and to occupy witli your army the central space between a hos- tile army and its base, is the chief idea in the science of war; and that so to manoeuvre your army as either to compel or to outwit the enemy into permitting you thus to seize and to occupy with your army such central space, is the chief process in the art of warfare. To effect the perfect union of science and of art is the province of mathematics. In this connection, as every mathematician knows, — " Things tliat are equal to the same thing are equal to each other. ^' Every student of military science knows that if a su- perior force can unexpectedly be precipitated between two inferior bodies of troops, that one and possibly both of the latter will be destroyed. Every student of this theory knows that if the point of command in any evolution be properly occupied by a kindred Prime Tactical Factor, the adverse force is lost. Any man can understand that if a body of troops, or a body of chesspieces, can take up such a position that the occupation of this point of command, whether on the battlefield or on the chessboard, is assured, such occupation is equivalent to the actual occupation of the point of command, — for things that are equal to the same thing are equal to each other. That ancient Israelite, Shylock, was a strategist, and that he under- PROCESSES OF GREATER LOGISTICS. 85 stood the truth of the foregoing proposition is shown bv his logical and conclusive statement : — " You do take my house when you do take the prop by which my house stands ! " This statement admittedly is true ; and cliessplayer, soldier, and mathematician alike, having accepted it as a point of departure, may now start out in full accord to find out what the great Corsican was doing as he lay prone on his map of Europe, whisking his dividers over its surface, and sticking into it here and there divers- colored headed pins. " It is much easier to defeat an enemy than commonly is supposed," says Napoleon ; " the great art lies in not making any but decisive movements." Thus, logically, it is obvious that when Napoleon, stretched out upon his map of Europe, was whisking his dividers about from point to point, he was planning a " decisive movement .'' Furthermore, as he had selected a " decisive point," and was combining by a " logistic movement " the concentration of his corps d^armee at that point, it again logically is evident that this deci- sive point was nothing more nor less than one of two things : — I. The tactical key of a proposed field of battle ; or, II. That point whose occupation would insure the subsequent occupation of the tactical key of a proposed field of battle. The military mind will recognize the logic of this assertion at a glance ; for the benefit of others it may be well to remark that a diagram goes with this state- ment, which will be shown later. Now, the tactical keys always are in the possession of the enemy (unless the situation is merely one of Major Tactics, and in which the opponent has committed 86 CHESS STEATEGETICS. a tactical blunder ^hich subjects him to loss, by means of a routine evolution), and the occupation of a tactical key in actual warfare is the normal outcome of a line of operations and the direct result of a pitched battle. In the matter under consideration, it is obvious that Napoleon is not planning a battle ; this is shown by the fact that he has selected, as the " decisive point," some place other than the one at which he then is ; were a battle being planned, his corps would be concentrating about his present headquarters, for on the eve of a battle the great captain always is with his vanguard. Hence, no battle being planned, it is evident that no line of operations exists, for a line of operations consists of a battle or a series of battles. Thus, Napoleon, not being engaged in destroying the enemy, is engaged in planning how to destroy the enemy, and consequently he is planning and preparing to act upon a line of manoeuvre. A line of manoeuvre always is directed for one of the three following purposes : — IN WARFARE. I. To cut off the adverse army from communication with its base of operations. II. To cut an army off from communication with a kindred army. III. To cut portions of the same army off from communication with each other. IN CHESSPLAY. I. To cut the bulk of the Determinate Force off from communication with the King. II. To cut the Hypothetical Force off from commu- nication with the Logistic Horizon. n PROCESSES OF GREATER LOGISTICS. 87 III. To cut off adverse pieces from commimication with the bulk of the adverse Determinate Force. Even the layman thus readily may understand that the objective of a line of manoeuvre necessarily must be a point situated between two hostile masses, and that this point is a decisive point, provided the occupying force is strong enough to hold one of the hostile masses in check, while with the superior force it falls upon and destroys the second hostile mass. Applied to chessplay, the student readily sees that this idea merely is the elaboration of what in Major Tactics is termed the subgeometrical symbol. In all such situations there being the choice of two battles, — i. e., a battle against the one or against the other of the hostile bodies, — there necessarily must be two tactical keys. As it is required that the kindred force, when posted at the decisive point, shall act simultaneously against both of these tactical keys, or against those points whose occupation insures the subsequent occupa- tion of at least one of the given tactical keys, it also is evident that this decisive point always is the centre of that geometric symbol of which the two tactical keys, or those points from whence they are commanded, are perimetal points. Furthermore, it is obvious that the kindred piece which occupies the decisive point must be that integer of chess force to which this geometric symbol appertains. But it will be observed by the student that there is yet another consideration no less important than the foregoing, and that is : victory always is decided by the operation of the basic law of strategetics, — the greater force always overcomes the lesser, — and there- fore it is imperative that the radii of offence operated 88 CHESS STRATEGETICS. by the attacking body shall be in excess numerically of the radii of defence operated by the defending body. Now it is obvious that in all situations wherein the forces are equal, one antagonist can obtain no advantage over the other except tkrough the latter's error, and that the effect of snch error always is to expose two points to be simultaneously attacked when such points can- not be defended in a single move, — that is to say, in the situation taken as an entirety, — the attacking force will operate at least one more radius of oiTence than the number of radii of defence operated by the opponent. Furthermore, it is obvious that the point from which this additional radius of offence is operated is the deci- sive point, and that this decisive point or strategic key naturally takes the form of the vertex of a triangle, or of the centre of a straight line whose extremities are occupied by tactical keys ; i. e., of those centres and vertices which in Major Tactics are termed points of command. Hence, to the student of war, or of chess, or of mathematics, the following is true and valid : — FIFTH LAW OF THE ART OF CHESSPLAY. Whenever two tactical Jcei/s, or tic o points of command, or a tactical key and a j^oint of command, are situated on the perimeter of the same geometric symbol, then the centre of the given geometric symbol is the strategic key. PROCESSES OF GREATER LOGISTICS. 89 THE STRATEGIC KEY. Figure 47. Paul Morphy. i^ mi 'i'm/iV/ Hi i » ip ^M fl % t#j ^: ■^lAl m. ,jmm.., m isi W////yM ^ ^^^P M S a Jacob Lowenthal. This position occurred in the first game of the match between these masters. 90 CHESS STRATEGETICS. THE PLAY. Hekk Lowenthal. IVIk. Moepht. 18. P-QE3. Had "White played otherwise, he would have lost a pawn. Black threatened to occupy the Strategic Key (Black Q Kt 5) with his Q, whence he would command the undefended White Q and the undefended White Q Kt P. As White could not in a single move have defended both of the pieces thus simultaneously attacked, one of them necessarily would be lost. It is now easy for the student to understand that when Napoleon spread out his map on the ground and lay down upon it, the first thing he did was to stick into it a number of pins, each of which was surmounted by a wad of green sealing-wax, and represented a French corps d^armee and its position at the moment, and then to stick into the map as many pins covered with red sealing-wax as his information led him to decide was the number and position of the hostile corps d'armee. So far Jomini got the right idea, and the distinguished Swiss also is correct in his statement that Napoleon used his dividers to estimate distances and the marches of his troops. But here Jomini's knowledge of the Napoleonic process leaves off, and the real understanding of the subject begins. Napoleon did not determine the decisive strategic point " in his closet," as Jomini states. It was only after the great Corsican had specified the position of his own, and of the opposing bodies of troops, that he did, or even that he could, so determine this decisive point ; and he de- termined it in this way. After Napoleon had marked out on his map the posi- tion of the contending armies, his next step was to find PROCESSES OF GREATER LOGISTICS. 91 a means for '' acting against the enemy's communications ; " or, as Frederic puts it, " to divide up the enemy's forceP His method was this : — Locating the extremities and the configuration of the enemy's strategic front, and noting exactly the relations of the latter to the existing topographical conditions, the great Corsican remarked that point which if occupied by his army would — 1. Cut the adverse army in two ; or, 2. Would cut the adverse army off from its base. Then, regarding the army thus separated, either from its remaining integrals or from its base. Napoleon located, in the position occupied by these two pro- spective isolated integrals, those two points which, if occupied by his troops, would lead to the destruction in detail of each isolated hostile mass. These commanding points always are the tactical keys and usually are heights from which the whole of each prospective battle- ground may be enfiladed by artillery. In chessplay, the tactical key always is that point whose occupation either checkmates the adverse king^ eliminates an adverse piece from the hoards or queens a kindred pawn. Whenever the hostile army was massed in a single body, Napoleon always employed the second process, and manoeuvred to cut the adverse army off from its base without exposing his own. But whenever the adverse army was not massed in a single body, he always made use of the first process, which in military mathematics may be expressed thus : — - 92 CHESS STRATEGETICS. Figure 48. d' c^ D^ ♦ •. k: — ' ^: — c » - V Qi A Topographical Centre. B^ Point of Command in left wing. B'^ Point of Command in right wing. C^ >- Hostile Corps of left wing and tactical keys. ^;) . D" > Hostile Corps of right wing and tactical keys. PROCESSES OF GREATER LOGISTICS. 98 In order to understand how to locate these points of command, the student of war must study the campaigns of the greater captains, and the student of chess must study "The Major Tactics of Chess." PRINCIPLE. Having located two tactical keys^ or two points of com- mand^ or a tactical key and a point of command^ connect these hy their most direct lines of communication and the points upon such lines equidistant in time between the two strategic vertices will he the topographical centre. It is evident from this diagram that a kindred force posted at the point A commands the communications between the points B^ and B^ and thus prevents the ad- verse corps d^armee^ C^, C^, and C^, from co-operating with the adverse corps d''armee^ D^, D^, and D^o Never- theless, it is equally easy to see that the kindred force will lose the advantage of this central position, if it per- mit all the adverse corps simultaneously to attack it at A, and consequently it obviously is imperative that the kindred force keep both of the adverse forces divided and at arms' length, so to speak, and that it attack them separately and not at the same time. Hence it follows that while the kindred superior force is destroying one of the inferior adverse forces, the kindred column on the opposite wing must hold the second hostile force in check and prevent it from interfering in the battle, or series of major tactical evolutions, which is being exe- cuted by the united kindred columns of the centre and left, against the first-mentioned hostile force. All this is applicable to chessplay, and may be de- picted on the chessboard thus : — 94 CHESS STRATEGETICS. FiGrPvE 49. Black. ■r^^'w p m 'mm. m ,^^^ a I^H A White. XoTE. — A = Tactical Key which, if occupied by an adverse Queen, the existing Objective Plane (Class B) will be commanded. White Q Kt 2 = Tactical Key which, if occupied bv any adverse piece, will result in the loss of the White Q B. As the B cannot be posted at White K Kt 2, and as a point cannot move, there is no Line of Communication. PROCESSES OF GREATER LOGISTICS. 9o The military principle may also be adapted to the chessboard, viz. : — SIXTH LAW OF THE AET OF CHESSPLAY. Having located two tactical keys^ tivo points of command^ or one tactical key and one point of command^ then con- nect these two points hy logistic radii., and those points at which the given logistic radii intersect will he points of communication, and that point of communication common to both ivill he the topographical centre. Having first disposed of this most important prelimi- nary calculation, Napoleon next proceeded to determine the strategic key of the adverse position, that is, the point from which — his columns of the right and the left liaving taken up their proper positions against the hostile left and right, respectively — he could throw his column of the centre against whichever of the adverse isolated masses that he might choose. Consequently the student of mathematics readily sees that it is imperative that this decisive point be : — 1. Nearer in time to that topographical centre which in the given situation is the true point of communica- tion, than is any equal adverse force ; in order to pre- vent its being occupied by the enemy. 2. Equidistant in time from the two tactical keys ; or the two points of command, or the tactical key and the point of command, in order to be able to attack either with like facility. Consequently the rule for locating this strategic key is easy to deduce, and both Napoleon and the student of mathematics solved the problem Avith equal readi- ness, viz. : — 96 CHESS STRATEGETICS. RULE. The Topographical Centre being given, describe a circle of which this point is the centre, and whose circumference passes through the points of command ; then draw a second diameter at right angles to the first diameter, and the point where the second diameter intersects this circumference is the strategic key. This may be mathematically expressed thus : — Figure 50. B' c Topographical Centre. Point of Command in hostile left wing. A B^ ' Point of Command in hostile right wing. C'^ >- Hostile Corps on left wing and tactical keys. C^ ) DM D"- V- Hostile Corps on right wing and tactical keys. E Strategic Key. PROCESSES OF GREATER LOGISTICS. 97 This also is applicable to chessplay, and may be de- picted on the chessboard thus : — Figure 51. Black. White. A = Tactical Key. White Q Kt 2 = Tactical Key. B = Strategic Key. Black Q R 3 = Point of Manoeuvre of White corps of the centre. Black Q R 3 + B = Eoute of White corps of the centre. 98 CHESS stuategetics. The student thus will perceive that, by the plain and exact process of logical deduction, a tangible situation now is established and that this situation is composed of a prime strategic point, two prime tactical points, one or more known points occupied bj kindred cor/?s d'armee, and two or more known points occupied by adverse corps d'armee. Napoleon, having thus mathematically determined the strategic key, then, according to Jomini, proceeded to whisk his dividers about the map and to calculate the movements of a " logistic operation," in order to get each of his eorys d'arime " to where he wished to have it on a given day." As neither the Baron de Jomini nor any other mil- itary writer has seen fit to inform us of the nature of this " logistic operation," nor to elucidate the pro- cesses incident to its execution, it seems proper and even necessary for us to make the discovery for our- selves. At the very beginning of this logistical calculation, we must, of course, get down to first principles and come at once to a correct understanding of what we want to do. As a matter of fact, the object of this logistical operation is to place, in the briefest time, the attacking force at those points where, — 1. It divides the hostile force into at least two isolated masses. 2. Controls the communication between these two or more isolated masses, thus preventing them from reuniting. 3. Acts simultaneously against two tactical keys, or two points of command, or a tactical key and a point of command ; and proposes, from a central post, to con- versre a third column ao;ainst one or the other of the J *-^ PROCESSES OF GREATER LOGISTICS. 99 adverse points at a time when it is impossible for such adverse point to be properly reinforced. This projected situation may be mathematically ex- pressed thus : — bV Figure 52. A C^ ^B' Q A B^ E a b Topographical Centre. First Point of Command, or tactical key. Second Point of Command, or tactical key. Strategic Key. Kindred Corps of the Centre. « " " Eight. " " Left. From this diagram the student readily sees that each of the kindred corps has a specific destination. Napo- leon determined this destination, as the mathematical mind readily perceives, by the following : EULE. Given the strategic key and taking it as a centre, describe a circle whose circumference shall pass through the topographical centre ; then, unite the strategic key with the adverse points of command by straight lines, 100 CHESS STRATEGETICS. and the points where these lines intersect the given circumference will be the destinations of the kindred columns of the right and of the left, respectively. Obviously, the strategic key always is the destination of the column of the centre. This position may be depicted on the chessboard thus : Figure 53. Black. White. K Kt 1 = An Objective Plane of Class B which may be commanded by a Q at K Kt"^2. Q Kt 2 = Exposed Point Material. K Kt 2 — Q Kt 2 = Strategic Plane of Class B capable of beinf^ commanded hv a Q or E. PROCESSES OF GREATER LOGISTICS. 101 B = Strategic Key whicli in this position should be occupied by a Q in order to threaten mate at K Kt 2. Q R 3 — Point of Departure of Col. of Centre. QR1= " " " Right. K B 3 = " " " Left. C = Point of Command in Left Evolution. D = " " Right Evolution. The military principle may be adapted to the chess- board, viz. : — SEVENTH LAW OF THE ART OF CHESSPLAY. Given the strategic vertices^ then unite each of these with a kindred piece by means of logistic radii which appertain to the kindred piece, and the line formed hy these logistic radii will he the route of the given piece ; and the number of logistic radii contained in such route will he the number of marches required of the given kindred piece. It now remains to explain in detail the routes and the reasons therefor which must be taken by the three kindred columns. The student will recall the Napoleonic dictum, " Unity is the soul of strategy," and will ob- serve that Napoleon's calculation is based upon the fact that this law has been violated by the enemy. Conse- quently the logical mind sees at a glance how imbecile it would be to imitate the error of the opponent, and easily comprehends that these three columns must march, not necessarily as a single mass, but at least as three united masses, i.e.., in such relative position that each may effectively cover and support the others. 102 CHESS STRATEGETICS. Hence, while not moving as one body, the three col- umns yet must constitute the right, the centre, and the left of a grand army, and must simultaneously move toward three distinct and specific points, the mere occu- pation of which, all else being equal, will insure victory. Thus, to the military student and to the mathematical mind it is obvious that the following is true and valid : EIGHTH LAW OF THE ART OF CHESSPLAY. The destinations of the Corps Offensive being determined, unite these hy logistic radii with the points of departure, and the resultant lines will he the routes of the kindred corps respectively. PROCESSES OF GREATER LOGISTICS. 103 This situation may be mathematically expressed thus : FlGUKE 54. (-^-st. A B- Topographical Centre. Point of Command in hostile Left. Point of Command in hostile Right. Hostile Corps on Left Wing and Tactical Keys. Hostile Corps on Eight Wing and Tactical Keys. 104 CRESS STRATEGETICS. E Strategic Key. F^ Destination of kindred Left Column. F^ " " " Eight Column. G Point of Departure of Centre Column. H " " " " Right '' I " " " » Left '^ EG- Route of kindred Column of the Centre. F^I Right. Left. All this appertains to chessplay, and the situation may be depicted on the chessboard thus : — FlGUKE 55. Black. White. PROCESSES OF GREATER LOGISTICS. 105 A =: Tactical Key in Left Evolution. White Q Kt 2 = Tactical Key in Kight Evolution. B = Strategic Key. Q =: Corps of the Centre. Q R = Corps of the Eight. K R = Corps of the Left. C = Point of Command in Left Evolution. D = Point of Command in Right Evolution. Q R 1 = Right Point of Manoeuvre. K B 3 = Left Point of Manoeuvre. Q R 3 = Central Point of Manoeuvre. Q R 1 - D == Route of Corps of the Left. Q R 3 — B = Route of Corps of the Centre. K B 3 - C = Route of Corps of the Right. STRATEGIC HORIZONS. The method whereby the great Corsican constructed his Strategetic Horizon thus having been outlined, and the adaptation of this method to the chessboard indicated, the student readily will understand that the detail pro- cesses which appertain to the method thus adapted to the chessboard necessarily are but logical sequences, — mere corollaries of the general principles laid down in the preceding volumes of this series. As the first and a most essential detail in the applica- tion of Napoleon's system of warfare to chessplay, the attention of the student is called to the mathematical figure formed by combining the strategic key with the two tactical keys, or by combining the strategic key with the two points whence these tactical keys are commanded. This mathematical figure is termed in this theory the Strategic Horizon^ and these strategic horizons, it is im- portant for the student to observe, are divided into three classes, viz. : — STRATEGIC HORIZONS. 107 I. Strategic Horizons in which the three vertices which appertain to the mathematical figure are a strate- gic key and two tactical keys. STRATEGIC HORIZON. (a.) Figure 56. Black. White. Note. — The White Kt occupies the strategic key. The Black K B and R occupy the tactical keys. 108 CHESS STRATEGETICS. 11. Strategic Horizons in which the three vertices are a strategic key, a tactical key, and a point of command. STRATEGIC HORIZON. (6.) FlGUEE 57. Black. m ./mm.. % m^/VA ^IM m ^» White. Note. — The White Kt occupies the strategic key ; the P at Black Q B 5 occupies the tactical key, and the point of command is Black's K B 4. STRATEGIC HORIZONS. 109 III. Strategic Horizons in which the vertices are a strategic key and two points of command. STRATEGIC HORIZON. FlGUKE 58. Black. White. Note. — Tlie White Kt occupies the strategic key ; the points of command are Black's K B 5 and Q B 4. 110 CHESS STRATEGETICS. That vertex contained in the strategic horizon and which is designated as the strategic key always is the centre of a geometric symbol, of which the other two strategic vertices are points on a common perimeter. In consequence, there are fifteen mathematical figures which appertain to the strategic horizon, and the prac- tical application of these fifteen mathematical figures to the chessboard is governed by the following : — NINTH LAW OF THE ART OF CHESSPLAY. Whatever the form of the strategic horizon, two of its sides always are radii of offence appertaining to the kindred corps of the centre, and the point where these radii intersect always is the strategic key. STRATEGIC HORIZONS. Ill A strategic horizon 1 is limited to the attack of two adjacent tactical keys or to two adjacent points of com- mand situated diagonally on the front. It is typified by the geometric symbol of the Pawn, and in this system of chessplay it is designated by the letter t. The strategic key always is the apex and may properly be occupied either by the P, B, Q, or K. STRATEGIC HORIZON {t). Figure 59. Black. White. 112 CRESS STRATEGETICS. A strategic horizon 2 is limited to the attack of the logistic horizon. This attack always is directed against two points of junction, one of which also is an exposed Point Material. It is typified by a right-angled triangle and is designated by tlie letter r. The strategic key always is a point in the seventh horizontal for White and in the second horizontal for Black, and cannot be properly occupied except by a kindred P. STRATEGIC HOEIZOX (/•)• FiGUEE 60. Black. White. STRATEGIC HORIZONS. 113 A strategic horizon 3 is expressed by a triangle composed of the obliques which unite the centres of three knights octagons, the extremities being points of command in evolutions appertaining to the knight, and the vertex being the strategic key. This horizon is designated by the letter 0, and cannot properly be occupied except by a kindred Kt. STRATEGIC HORIZON (0). Figure 61. Black. White. 114 CHESS STRATEGETICS. A strategic horizon 4 is expressed by an oblique line, upon which are located tlie centres of three knights octagons, the extremities being either tactical keys or points of command in evolutions appertaining to the Kt, and the central point being the strategic key. This horizon is designated by the letter o, and cannot prop- erly be occupied except by a kindred Kt. STRATEGIC HORIZON (o). Figure 62. Black. White. The oblique line is formed by the white points Q 2, K 4, and K B 6. The centre is the strategic key, and the extremities are points of command in evolutions appertaining to the Knight. STRATEGIC HORIZONS. 115 A strategic horizon 5 is expressed by the geometric symbol of the B. Its sides are diagonals, and the vertex is the strategic key. The latter properly may be occupied by the B or the Q. The extremities always are either tactical keys or points of command in other Bishop's triangles ; or the centre of a Queen's polygon. It is designated bv the letter T. STRATEGIC HORIZON {T\ Figure 63. Black. m »^J m I v/m;^y._ Wa ....wm. ^mm. Wldte, 116 CHESS STRATEGETICS. A strategic horizon 6 is expressed by a diagonal upon which are situated the vertices of three Bishop's tri- angles and Queen's polygons, the extremities being either tactical keys or points of command in evolutions appertaining to the Bishop or to the Queen, and any point between these being the strategic key. This horizon is designated by the letter i), and cannot properly be occupied except by a kindred B or Q. STRATEGIC HORIZON (D). Figure 64. Black. White. For the Q, the diagonal is formed by the white points, R 2, Q B 4, and K 6 ; for the Bishop, the diagonal is formed by the white points, K 4, Q B 6, and Q Kt 7. STRATEGIC HORIZONS. 117 A strategic horizon 7 is expressed by a diagonal composed of three adjacent points, the extremities being either tactical keys or points of command appertain- ing to the B, Q, or K, and the central point being the strategic key. This horizon is designated by the letter d and cannot properly be occupied except by a kindred B, Q, or K. STRATEGIC HORIZON [d). Figure 65. Black. White. 118 CHESS STRATEGETICS. A strategic horizon 8 is expressed by the geometric symbol of the Rook. Its sides are right lines, the angle is the strategic key, and the extremities are either tactical keys or points of command in evolutions which appertain to the R or Q. It is designated by the letter Q, and cannot properly be occupied except by the kin- dred R or Q. STRATEGIC HORIZON (Q). Figure 66. Black. y//////m, ^ ^1 ''<^^^. y/. y/////M m White. m m m STRATEGIC HORIZONS. 119 A strategic horizon 9 is expressed by a right-angled triangle formed by three adjacent points, the angle being the strategic key and the extremities being either tactical keys or points of command in evolutions apper- taining to the R, Q, or K. It is designated by the letter q, and may properly be occupied only by a kindred R, Q, or E. STRATEGIC HORIZON {q). Figure 67. Black. ^mg m^jM ^.^ ^ 1 m mm. Wy. MA VA Wm^A White. 120 CHESS STRATEGETICS. A strategic horizon 10 is expressed by a straight line formed by three points situated on the same horizontal, the extremities of which are either tactical keys or points of command in evolutions appertaining to the R or the Q, and the strategic key being any point between. This horizon is designated by the letter H, and properly is occupied only by a kindred R or Q. STRATEGIC HORIZON [H). Figure 68. Black. White. STRATEGIC HORIZONS. 121 A strategic horizon 11 is expressed by three adjacent points situated on the same horizontal, the central one being the strategic key and the extremities being either tactical keys or points of command in evolutions apper- taining to the R, Q, or K. This horizon is designated by the letter A, and cannot be properly occupied except by a kindred R, Q, or K. STRATEGIC HORIZON {h) Figure 69. Black. m M yyy////y/yA If 1 ii"^~ m. mm.,. m mm. White. 122 CHESS STRATEGETICS. A strategic horizon 12 is expressed by a straight line formed by three points situated in the same vertical, the extremities being either tactical keys or points of command in evolutions appertaining to the R or the Q, and the strategic key being any point between. This horizon is designated by the letter F", and properly is occupied only by a kindred R or Q. STRATEGIC HORIZON (F). Figure 70. Black. White. STRATEGIC HORIZONS. 123 A strategic horizon 13 is expressed by three adjacent points situated on the same vertical, the central one being the strategic key and the extremities being either tactical keys or points of command in evolutions apper- taining to the R, Q, or K. This horizon is designated by the letter -y, and cannot be properly occupied except by a kindred R, Q, or K. STRATEGIC HORIZON (t). Figure 71. Black. White. 124 CHESS STRATEGETICS. A strategic liorizon 1-i is expressed bj the geometric symbol of the Q, the centre being the strategic key and the extremities being either tactical keys or points of command in evolutions appertaining to the Q. This horizon is designated by the letter P, and can properly be occupied only by the kindred Q. STRATEGIC HORIZON (P). Figure 72. Black. White. STRATEGIC HORIZONS. 125 A strategic horizon 15 is expressed by the geometric symbol of the King, the centre being the strategic key and the extremities being either tactical keys or points of command in evolutions appertaining to the Q or K. This horizon is designated by the letter R^ and properly is occupied only by the kindred Q or K. STEATEGIC HORIZON {R). Figure 73. Black. % y/y. kmii m...^ i i 1 ^H m If %^ ^- White. TACTICAL HORIZONS. The student will observe that whenever the strategic horizon consists of a strategic key and two tactical keys, the process is direct, and by the occupation of one of these tactical keys, either the adverse king is checkmated, or an adverse piece is captured, or a kin- dred pawn is queened. But when the strategic horizon contains one or more points of command, there exists what is termed in this theory a Tactical Horizon. Tactical Horizons are formed by the union of the objective plane with the logistic horizon, or with the geometric symbols appertaining to the various integers of chess force, or with the formations appertaining to the several strategic fronts ; or by the union of these latter with each other. Tactical Horizons are divided into ten classes and are governed by the following : — TACTICAL HORIZONS, 127 TENTH LAW OF THE ART OF CHESSPLAY. Every Corps Offensive must he a competent Prime Tactical Factor in that geometric plane against which it is directed. 128 CHESS STRATEGETICS. A Tactical Horizon of Class I. is composed of a Strategic Plane. It results from a strategic weakness of Classes I. or 11. ; it is the legitimate outcome of a complex line of manoeuvre and always is the ultimate situation in a strategic line of operations. TACTICAL HORIZON. (First Class.) Figure 74. Paul Morpht. i 'm •yyM yy/////M,. iiili i M #7S7^7?^ mZW/, ^=- V/7^y7/. Louis Paulsen. This position occurred at the First American Chess Congress in the match between these masters. TACTICAL HORIZONS. 129 THE PLAY. Herr Paulsen. Mk. Mokpht. • 17. Q X B. 18. P X Q. 18. E-Kt3(ck). 19. K-Rl. 19. B-R6. 20. E-Ql. 20. B - Kt 7 (ck). 21. K - Kt 1. 21. B X P ((lis ck), 22. K-B 1. 22. B - Kt 7 (ck). 23. K - Kt 1. 23. B - R 6 (ck). 24. K-El. 24. B X P. 25. Q - K B 1. 25. B X Q. 26. RxB. 26. R - K 7. 27. R - Q E 1. 27. R -K R 3. 28. P-Q4. 28. B - K 6. Black won. 130 CRESS STRATEGETICS. A Tactical Horizon of Class II. is formed by the union of a Strategic and a Logistic Plane. It results from a strategetic weakness of Class lY. ; it is the legitimate outcome of a complex line of manoeuvre, and always is the ultimate situation in a strategic or a logistic line of operations. TACTICAL HOEIZON. (Second Class.) Figure 75. Paul Morphy. ■ in ^^7^^^ 7///y. w/////%, ■^ I mk V/7P^////. 'mm m. Wa ^-^ #^S^ V////////A wm> ^ i"" Mr. Barxes. i TACTICAL HORIZONS. 131 THE PLAY. Mb. Barnes. Mr. Mobpht. 14. Kt - Q Kt 5. 15. Kt - Q R 3. 15. B X K P. 16. B X B. 16. Kt - Q 6 (ck). 17. Q X Kt. 17. P X Q. 18. Castles Q E. 18. B x Kt. 19. B - Kt 3. 19. P - Q 7 (ck). 20. K-Ktl. 20. B~B4. 21. Kt-K5. 21. K-Bl. 22. Kt-Q3. 22. E - K 1. 23. Kt X B. 23. Q X E. Black won. 132 CHESS STRATEGETICS. A Tactical Horizon of Class III. is formed by the union of a Strategic and a Tactical Plane. It results from a strategetic weakness of Class III. ; it is the legit- imate outcome of a complex line of manoeuvre, and it always is the ultimate situation in a strategic or a tactical line of operations. TACTICAL HORIZON. (Third Class.) Figure 76. M. Baucher. ^#1 m^t illi.»l Hi V/w7////. fe M t^^wi. pi mztz'.m 'wm, i ^ "—^ 'y//////M 'mm ^p Paul Morpht. This position occurred at Table No. 1 in the famous blindfold exhibition at Paris, 1858. TACTICAL HORIZONS. 133 THE PLAY. Mk. Morpht. M. Baucher, 22. R-R3. 22. P-KE3. 23. Q-Q2. 23. K-E2. 24. Q X B. 24. B--Q3. 25. E X P (ck). 25. K X K. 26. E-Q3. 2Q. K-E4. 27. Q-B 7 (ck). White won. 134 CHESS STRATEGETICS. A Tactical Horizon of Class lY. is formed by the union of a Strategic Plane and a Strategic Front. It results from tactical errors on the part of the opponent ; it is the legitimate outcome of a simple line of manoeuvre, and properly is preliminary to a complex line of ma- noeuvre. TACTICAL HOEIZOK (Fourth Class.) Figure 77. Paul Morpht. ////////^//A M P m #' i 4M i y/M, Wa. 'mm. M.i. ■ m i # 'yy//////Y/, ...<^^^ *^S3=, '^//////^/, '^//y Mr. H. E. Bird. TACTICAL HORIZONS. 135 THE PLAY, Mr. Bird. Mr. Morpht. 16. R - Q Kt 1. 17. Castles Q K. 17. B X K B P. 18. B X R. 18. Q - Q R 6. 19. P-B3. 19. Q X RP. 20. P - Kt 4. 20. Q - R 8 (ck). 21. K-B2. 21. Q - R 5 (ck). 22, K - Kt 2. 22. B X Kt P. 23. P X B. 23. R X Kt P (ck), 24. Q X R. 24. Q X Q (ck). 25. K - B 2. 25. P-K6. 26. B X P. 26. B - B 4 (ck). 27. E-Q3. 27. Q - B 5 (ck). 28. K-Q2. 28. Q - R 7 (ck). 29. K - Q 1. 29. Q - Kt 8 (ck). Black won. 136 CHESS STRATEGETICS. A Tactical Horizon of Class Y. is formed bj the union of two Logistic Planes. It arises from a strategetic weakness of Class Yll. ; it is the legitimate outcome of a compound line of manoeuvi-e, and it always is the ultimate situation in a logistic line of operations. TACTICAL HORIZON. (Fifth Class.) FlGUEE 78. Herr Harrwitz. *^ %. J '■mma ""W/4 ^^^^ % %m Pi' 4M. % i '//7^///y Paul Morpht. This position occurred in the eighth game of the match between these masters. TACTICAL HORIZONS. 137 THE PLAY. Mr. Mokphy. Herr Harrwitz. 28. P - Kt 5. 28. Kt - Kt 1. 29. P-B6 (ck). 29. K-Kl. 30. P-B 7. 30. Kt - Q B 4. 31. P X Kt (Q ck). 31. Kx Q. 32. B X Kt. 32. B xB. 33. Q - K 2. 33. Q-K3. 34. Kt - Q 2. 34. K-E 1. 35. B - Kt 4. 35. Q-K2. 36. Kt - B 3. 36. E-Ql. 37. P-R4. 37. E-Q3. 38. K X E. 38. PxE. 39. Q-B4. 39. E-KBl. 40. Q-K6. 40. B - K 6 (ck), 41. K-Ql. 41. Q - Q B 2. 42. Kt - Q 2. 42. B-B5. 43. Kt - B 4. 43. Q - B 4. 44. Q-Q5. #4. Q x;'Q (ck). 45. P X Q. •45. E-Ql. 46. R-B3. 46. K - Kt 2. 47. P-B 3. White won. 138 CHESS STRATEGETICS. A Tactical Horizon of Class YI. is formed by the union of a Logistic and a Tactical Plane. It arises from a strategetic weakness of Class Y. ; it is the legitimate outcome of a compound line of manoeuvre, and it is the ultimate situation either in a logistic or a tactical line of operations. TACTICAL HOKIZON. (Sixth Class.) Figure 79. Paul Morpht. ^P « ■. ■— • m.l % --^'^-. m mm. "1 ■ m Adolph Axderssex. This situation occurred in the tenth game of the match between these masters. TACTICAL HORIZONS. 139 THE PLAY. Adolph Anderssen. Mk. Morpht. 60. P - K B 5. 61. P X p. 61. P-K6. 62. B-K7. 62. P - K 7 (ck). 63. R X P. 63. R - E 8 (ck). 64. K-B2. 64. Kt - Q 5 (ck) 65. K moves. 65, Kt X R. 140 CHESS STRATEGETICS. A Tactical Horizon of Class VII. is formed by the union of a Logistic Plane and a Strategic Front. It arises from tactical errors on the part of the opponent ; it is the legitimate outcome of a simple line of manoeuvre, and properly is preliminary to a complex line of ma- noeuvre. TACTICAL HORIZON. (Seventh Class.) Figure 80. Amateur. V/^^/^.. /A 1 i^i ^^ i Hi m. i III mm^_M m m i^^ isi^ ■ m Paul Morphy. This position occurred in an exhibition at New Or- leans, Mr. Morphy playing six games simultaneously without sight of. boards or men. TACTICAL HORIZONS. 141 THE PLAY. Mr. Morpht. AjMATEUR. 21. E-K8. 21. Q X E. 22. Q X R. 22. Q-K2. 23. Q X KtP (ck). 23. Q X Q. 24. P - B 6. 24. Q X Kt P (ck) 25. K X Q. 25. B X P (ck). 26. K X B. 26. P - K E 4. 27. R-KKtl. White WOJl. 142 CHESS STRATEGETICS. A Tactical Horizon of Class VIII. is formed by the union of two Tactical Planes. It arises from a strate- getic weakness of Class VI. ; it is the legitimate out- come of a compound line of manoeuvre, and always is the ultimate situation in a tactical Ime of operations. TACTICAL HOKIZON. (Eighth Class.) ElGUKE 81. Hekk Harewitz. Paul Morphy. This position occurred in the fourth game of the match between these masters. TACTICAL HORIZONS. 143 THE PLAY. Mr. Morphy, Here Harrwitz. 30. P - Q B 5. 30. E X P. 31. E X P (ck). 31. K X E. 32. Q-KR5 (ck). 32. K-Ktl. 33. Kt X B (ck). 33. K-Kt2. 34. Kt - B 5 (ck). 34. K-Ktl, ^o. Kt X P. White won. 144 CHESS STRATEGETICS. A Tactical Horizon of Class IX. is formed by the union of a Tactical Plane and a Strategic Front. It arises from tactical errors on the part of the opponent ; it is the legitimate outcome of a simple line of manoeuvre, and properly is preliminary to a compound line of manoeuvre. TACTICAL HOKIZON. (Ninth Class.) Figure 82. Adolph Anderssen. mi iSil 'mm wm i ■:« ^ '/^//////V/, 4^my^. wy////M w/////Z^, Jl ^ 1 ^^^;^ I Paul Morphy. This position occurred in the third game of the match between these masters. It is a fine study in the construction of the major front by the right when K file is open. TACTICAL HORIZONS. 145 THE PLAY. Mr. Morpht. Herr Anderssen. 10. R - K 1 (ck). 10. K-Bl. 11. B X B. 11. Q X B. 12. P - Q J3 3. 12. P-Q4. 13. P X P. 13. B-K3. 11. Kt - B 3. 14. P-QE3. 15. R-K5. 15. E-Ql. 16. Q-Kt3. 16. Q-K2. 17. QR-Kl. 10 146 CHESS STRATEGETICS. A Tactical Horizon of Class X. is formed by the union of a strategic front witli any of the supplementary for- mations appertaining thereto. It arises from errors in tactics on the part of the opponent ; it is the legitimate outcome of a simple line of manoeuvre, and properly is preliminary to a complex line of manoeuvre. TACTICAL HORIZON (Tenth Class.) ElGUEE 83. Paul Morphy. m m ... m m im»imkm m m 'mm. Bl ^AnPK^ m m 181 W'^^4 m ^m. Adolph Anderssen. This situation occurred in the second game of the match between these masters. TACTICAL HORIZONS. 147 THE PLAY. Heer Anderssen. Mr. Morphy, 18. B - Q B 5. 19. Kt - K B 5. 19. B X E. 20. Q X B. 20. Kt - K 2. 21. KKt-KR4. 21. Kt X Kt. 22. Kt X Kt. 22. Q-Q2. 23. B X P. 23. PxB. 24. Q-QBl. 24. B X QP. 2b. Q X E, P, etc. LOCxISTIC EADII. The student, now being familiar with the mathematical forms of the strategic and the tactical horizons, readily sees that these are united to each other and to the strate- gic front by verticals, horizontals, diagonals, and obliques, along which latter the kindred pieces move from one point to other points contained within the strategetic horizon. These radii of movement, as the student already has been informed (" Major Tactics," p. 18), are entirely distinct from radii of offence and of defence : their char- acter is purely logis-tic, and their direction and extent always is determinate. A logistic radius always is either a vertical, a horizontal, a diagonal, or an oblique, and its extremities always are points of mobilization, devel- opment, manoeuvre, or operation. LOGISTIC RADII. 149 ELEVENTH LAW OF THE ART OF CHESSPLAY. A Logistic Radius is not valid if it is interrupted hy a point of impenetrahility ^ or if its terminus is commanded hy an adverse piece. POINTS OFFENSIVE. In the formulas of " Grand Tactics," the student per- ceives how the primary bases of minor tactics are amal- gamated into the various minor, major, and grand strategic fronts ; and by means of the foregoing expla- nations and diagrams the amalgamation of the evolutions of Major Tactics into the strategic front is made equally clear. But in order that the student may thoroughly compre- hend that method by which the movements of each kindred piece are harmonized for the perfect amalgama- tion of the primary bases of minor tactics, the evolutions of major tactics, and the strategic fronts of grand tac- tics, and by which is made possible a mathematically exact survey of the Strategetic Horizon, it first is neces- sary to explain the two great subdivisions into which the latter is divided, viz.: — Strategetic Horizons are of two dimensions. In its second dimension the Strategetic Horizon is limited to the processes of Lesser Logistics (vide " Grand Tactics," p. 279), and comprehends nothing outside of Lines of Mobilization and Lines of Development. The topography of a strategic horizon of the second dimension is as follows : — (ci) Normal Posts. (6) Posts of Mobilization. (c) Posts of Development. (d) The Strategetic Objective. POINTS OFFENSIVE. 151 The Normal Posts are those points which are occu- pied by the pieces originally (vide " Minor Tactics," pp. 51-56). The Posts of Mobilization are those points to which the pieces are deployed in the construction of a minor front (vide " Minor Tactics," pp. 94-169, and " Grand Tactics," pp. 114-158). Posts of Development are those points to which the pieces are developed in the construction of major and of grand strategic fronts (vide " Grand Tactics," pp. 159-275). The Strategetic Objective is that point whose proper occupation is the aim of Lines of Mobilization and of Lines of Development (vide " Grand Tactics," pp. 19-22, and 370). In its first dimension the Strategic Horizon com- prises both Lines of Manoeuvre and Lines of Operation. The processes of Greater Logistics are divided into three classes : ■ — (a) Minor processes. (b) Major processes. (c) Grand processes. The major processes of Greater Logistics appertain exclusively to Lines of Operation and to compound and complex Lines of Manoeuvre. The minor processes of Greater Logistics appertain exclusively to simple Lines of Manoeuvre. The grand processes of Greater Logistics appertain to that calculation by which in any given situation is determined the true strategetic horizon. Following is the mathematical expression of a strate- getic horizon, which comprehends a strategetic weak- ness in the adverse position. 152 CHESS STRATEGETICS. Figure 84. STRATEGETIC WEAKNESS PM+TO K POINTS OFFENSIVE. 153 T K = Tactical Key. S K = Strategic Key. To K = Topographical Key. P C = Point of Command. P Jf= Point of Manoeuvre. P M = Post of Mobilization. P D = Post of Development. P D = Point of Departure. L R = Logistic Padius. N P .= Normal Post. C L M = Compound Line of Manoeuvre. S L M = Simple Line of Manoeuvre. X L M = Complex Line of Manoeuvre. 154 CHESS STRATEGETICS. The Topography of a Strategetic Horizon of the first dimeusion is as follows : — (a) Points of Departure. (5) Points of Manoeuvre. ((7) Points of Command. (t?) The Strategic Key. (e) Tactical Keys. (/) The Objective Plane. (^) The Strategic Horizon. (A) The Tactical Horizon. (i) The Logistic Horizon. (j) Logistic Radii. A Point of Deparf.ure is one extremity of that Logis- tic Radius of which a Point of Manoeuvie is the other extremity. It always is occupied by a kindred piece. A Point of Manoeuvre is one extremity of that Logistic Radios of which a Point of Command is the other extremity. It may or may not be occupied either by a kindred piece or by an adverse piece. A Point of Command is one extremity of that Logistic Radius of which a Tactical Key is the other extremity (" Major Tactics," pp. 50-52). It may or may not be occupied either by a kindred or by an adverse piece. A Tactical Key always is either a point of junction ("Major Tactics," p. 68), or a point material (''^Major Tactics," p. 42), or that point which when occupied by a given piece, the adverse king is checkmated. It may or may not be occupied by an adverse piece, but never by a kindred piece. POINTS OFFENSIVE. 155 POINTS or DEPARTURE, OF MANOEUVRE, AND OF COMIVIAND. Figure 85. Black. ^-"ir^m m Wa W////M.. V/, ,y//~M a.,.,,_w^^^ ■JSI 'm '^^J 1^1 i White. Note. — The White Q R 1 is the Point of Departure ; the White K 1 is the Point of Manoeuvre, and the White K 8 is the Point of Command against the two Tactical Keys, Black K Kt 1 and Q B 1. 156 CHESS STRATEGETICS. The Strategic Key is that vertex of a mathematical figure of which either two points of command, or two tactical keys, or a tactical key and a point of command are the other two vertices (see this volume, p. 88). The Strategic Vertices are those points on the peri- meter of that geometric symbol of an integer of chess force of which the strategic key is the centre, and which geometric symbol constitutes, in the given situation, the strategic horizon. POINTS OFFENSIVE. 157 THE STRATEGIC VERTICES. Figure 86. Black. White. Note. — The Strategic Horizon consists of Black's K 4, and the points occupied by the R and B. The Strategic Key is Black's K 4, and this point, together with the Tactical Keys (Black K Kt 3 and Q B 5) con- stitute the Strategic Vertices. 158 CHESS STRATEGETICS. The Objective Plane already has been described ("Minor Tactics," pp. 42-44, and "Grand Tactics," pp. 25 and 82-92). The Logistic Horizon already has been described (" Grand Tactics," p. 19). The Tactical Horizon already has been described (see this volume, p. 127). The Strategic Horizon already has been described (see this volume, p. 106). The Logistic Radius extends from the Point of De- parture to any other point offensive (" Major Tactics," pp. 18-23). LINES OF MANCEUVRE. Lines of Manceuvre are divided into Simple, Com- pound, and Complex (" Grand Tactics," pp. 53, 312, 377- 386). Compound and Complex Lines of Manoeuvre are divided into three classes, viz. : — A Compound or a Complex Line of Manceuvre of the first class is composed of eleven points offensive and ten logistic radii, and two of its strategic vertices are tactical keys. It may be mathematically expressed thus: — 160 CHESS Sr R ATE GE TICS. COMPOUND OR COMPLEX LINE OF MANGEL^YKE. (First Class.) Figure 87. T.K. RC<' RM." i> PC. RMf PM." RD.' PD.* *RD. LINES OF MANCEUVRE. 161 Adapted to the chessboard, this proposition of mili- tary art and science may be represented thus : — COMPOUND OR COMPLEX LINE OF MANCEUVRE. (First Class.) Figure 88. Black. White. Note. — The White Kt will occupy the strategic key Q 5, and the tactical keys, Black Q Kt 3 and K 2, will be simultaneously attacked by a superior force. 11 162 CHESS STRATEGETICS. A Compound or a Complex Line of Manoeuvre of the Second Class is composed of ten points offensive and nine logistic radii, and one of the strategic vertices always is a tactical key, and the other always is a point of command. It may be mathematically expressed as follows : — COMPOUND OR COMPLEX LINE OF MANCEUVRE. (Second Class.) Figure 89. RMv RD* RM. iPD. ^'PM. *PD LINES OF MAN(EUVRE. 163 Adapted to the chessboard, this proposition of militarj art and science may be represented thus : — COMPOUND OR COMPLEX LINE OF MANCEUVKE. (Second, Class.) ElGUKE 90. Black. y/z/z/zz/y^''^^''^^''''^''' ^^/z-^- 111 ^ % -^ ill fMf White. Note. — The White Kt will occupy the strategic key (White Q B 5), attacking simultaneously the tactical key (Black Q R 3) and the point of command (Black's K3). 164 CHESS STRATEGETICS. A Compound or a Complex Line of Manoeuvre of the third class is composed of nine points offensive and eight logistic radii, and both of its strategic vertices are points of command. It may be mathematically expressed thus : — COMPOUND OR COMPLEX LINE OF MANCEUVRE. (Third Class.) FlGUEE 91. PC. RM.4 RD-i PM.<' RD> RM, RD. LINES OF MANCEUVRE. 165 Adapted to the chessboard, this proposition of military art and science may be represented thus : — COMPOUND OR COMPLEX LINE OF MANCEUYRE. (Third Class.) Figure 92. Black. Bl a$ ■^//Jr'^'^'Vy^ il ■ mm ^ ^»^".. ^p ^P" ^ ^i~p White. Note.— The White Kt will occupy the strategic key (White KB 4), and threaten to occupy one of the points of command (White Q 5 and Kt 6). LINES OF OPERATION. Lines of Operation are the natural outgrowth of Compound and of Complex Lines of Manoeuvre ('' Grand Tactics," pp. 57, 318-337). Every line of manoeuvre contemplates the bringing about of a position in which the occupation of two strategic vertices by a kmdred force is assured ; and when this position is brought about, the line of manoeu- vre becomes transformed into a line of operations. The process whereby this transformation is brought about varies in each of tlie three classes of compound and complex lines of manoeuvre ; but in each and every case it is contingent upon the inadequacy of the defen- sive resources of the strategic vertices. The defensive resources of the strategic vertices are expressed by numerical exponents, and the quantity of their defensive powers is denoted by letters, viz. : — (a) Signifies that the strategic vertices contained in the given compound or complex line of manoeuvre are not supported by any kindred piece. This situation is designated thus : — FORMULA FOR LIXE OF MANCEUVTEIE. Cxi a, C X 2 a, ot C x 3 a. In this position, if the corps of the centre can occupy the strategic key and the enemy cannot defend both strategic vertices in one move, then the line of ma- LINES OF OPERATION. 167 noeuvre may "be transformed into a line of operations, and the resulting situation is expressed thus : — FORMULA FOR LINE OF OPERATION. Cxla={TK' -^ TK^)SK^^LO. Cx2a = (TK'+ F C) SK' = LO. C X 3 a = (F C + F C) S K^ = L 0. The logistic operation in all the foregoing situations is limited to two marches by the corps of the centre ; i. e., one march from the Point of Departure to the Point of Manoeuvre, and one march from the Point of Manoeuvre to the Strategic Key. This logistic opera- tion is expressed thus : — FORMULA FOR LOGISTIC RADII. C C\ (b) This letter signifies that one of the strategic ver- tices contained in the given compound or complex line of manoeuvre is supported by a kindred piece, but that the other vertex is not supported by a kindred piece. This situation is designated thus : — FORMLT.A FOR LINE OF MANCEUVRE. Cxlb, Cx2b, or GxSb. In this position, if the corps of the centre can occupy the strategic key, while the corps of the right or of the left occupies a point of command against that tactical key, or a point of manoeuvre against that point of com- mand defended by the enemy, and if the enemy cannot defend both of the strategic vertices in one move, then the line of manoeuvre may be transformed into a line of operations, and the resulting situation is expressed thus : 168 CHESS STRATEGETICS. PORMULA FOR LINE OF OPERATION. Cxlh= (TX^+ T K'') (SK^ + FC^) = L 0. Cx2b = {TK^- + FC) (SK^- + F C"-) = L 0. Cx3b=: (FC^ + FC) {SK^ + FC^)=LO. The normal logistic movement in the first two of the foregoing situations is limited to four marches ; i. e.,two by the corps of the centre, one from the point of depar- ture to the point of manoeuvre, and one from the point of manoeuvre to the strategic key, and two \j the corps of the right or of the left, one from the point of depar- ture to the point of manoeuvre, and one from the point of manoeuvre to the point of command. But in the Cx^a the total number of marches is only three, as the flank- ing corps has but one march to make; i. e.^ from the point of departure to the point of manoeuvre, from which latter point it attacks the point of command. This logistic movement is expressed thus : — FORMULA FOR LOGISTIC RADIL (7icl5and Cx2h= C C + F C\ CxZh= CC^ + FC.^ (c) This letter signifies that both of the strategic vertices contained in a given line of manoeuvre are sup- ported by kindred pieces. The situation is denoted thus : — FORMULA FOR LINE OF MANCEUVRE. Gxlc, Cx2c,ovCx3c. Ill this situation, if the corps of the centre can occupy the strategic key, while the corps of the right and left occupy tlie points of command against their respective tactical keys, or points of manoeuvre against their re- LINES OF OPERATION. 169 spective points of command, and if the enemy cannot defend both of the strategic vertices in one move, then the line of manoeuvre may be transformed into a line of operations, and the resulting situation is expressed thus : FORMULA FOR LINE OF OPERATION. Cxlc= {TIO -{- TK^) (SIO + FC^ + P C^) = L 0. Cx2g^{TK^ + PC) {SIO -\- PC + PC^) =L0. Cx^G= (PC^ + P C) (SIO + P C^ + P C) = L 0. The normal logistic movement in the Cxi c is the maximum ; it consists of six marches : two by the corps of the centre, i. e.^ one from the point of departure to the point of manoeuvre, and one from the point of manoeuvre to the strategic key ; two by the corps of the right, i. e., one from the point of departure to the point of manoeu- vre, and one from the point of manoeuvre to the point of command ; and lastly, two marches by the corps of the left, i. e., one from the point of departure to the point of manoeuvre, and one from the point of manoeuvre to the point of command. FORMULA FOR LOGISTIC RADII. CC-'+ CE^ -{- 0^" = ^. The normal logistic movement in the Cx 2 c is but one march shorter than that of the Qx\g., and exceeds all other normal logistic movements. The corps of the centre and that flanking corps which is directed against the tactical key each have two marches to make, but that flanking corps which is directed against the point of command only has to march from the point of departure to the point of manoeuvre, making five marches in all. FORMULA FOR LOGISTIC RADIL CC ^ CPy} -^ CL^ = ^. 170 CHESS STRATEGETICS. The normal logistic movement in the Cx^c consists of two marches by the corps of the centre from the point of departure, via the point of manoeuvre to the strategic key, and one march by each of the corps of the right and the left from the point of departure to the point of manoeuvre. FORMULA FOR LOGISTIC RADII. CC2+ CE" -[- CL^ = 4.. Thus the student of chess, of mathematics, or of mili- tary science readily will see the validity of the following : TWELFTH LAW OF THE ART OF CHESSPLAY. I. A compound or a complex line of manoeuvre is transformed into a line of operations whenever the sum of the exponents of the corps offensive exceeds the sum of the exponents of the defensive radii luhich appertain to the strategic vertices ; and II. A projected logistic movement on a line of operation! is valid whenever the number of inarches to be inade by the corps offensive is less than the number of marches required to be made by the corps defensive^ in order that the sum of defensive exponents may equal the sum of the exponents of the corps offensive. There are four mathematical symbols typical of lines of operation, viz. : — LINES OF OPERATION. 171 LINES OF OPERATION, (a.) Figure 93. 172 CHESS STRATEGETICS. In this situation the line of operations is established for the reason that the corps offensive occupy the strate- gic key and both points of command. The corps offensive having the move win by simultane- ously attacking, from the strategic key and either point of command, the common tactical key, which, not having the right to play, is immovable, and consequently is un- able to avoid this attack, and being the lesser force is unable to repel it, according to the basic law of the sci- ence of Chess Strategetics (" Grand Tactics," p. 3). The corps offensive also win without the move, for, a strategetic weakness existing, neither of the adverse forces are able to support each other in a single move. Consequently, while, by means of the right to play, the opponent may retire one of his exposed pieces, he obviously is unable simultaneously either to defend or to vacate both tactical keys. Hence, that exposed force remaining immovable at the close of the opponent's right to play is lost according to the preceding demonstration. Adapted to the chessboard, this proposition of military art and science may be represented thus : — LINES OF OPERATION. 173 LINE OF OPERATIONS. FiGtrKE 94. Black. if fc fm mm... ■ SI ^!Mli ^^^.^. vMa .jmrn. m M TFA/^e. Note. — The Black Kt and B occupy tactical keys; the White B and R occupy points of command, and the strategic key is occupied by the White Kt. White wins either with or without the move. 174 CRESS STRATEGETICS. LINE OF OPERATIONS. ElGURE 95. STRATEGETIC WEAKNESS LINES OF OPERATION. 175 In this situation the corps offensive having the move win by occupying the strategic key with the corps of the centre. Inasmuch as the kindred corps of the right and of the left are in possession of both points of com- mand, the situation after the capture of the strategic key is identical to the final situation in the preceding diagram. 176 CHESS STRATEGETICS. Adapted to the chessboard, this proposition of iQilitary art and science may be represented thus : — LIXE OF OPERATIONS. (6.) FlGUEE 96. Black. White. Note. — The Black Kt and B occupy tactical keys ; the White Kt occupies a point of manoeuvre. The strategic key is White's Q 5. White having the move will win. LINES OF OPERATION. 177 LINE OF OPERATIONS. Figure 97. STRATEGETIC WEAKNESS TK Obviously the corps offensive having the move vrin by occupying the right point of command with the corps of the right, the resultant situation being identical to the foregoing situations. 12 178 CHESS STRATEGETICS. TK TlGUKE 98. STRATEGETIC WEAKNESS TK The corps offensive having the move win in this posi- tion by occupying the left point of command with the corps of the left. The student will observe that no line of operations exists in the last three situations if the corps offensive have not the move. PKOCESSES OF GREATER LOaiSTICS (MINOR). PROCESSES OF GREATER LOGISTICS (MINOE). The minor processes of Greater Logistics are con- tained exclusively in simple lines of manoeuvre. These processes contemplate neither the gain nor the defence of material, but their sole object always is to divide up the opposing force and especially to intensify and per- petuate that unscientific isolation of the adverse pieces which exists at the beginning of every game of chess. These processes always must be combined with the deployments of Lines of Mobilization, in order that the unscientific isolation of the kindred pieces which exists at the beginning of every game of chess may be elimi- nated, at the same time that the isolation of the adverse pieces is perpetuated. This idea is fundamental and underlies all the earlier moves of the chesspieces. Upon it all debuts which are true and valid are based, and no analysis is worthy of consideration whose every move does not conform to this basic truth. THIRTEENTH LAW OF THE ART OF CHESSPLAY. Every movement on a Simple Line of Manoeuvre should be a deploymeyit or a development, and the logistic radius should have its origin in a normal jjost or in a post of mobilization, and its terminus in a topographical key. If the student will set up the pieces and inspect the normal position, he will observe that with the exception 182 CHESS STRATEGETICS. of the knights and the pawns, all of the chesspieces are immovable, and that many of the latter must remain thus immovable for a number of moves. In short, it readily may be perceived that before the K R can be brought to K B 1, that the K Kt and the K B must be moved, and that before the Q R can be brought to K 1, that the Q Kt, the Q B, the Q, and the K must be moved. Obviously, then, these two pieces (K R and Q R) are isolated from each other, and eight moves must elapse before they can be brought into communication at their proper posts in the primary base. Again, it easily is discernible that the King is unsci- entifically posted at K 1, inasmuch as he not only is dangerously exposed, but he constitutes a point of impenetrability on the logistic radii of his own pieces and thereby prevents the proper deployment and co- operation of the latter in the formation of the strategic front. Furthermore, it is easy to see that this isolation of the K from the two powerful pieces of the right and the left wings respectively must, if perpetuated, result in a serious, if not a fatal, weakness in the general position. Understanding and accepting this premise, the student easily will see that after the move of 1. P — K 4 by White, the best and most quickly executed series of de- ployments possible to Black are 1. P — K 4, 2. Kt — Q B 8,3. K B — B 4, and 4. P — Q 3 ; whereupon results the following situation : — PROCESSES OF GREATER LOGISTICS. 183 Figure 99. Black. White. The student now will observe that, these four deploy- ments having been completed, Black will have no diffi- culty in making what further deployments are needed, viz. (K Kt — B 3 and Castles K R), in order to con- centrate all his originally scattered pieces into one united mass, whose communications in all respects are free and protected. This, then, necessarily, is the fundamental opening formation for Black, and, having established it, he has every reason to await the outcome of the game with confidence, for there is no apparent hope of victory for White, provided the subsequent play be equally good on 184 CHESS STRATEGETICS. both sides. The reason why this is so is that White has frittered awav his inestimable advantage of the initiative; i. e., instead of intensifying the isolation of the black pieces, he has Yolimtarily and as the direct outcome of a series of unscientific moves, permitted Black to make a series of scientifi.c moves and thereby to establish a scientific position, which, although inferior (being by the right refused), still is powerful enough to withstand any attack which White may bring to bear against it, and not improbably, on account of the unscientific processes of White, of becoming by com- parison the superior position and one possessing the germ of legitimate victory. Upon contemplating this black situation, the student will note two facts : {a) that the Black K B was deployed at Q B 4 before the Black Q P was moved, and that, as the result of this deployment of the Black K B (5), the communication of the Black K wing with the centre is assured, inasmuch as the Black K Kt can readily be deployed to its proper post at K B 3. A little thought will convince the student that the single deployment of K B — B 4 has vastly relieved Black's original situation ; inasmuch as it not only has brought this piece into a commanding position from whence it attacks directly the White K B P (which prior to castling K R is the vulnerable point in the King's position), but also, by removing a point of impenetra- bility (K B 1) from the logistic radius of the Black K, that it has insured him the privilege of castling K R and tlie union of the black centre and K wing. Hence, it needs no argument to prove that the deploy- ment of K B at Q B 4 is of the utmost consequence to Black, and that a prime object of White's simple line of manoeuvre sliould be to make this deployment of the Black K B at Q B 4: impossible. PROCESSES OF GREATER LOGISTICS. 185 The student next will observe that the deployment of the Black Q P at Q 3 absolutely perfects this initial black formation, and that this deployment is second in importance only to the deployment of the Black K B at Q B 4. The reason of this is that after the move of P — Q 3 the point K 4 is supported, and consequently not only is the Black K P securely defended, but the White K P is prevented from occupying the vertex of a major right oblique, and also prevented from either dislodging the Black K Kt from K B 3, or from making it impossible for this piece to occupy the last-mentioned point. Just here, it may be well to explain that the Black Q P is never properly played to Q 4, whenever the opponent can establish a valid major strategic front by occupying White K 5 with a pawn or with a piece. Again, after K B — B 4 and P — Q 3, it is obvious that the Black Q B will deploy without hindrance, and that the communications of Black's right, centre, and left will become free and open, and the mobilization of his originally isolated masses now easily effected. Therefore, again it is beyond dispute that after 1. P — K 4, a prime object of White's Simple Line of Ma- noeuvre should be to prevent the deployment of the Black Q P at Q 3. The student now will observe that the position of th€ Black K at K 1 prevents anything like a scientific massing of the black pieces and that, in short, it is imperative that the Black K castle at the earliest prac- ticable moment and usually on the K side. In any event it obviously is imperative that the point of impene- trability formed by the Black King be eliminated from the logistic radius of the Black K R and Q P. Therefore, it also is beyond dispute that a prime 186 CRESS STRATEGETICS. object of White's simple line of manceuvre should be to prevent the Black K from castling. Again, the student will notice that the Black K B P at K B 2 is the peculiarly weak spot in the black posi- tion prior to castling K R, inasmuch as it is supported only by the Black K, and consequently if it be captured that the Black K after taking the adverse piece deprives himself of the privilege of castling. Hence, it equally is beyond dispute that a primary object of White's simple line of manoeuvre should be to attach the Black KB P at K B2 whenever this P is left supported only hy the Black K. Finally, the student will easily discern that after 1. P - K 4 by White and 1. P - K 4 by Black, a strate- gic horizon exists for White, the two tactical keys of which are Black K B 2 and K 4, and the strategic key being White K B 5. The white corps of the centre is the Q, and the white point Q 1 is thus raised from merely a normal post to a point of manoeuvre. But the student readily observes that a line of manoeuvre against this strategic horizon is not valid, inasmuch as it is not based on a strategetic weakness for the reason that the Black Q by deploying at K 2 or K B 3 defeyids both tac- tical keys in a single move. Furthermore, the student will observe that by deploying the Black K Kt at K B 3 the occupation of the strategic key K R 5 by the White Q is prevented. But that the occupation of this point K R 5 by the White Q is a serious menace to Black both before and after castling K R, is manifest, and equally so that it is of the utmost importance that the Black K Kt maintains its post of mobilization at K B 3, or that it keep in easy communication with that point, in order to prevent the occupation of, or to dislodge the White Q from the White point K R 5. PROCESSES OF GREATER LOGISTICS. 187 Hence, it also is beyond dispute that a prime object of White's simple line of manoeuvre should be to prevent the posting of the Black K Kt at K B S ; or, to dislodge the Black K Kt as soon as possible from this post when- ever the objective plane is located on the right or on the centre. These facts being established, it is not difficult to determine, by the process of logical deduction, the proper deployments for White and for Black which appertain to simple lines of manoeuvre. Reverting to the initial move of White, i. e., 1. P — K 4, it is first all-important that the student understand and accept once and for all the basic truth which underlies all true processes appertaining to Black, viz, : — Black never should adopt the Left Oblique Refused after White has initiated the open game by \. P — K ^. The reason for this is that, in order to prevent being overwhelmed by White's Major Right Oblique, Black will be obliged to play prematurely P — Q 4 in the open- ing, and thus to leave his K 4 unsupported by a black pawn at Q 3, which will permit White again to establish the Major Right Oblique by Kt - K 5. Furthermore, the obverse of this equally is true, and the student will understand, once and for all, that : Whenever Black adopts the close game, White never should permit the exchange or the advance of the Black K P, but should confine it immovable at Black's K S. Thus, by memorizing these few and simple basic truths, the student readily will grasp the true processes which apply to what is termed the opening of a game of chess. Furthermore, he readily will note the absurdities of the books of so-called "chess analj^sis," most of which are manufactured by fourth and fifth class chess- players, and all of which are destitute of anything in the 188 CHESS STRATEGETICS. nature of a scientific foundation. For it is easy to see that, such books being governed by no system of play, tliey necessarily and admittedly are in a continual " state of transition ; " i. e., what is true to-day is false to-mor- row, and vice versa. Finally, it is an open secret that the cliess-master puts no reliance whatever in such books of analysis, but makes his own analysis as he needs it. Thus, White opens the game by 1. P — K 4, for the reason that he at once establishes the open game and dictates Black's reply by threatening to play 2. F — Q 4, which would insure to White a major front, either by the right by P — K 5, or to the left by P — Q 5, accord- ingly as Black's formations should make most advisable. White, of course, on his initial move can play 1. P — Q 4, and 1. Kt — K B 3 ; but to these Black's best reply is 1. P — K B 4, by which reply Black will prevent the deployment of the White K P at K 4 and establish the Close Primary Base 3 A (C P B 3 A, see " Minor Tac- tics," pp. 166-168), having the preferable position and a strong counter-attack against the White K. In reply to White's moves of 1. P — Q 4 and 1. Kt — K B 3, Black safely may reply 1. P — Q 4, but the reply of 1. P — K B 4 is preferable, for the reason that in the latter instance Black's strategic front extends towards the White K, and his advantage in position arises from the fact that White's strategic front will not extend towards the Black K, so long as Black can pre- vent the exchange or the advance to K 4 of the White K P, which Black should hold immovable on W^hite's K 3. Any initial move made by White other than 1. P — K 4 and 1. Kt — K B 3 always should be met by Black with 1. P — K 4. The reason of this is that mathematically White should wi7i the game hy the advantage of the first PROCESSES OF GREATER LOGISTICS. 189 move. This advantage, derived from the first move, consists in the ability of White to establish his minor front on that great central diagonal extended toivards that side of the hoard on tvhich Black luill castle. Consequently, Black having originally a lost game, can win only by becoming transformed into White, so to speak ; i. e., hy establishing his j^ieces on the great central diagonal leading towards the White King^ and preventing White from establishing his pieces on the great central diagonal leading toward the Black King. In either case, it is obvious that the opposing king's pawns must be posted at their fourth squares, and that he ivho can post his own K P at K 4, and prevent the op- ponent from so doing, thereby attains a decided advantage. Thus, it follows that all initial moves except 1. P — K 4 on the part of White are inferior for the reason that by no other move can White be certain of establishing his strategic front upon the strategetic centre. TOPOGRAPHICAL KEYS. As the student readily perceives, it should be the ob- ject of every movement made on a simple line of manoeu- vre on the part of White to deploy a kindred piece and, moreover, to deploy the given piece to that point whereat it prevents the deployment of the Black K B at Q B 4, or of the Black Q P at Q 3, or of the Black K Kt at K B 3, or to prevent the Black K from castling, or to capture the Black K B P at K B 2. Whenever such point exists, it is termed in this theory a Topographical Key. Topographical Keys are divided into three classes, viz. : — I. Those which are combined with a Post of Mobiliza- tion. II. Those which are combined with a Post of Devel- opment. III. Those which are not combined either with a Post of Mobilization or with a Post of Development. TOPOGRAPHICAL KEYS. 191 SIMPLE LINE OF MANCEUVRE. Figure 100. TK + PM TK TK+PP NP = Normal Post. TK = Topographical Key. TK + PM = Topographical Key + Post of Mobilization. TK + PD =: Topographical Key + Post of Development. 192 CHESS STRATEGETICS. Adapted to the chessboard, this proposition of military art and science may be expressed thus : — TOPOGRAPHICAL KEY COMBINING POST OF MOBILIZATION. Figure 101. Black. ^I^mmi 11 imikmt m i m m m v/. y///////A Whit Note. — White played on his last move P to Q 4, whereby he deployed his Q P to its proper post in the strategic front, and prevented Black from playing K B - Q B 4. TOPOGRAPHICAL KEYS. 193 TOPOGEAPHICAL KEY COMBINING POST OF DEVELOPxMENT. Figure 102. Black. if iimimi mi i m ■mm % er se is of far less avail than is art j^er se and justifies the proverb of the ancient Persian : — " A pound of knowledge requires for its application ten pounds of common sense." But there is another type of man who at long inter- vals becomes manifest in the flesh, and before whom the mere scientist and the mere artist are as nought. The world, for want of a better name, sees fit to term such a character a "genius," to regard him as "in- spired " in some particular way, and assumes that his powers of mind are " supernatural." Such a man was Morphy in chess, and Epaminondas, Alexander, Hannibal, Caesar, Gustavus Adolphus, Turenne, Prince Eugene, Frederic II., Washington, Napoleon, and Yon Moltke in war. A character who thus combines in himself both the erudition of the theorist and the discrimination of the artist is so rare, both in chess and in war, that the former has produced but a single and the latter but eleven examples, out of the billions who have populated the earth during the last twenty-four centuries. It is very easy and probably very complimentary to term such a character a " genius," and it unquestionably saves much mental labor to assume that his superior understanding is " supernatural." Nevertheless, it is a singular circumstance that the minds of these great men invariably have run in similar channels, and that their processes were so nearly iden- tical that it has seemed possible to the student of war, of chess, and of mathematics to reduce these processes to a system, and thereby to show that the only differ- ence between these " supernatural " processes and the ordinary processes of nature lies in the mere fact that the former are not understood. 198 CHESS STRATEGETICS. It is the history of chess and of war that men who were extremely skilful in the art were able to under- stand but little of the science, and, vice vei^sa^ that men profoundly erudite in matters relating to the science were able to comprehend but little of the art. That is, while these men had the same facilities and the same opportunities, neither could comprehend the secret of combining both the art and the science, and ultimately each would abandon tlie one branch and devote him- self exclusively to the other. Why this peculiar fact is so, we do not know ; but that it is so, is established by the history of mankind from the beginning of the world, and for want of a better reason its cause is ascribed to the difference in temperament among men. Hence, the mere tactician and the mere theorist have all sooner or later found themselves in exactly the situation that the student of these volumes finds himself at the present moment. Past masters either in the knowledge of the game or in the art of utilizing what knowledge they were possessed of, nevertheless, they were forced to admit that there was a limit beyond which their processes did not apply, and where neither the theorist nor the tactician could do more than grope ; and, furthermore, that it was when lost in this impene- trable maze that they were routed, horse, foot, and dragoons by the so-called ''genius" in the person of Morphy or Napoleon; who for some reason or other appeared to have no difficulty wha*tever in finding his way about in what to his victims was a night of Stygian blackness. Thus it appears that in the last analysis the term <' genius," as applied to the greater masters of chess and of war, is used by the world at large to designate men GRAXD PROCESSES OF GREATER LOGISTICS. 199 who were alike superlatively equipped both in the theory and in the practice of their respective professions. Furthermore, it appears that the " genius " possessed by these great characters consisted in the fact that they knew how to bridge that vast impassable gulf which separates the tactician and the theorist, and to produce, by a method unknown to the mere artist or to the mere scientist, tJie perfect co-operation of theory and practice. Obviously, then, perfect comprehension of a science, or perfect comprehension of an art, is not enough to make of any man a " genius." In addition to this he also must perfectly comprehend that method of calcvlation whereby in any situation the laws of the art and the principles of the science may be reduced to mathematical harmony, in order that these may perfectly co-operate for the attainment of a mutually desired end. It therefore is evident that the science of chess strate- getics culminates in that calcidation whereby the prin- ciples upon which the art of chessplay is founded are correctly interpreted and properly applied to any given situation on the cliessboard. By his understanding of the minor and the major processes of greater logistics the student is enabled to treat correctly any chessic condition which may be com- prehended in a single strategetic horizon. But when two or more strategetic horizons are contained at the same time in a given topographical zone, it is imperative that the student be equipped with knowledge which will enable him to detect the true strategetic horizon and to describe the true course of procedure ; i. e., in the vernacular of tlie game, " to pick out the best move:' The student, therefore, must clearly understand that there is a difference between Science — the knowledge of 200 CHESS STRATEGETICS. wliat to do — and Art — the understanding of how to do it ; and that this difference is all the difference in the world. If, in a game of chess, the ojjpo sing force had no poiver of movement, all chess knowledge would be limited to Lines of Mobilization and Lines of Development, and the whole art of chessplay would be contained hi the processes of Lesser Logistics. All the conditions would be known, the proposition would be exact, the calculations would be merely those of simple arithmetic, and White would Avin by establish- ing his pieces on a grand front by the right oblique. But it so happens that the opposing force not only is able to move, but it is capable of being moved with vigor and effect ; and the resultant of all this is that the opposing force possesses, and can exert, a foicer for resistance which in common practice is quite equal to the power of attack put forth by White. Li war, this fact is emphasized, and often laughably exaggerated. The basic proposition of military science is that two men can whip one ; but the history of war is the story of the victory of the under dog, and in actual warfare the difficulty always is to prevent the one man from trouncing seriatim both of his usually unprepared and isolated enemies. Again, the powers for attack and the powers for resist- ance possessed by the opposing forces are indeterminate and irregularly distributed. The reason for this is, that while the right of move- ment appertains equally to every chesspiece, not more than one chesspiece can be moved at any given turn to play, and consequently the vigor and effect of any given move is problematical, and is dependent upon and pro- portionate to the support subsequently accorded it by kin- GRAND PROCESSES OF GREATER LOGISTICS. 201 dred pieces and to the resistance offered to it by adverse pieces. Hence, it follows that it is imperative, from the midst of the strategic, tactical, and topographical differences which exist in every situation on the chessboard or on the battlefield, to establish mathematical harmony, and it is obvious that this harmony consists in consolidating as a unit the total strength of the kindred force, and in di- recting it against the strategic vertices of the true strate- getic horizon, whenever a strategetic weakness exists in the adverse position and against the To2:)ographical Key^ whenever a strategetic weakness does 7iot exist in the adverse position. With the minor processes of Greater Logistics which appertain exclusively to simple lines of manoeuvre, and with the major processes of Greater Logistics which ap- pertain to compound and to complex lines of manoeuvre, and to lines of operation, the student already is familiar, and, given the True Strategetic Horizon^ he will have no difficulty in detecting and describing the Strategic Ver- tices, the Points of Command, of Manoeuvre, and of Departure, the Topographical, Tactical, and Strategic Keys, and the Logistic Radii. That calculation whereby the True Strategetic Horizon is detected in the midst of a number of strategetic hori- zons coexisting in any given situation on the surface of the chessboard is the connecting link hetiveen the science of chess and the art of chessidlay ; it is that manifestation of " genius," whereby the greater master at chess and the greater master at war so easily and so completely over- throws his adversaries, and it is the touchstone by the use of which the mere theorist and the mere tactician may come to realize the full scope and the intellectual magnificence both of chess and of war, viz. : — 202 CHESS STRATEGETICS. BASIC PROPOSITION OF GREATER LOGISTICS. Theorem. To determine the TEUE Strategetic Horizon^ the true Tactical EvrAution^ and the true Tactical Sequence. Locate a tactical key in the adverse position^ the occupa- tion of which hy a given Mndred piece will — {a) Checkmate the adverse king ; (b) Or^ queen a kindred pawn ; (c) Or, win a hostile piece ; and connect this tactical key^ by a logistic radius, ivith that point of command ichich, at the given time, is occu- pied hy the given kindred piece. Locate a second hut vacant point of command, which, if occupied hy a second kindred piece, zvill operate radii of offence simultaneously against a second and third tactical keys in the adverse position ; and connect this point of command, hy a logistic radius, vAth that point of manoeuvre ichich, at the given time, is occupied hy the given second kindred piece. Then, if either the given second or third tactical keys, together ivith the strategic key (to he determined) and a third point of command occupied hy a third kindred piece, are contained in the same vertical, the same hori- zontal, or the same diagonal, and if the first tactical key and the tactical key last specified are hoth situated on the perimeter of that geometric symbol ivhich appertains to the third kindred piece, hut are not situated in the same topographical horizon ; (a) The occupation of the given second point of com- mand is the TRUE TACTICAL EVOLUTION ; (h) The tacticcd keys situated on the perimeter of this geometric symbol, together with the strategic key, — -which always is the centre of the given geometric symbol, — con- GRAND PROCESSES OF GREATER LOGISTICS. 203 stitute the strategic vertices of the TRUE strategetic HORIZON ; {c) Of which the third kindred piece is the column of the centre : the first kindred piece is the column of the rights or of the left, and the second kiyidred piece is the column of the left or of the right, respectively ; and the arrange- ment of moves required to occupy the strategic vertices constitutes the true tactical sequence. THE TACTICAL SEQUE^XE. The Tactical Sequence consists of those marches Tvhereby the Corps Offensive leave their respective points of departure or of manceuvre and advance along the logistic radii which appertain to the true strategetic horizon, to their respective points of command against the strategic vertices. rOURTEEXTH LAW OE THE AET OE CHESSELAY. A projected march hy a Corps Offensive is valid when it is directed against a Point Offensive, and : (a) When such Point Offensive is the point of com- mand in a tactical horizon of which the given Corjjs Offensive is the prime tactical factor ; {h) And luhen one of the tactical Jcegs contained in the given tactical horizon is situated on the perimeter of that geometric symbol of which the strategic key of the true strategetic horizon is the centre ; (c) And when the exponent of the given Corps Offensive is not less than the defensive exponent of either of those tactical keys which are contained in the given tactical horizon : (d) And when such march is in propter sequence with the other marches of the kindred Corps Offensive, All marches which properly appertain to Corps Offen- sive are combined in three distinct ways, each of which THE TACTICAL SEQUENCE. 2U5 methods constitutes a series of movements and is termed a Prime Logistic Operation, viz. : — FIRST TACTICAL SEQUENCE. March M. 1. — This march always is made either by the column of the Right or of the Left, which advances from a point of manoeuvre along an open logistic radius, and occupies a point of command against one of the tactical keys contained in that strategic weakness, which at the given time exists in the adverse position. March No 2. — This march always is made by that flank column which is not engaged in making March No. 1. It always advances from a point of manoeuvre along an open logistic radius, and occupies a ])oint of command against two or more tactical keys, one of which latter is contained in the perimeter of the same geometric symbol with that tactical key attacked by the first kindred column, but not in the same topo- graphical horizon. March No. 3. — This march always is made by the column 01 the centre, which advances from a point of manoeuvre along an open logistic radius, and occupies a point of command simultaneously against the strategic key of the true strategetic horizon and a tactical key. March No. ^. — This march always is made by the column of the centre, which advances from a point of command along an open logistic radius and occupies the strategic key of the true strategetic horizon. March No. 5. — This march always is made by that kindred column, whether of the Centre, Right, or Left, which can by that single move either win a hostile piece, queen a kindred pawn, or preferably checkmate the adverse king. 206 CHESS STRATEGETICS. FIRST TACTICAL SEQUENCE. Figure 104. Mr. Bukille. ■§^'m± IliBi ^ is e ^i5?^ tiii isi J| ^ ^s^..^ fiii. ^ mmA 1 I Mr. Youxg. XoTE. — In this situation it is obvious that if Black had the move he would win by playing P to Q 4. Hence, White must either act on a line of operations, or he must act on a simple line of manoeuvre and pre- vent the advance of the Black Q P. An exact reconnoissance of the situation shows that the Black force is divided into two s:reat isolated masses, THE TACTICAL SEQUENCE, 207 and that only one of these masses — i. e,, that composed of the Black K, Q, R, K P, K Kt P, and K R P— is in action. According to Napoleon's dictum it is necessary for White to act either against the communications of these two isolated masses or against the communications of the active adverse mass with its base ; i. e., the Black K. The latter course would be brilliantly decisive, but in this case no strategic line of operations can be mathe- matically demonstrated. Thus it is White's sole resource, being inferior in force, to act on a simple line of manoeuvre and endeavor to perpetuate and to intensify the unscientific isolation of Black's divided army. But the exact reconnoissance of the general situation also shows that there is a prospective complex line of manoeuvre open to White, provided that the Black Q can be compelled or enticed to withdraw the radius of defence which is operating for the support of Black K 2. This prospective complex line of ma^qmjvre results from the fact that White's corps of the iSt (White Q) already occupies a point of command against one tactical key (Black K Kt 2) and remotely against a second tactical key (Black's K K 1) ; and that if the White K P, which occupies a point of manoeuvre, can advance to its point of command (Black's K 2), and from whence it would attack simultaneously two tactical keys (Black K B 1 and K 1), the White K B also would be brought into co-operation with the White Q. But although this is so, it still is the fact that this prospective complex line of manoeuvre never may be realized, and, as the student must always recollect, the most pressing need ahvays must first he attended to. Therefore, although White should hold in view the 208 CHESS STRATEGETICS. possibility of this prospective attack against the Black K, nevertheless, he on his turn to play must be governed by the principles of the simple line of manoeuvre, as his immediate object is to prevent the play of P to Q 4 by Black. That is to say, "White must dictate Black's next move ; i. ^., White must retain the initiative. White no^ applies the tactician's rule, and at once sees that he can compel the Black Q to perform two functions; viz,. to defend the Black K 2 and at the same time to pro- tect itself against attack, and White further sees that such onus, if thrown on the Black Q, will prevent the move of P to Q 4 by Black, and will dictate as his next move a move by the Black Q. This, of course, is just what White wants to do ; and he can do this in three ways ; viz., by Kt — Q R 4, by B - K 3, or by P - Q Kt 4.^ Either of these moves by White is equivalent, in wai', to outflanking a hostile corps which is defending a strategic point. A detachment made for such a pur- pose may be sacrificed if such sacrifice insures a line of operations. j Consequently, White selects his Q Kt P as a Corps Detached to be sacrificed as the most judicious method to fulfil the requirements of the immediate simple line of manoeuvre and to bring about the prospective com- plex line of manoeuvre, and he plays: — ]\[k. Young. 1. P_QKt4. If the Black Q retreats to Q 3 or to K 2, then the complex line of manoeuvre begins, and the initiative is retained for White by Kt — K 4, or B — K Kt 5. So Black plays : — THE TACTICAL SEQUENCE. 209 Mr. Burille. 1. Q X Kt P. Still White must keep to the simple line of manoeuvre in order to retain the initiative and to prevent Black from playing P — Q 4 ; so he continues : — 2. E - Q Kt 1. 2. Q X Kt. Black evades the snare laid for him by the offer of the White Q; i. e., Black could have played 2. R — K B 8 (ck);3.BxR,QxQ;4.P-K7,Q-K3; 5. B-R3, P-Q4; 6. KtxQP, PxKt; 7. B-QKt5, B-Q2; 8. R - K B 1, and White wins. Of course, Black by taking the Kt permits White to act on a complex line of manoeuvre against the Black K. The situation is replete with instruction for the student of this theory. 3. B-KR6. This is another sacrifice of a Corps Detached to dictate Black's reply and thus to retain the initiative, and is the beginning of the strategic line of operations. 3. P X B. Black must avert the mate at the expense of a move and thus permit the White column of the centre to occupy its point of manoeuvre (White K B 1). This capture by Black also uncovers the Black K Kt 1 to the combined attack of the White Q and K B. 4. P-K7. White now advances his corps of the left to a point of command whereat it attacks simultaneously two tac- tical keys (Black K 1 and K B 1). 4. R-Kl. 14 210 CHESS STRATEGETICS. The Black R thus attacked is obliged to preserve it- self and to support the kindred point of junction against the attack of the White K P. It thus acts as a part of the column of manoeuvre by constituting itself a point of impenetrability. But by so doing, as the student readily sees, the Black R abandons the strategic key, i. e. (Black K B 2), for it is evident that if a White R be posted at Black's K B 2, it simultaneously Tvill attack both Black K B 1 and K Kt 2, both of which are tactical keys, and thus the strategic horizon will be complete, with the strategic ver- tices occupied by the Corps Offensive, and consequently it will be a winning position for White. 5. E-KBl. The White Corps of the Centre now occupies its point of manoeuvre and at the same time simultaneously attacks the strategic key and a tactical key, according to the grand law of chessplay as laid down in this theory. 5. Q-QB4. The student will observe that although Black has captured three detached corps for which White has no further use, his position not only is not further developed, but on account of the removal of the Black K Kt P from K Kt 2, it is even weaker than before his first move, and that White still retains the initiative and the right to move. 6. R - B 7. The White Corps of the Centre now occupies the strategic key from whence it simultaneously attacks THE TACTICAL SEQUENCE. 211 the two tactical keys, which also are attacked by the Corps of the Right and of the Left, respectively. The position now is a winning position for White either with or without the move. 6. R-Ktl. Black, obviously, cannot prevent both the threatened mate and the threatened occupation of the logistic horizon by the White K P. 7. E X E P (ek). 7. K x E. 8. Q X E (ck). Checkmate. 212 CHESS STRATEGETICS. SECOND TACTICAL SEQUENCE. March JVo. 1. — This march always is made by the column of the Right or of the Left, which advances from a point of manoeuvre along an open logistic radius and occupies a point of command against one of the tactical keys contained in the strategetic weakness which at the given time exists in the adverse position. March JVo. 2. — This march always is made by the column of the centre, which advances from a point of manoeuvre along an open logistic radius and occupies the strategic key of the true strategetic horizon. March No. 3. — This march always is made by that flank column which is not engaged in making March No. 1. It always advances from a point of manoeuvre along an open logistic radius and occupies a point of command against two or more tactical keys, one of which latter is contained in the perimeter of the same geometric symbol with that tactical key attacked by the first kindred column, but not in the same topograph- ical horizon. March No. 4- — This march always is made by that kindred column, whether of the Centre, Right, or Left, which can most effectively occupy a tactical key and in one move win a hostile piece, queen a kindred pawn, or, preferably, checkmate the adverse king. THE TACTICAL SEQUENCE. 213 SECOND TACTICAL SEQUENCE. Figure 105. Mr. Youxg. Mr. Harlow. Note. — This situation shows each of the three Black Corps Offensive posted on a point of manoeuvre. The strategetic weakness in the White position is that of Class III. (see " Grarud Tactics," p. 36). It consists of the undefended White^ B and the White K Kt P, which latter is defended only by the White K. The strategic horizon thus is formed, beiug composed of that part of the second horizontal which extends 214 CHESS STRATEGETICS. from White's K Kt 2 to his Q Kt 2. The strategic kej is White K 2, and this point is connected by an open logistic radius with Black's Q R 3, an adverse point of manoeuYre which at the present moment is occupied by the Black Q. An open logistic radius leads from White's Q Kt 2 to Black's Q Kt 1, which latter is a point of command for the Black Q R. This piece is connected with its point of command by an open logistic radius extending from the point of manoeuvre, Black Q R 1. Another open logistic radius leads from White's K Kt 2 to Black's K Kt 3, which latter is a point of com- mand for the Black K R. This piece is connected with its point of command by an open logistic radius extend- ing from the point of manoeuvre, Black K B 3. Following the rule which governs the first march in the Second Tactical Sequence, one of the Black flanking corps is deployed to its point of command. This choice necessarily falls on the Black Q R, inasmuch as no line of operation exists, it would be inadvisable to allow the White column of support the advantage of a passed pawn on the centre by B x Kt, which obviously would have to be done in order to play K R — K Kt 3. Hence, Black correctly deploys an inactive piece on the complex line of manoeuvre, viz. : — Mr. Youxg. 1. QR-QKtl. Obviously the White Q B cannot retreat to Q B 1, as in that case the White Q B P would fall victim to the Black Kt, which in this situation is a Corps Detached and prevents the occupation of the supporting posts, White KB 2 by the White R, and Q 2 by the White Q. The P at Black's QR7 also is a Black Corps Detached THE TACTICAL SEQUENCE. 215 preventing the White Q R from occupjing the supporting post, White Q Kt 1. White moved, viz. : — Mk. Harlow. 2. Q-QBl. This was a fatal error. It is imperative that White in a single move support the attacked tactical key (White Q Kt 2) and also defend the strategic key (White K 2). The only move to do both of these things simul- taneously was to play Q — Q B 2. 2. Q-K7. According to rule, the second march of a Corps Offen- sive in the Second Tactical Sequence always is made by the corps of the centre. White haying left the strategic key of the position undefended, Black at once occupies it with his Q, thus simultaneously attacking both tactical keys (White Q Kt 2 and White K Kt 2). This situation will command the attention of every student of strategetics, whether of war or of chess. It is the exact replica on the chessboard of those evolutions whereby Napoleon won the battle of Austerlitz, — the victory upon which he most prided himself. 3. R X P. It made no difference what White played. " War," says Napoleon, " is a business of positions." White loses, not because Black has two pawns plus, but because two Black Corps Offensive occupy two of the strategic vertices of the position and dictate Wliite's next move. 3. B X Kt. Here the student again sees the co-operation of a kin- dred corps detached. The White Kt prevented the occupation by Black's KR of the point of command, 216 CHESS STRATEGETICS. Black KKt3. White cannot take the Black KB, for he must prevent the Black K R from occupying its point of command, as then all three of the Black Corps Offen- sive would become posted on the strategic vertices, which would win offhand for Black, either with or without the move. (See Fig. 93.) 4. Q-Ql. White, of course, is beaten. But to prolong the con- test he adopts the only course, and plays to subordinate the dominant adverse Prime Strategetic Factor. That is to say, White is threatened with checkmate by the Black Q ; he removes this danger for the time being. 4. Q X Q. This is to dictate White's next move, and thus to gain the necessary time to save the Black K B. 5. E X Q. White thus saves his King. 5. B X B P. As the result of his tactical line of operation, Black has a piece and two pawns ahead, and, of course, wins easilv. THE TACTICAL SEQUENCE. 217 THIRD TACTICAL SEQUENCE. March No. 1. — This march always is made by the column of the centre, which advances from a point of command along an open logistic radius and occupies the strategic key of the true strategetic horizon. March No. 2. — This march always is made by the column of the Right or Left, which advances from a point of manceuvre along an open logistic radius and occupies a point of command against two or more tactical keys, one of which latter is contained in the perimeter of that geometric symbol with a tactical key attacked by the column of the centre, but not in the same tactical horizon. March No. 3. — This march always is made by the kindred flank column which is not engaged in March No. 2. It always is directed from a point of manoeuvre toward a point of command against two tactical keys in the adverse position and under like conditions. March No. J^. — This march always is made by that kindred column, whether of the Centre, Right, or Left, which can most effectively occupy a tactical key, and by that single move either win a hostile piece, queen a kindred pawn, or, preferably, checkmate the adverse king. 218 CHESS STRATEGETICS. THIRD TACTICAL SEQUENCE. ElGUKE 106. Mr. Waee. m i m^^. * mm isii 7/- ^^^z// ' m. ©PI m feM^ wmA, y/////////. White. Note. — The Black Kt is a covering corps, as it covers the Black K B P from the attack of the White R. 15 226 CEESS STRATEGETICS. All else being equal, a Corps Defensive is lost when- ever it is attacked bj an adverse force and is unable to retire, or to be properly supported, covered, or sustained, A Corps Defensive is unable to retire : — (a) When it is not its turn to move. CORPS DEFENSIVE SURPRISED. Figure 110. Black. 'm//M. m ^— — „ m i& % "^ 1 W/WA WMi. 'MW/i. m. White. White to move and win. In this situation the Corps Defensive is said to be surprised. CORPS DEFENSIVE. 227 (5) When there is no point to which it can move. CORPS DEFENSIVE SURROUNDED. Figure 111. Black. White. White wins either with or without the move. In this situation the Corps Defensive is said to be surrounded. 228 CHESS STRATEGETICS. (c) When it is posted in support of a more important kindred piece, which latter also is attacked. CORPS DEFENSIVE OUTNUMBERED. Figure 112. Black. White. White wins either with or without the move. In this situation the Corps Defensive is said to be outnumbered. CORPS DEFENSIVE. 229 (fZ) When it is covering a more important kindred piece. CORPS DEFENSIVE COMMANDED. FiGUKE 113. Black. White. White wins either with or without the move. In this situation the Corps Defensive is said to be commanded. 230 CHESS STRATEGETICS. (e) When it is posted in support to prevent the occu- pation of a point offensive. COEPS DEFENSIVE OUTFLANKED. Figure 114. Black. w--*. '»i s^'m VA y//////M Wa m m. White. White, having the move, wins a piece by R takes Kt as the Black K B cannot leave Black K B 3 unsupported on account of the White Kt winning the Black Q by Kt B 6 (ck). In this situation the Corps Defensive is said to be outflanked. CORPS DEFENSIVE. 231 (/) When it is posted to cover and prevent the occu- pation of a Point Offensive. COEPS DEFENSIVE OUTERONTED. Figure 115. Black. m. m\wM ^^ ■ i ^^ v/////////: ^_". White. White, having the move, wins a piece by P to K 5, as the Black Kt must cover the tactical key, Black K B 1. In this situation the Corps Defensive is said to be outfronted. COKPS DETACHED. A Corps Detached is any chesspiece which, in a given situation, although actively participating in an offensive movement, is not a corps of the Centre, nor of the Right, nor of the Left. Those marches which appertain to Corps Detached are termed Secondary Logistic Operations, and the object of such movements always is to eliminate or to neutralize the resistance of adverse Corps Defensive. Although a Corps Detached always acts independ- ently of the remaining kindred pieces, nevertheless it always must be a strategetic mass governed in its deploy- ments, developments, manoeuvres, and operations by the laws of the art of chessplay, and at all times it must act in harmony with the Prime Strategetic Factors. A Corps Detached eliminates or neutralizes an adverse Corps Defensive, by either surprising, surrounding, out- numbering, commanding, outflanking, or outf routing a compromised adverse piece. The Queen or the Knight can surprise and capture any adverse piece. The King, Rook, or Bishop can surprise and capture any adverse piece except the Queen. The Pawn cannot surprise and capture any adverse piece. The Queen can surround and capture an adverse Knio'ht or Pawn. CORPS DETACHED. 233 The King can surround and capture an adverse Knight or Pawn. The Rook can surround and capture an adverse Knight or Pawn. The Bishop can surround and capture an adverse Knight or Pawn. The Knight can surround and capture an adverse Knight or Pawn. Any piece aided by kindred pieces can surround and capture any adverse piece. Any piece aided by adverse pieces can surround and capture any adverse piece. Any piece can command, outflank, and outfront any adverse piece. Any two pieces can outnumber any adverse piece. Every movement of a Corps Detached is governed by the following : — FIFTEENTH LAW OE THE ART OF CHESSPLAY. At every turn to move note tJiose points which hy the last move of the opponent are left uncovered^ unsupported., and unsustained ; and ivhether the occupation of such point hy a kindred piece will outfront, outflank^ surround, outnumber, command, or surpi^ise one or more adverse pieces. And if so, combine this tactical defect with a similar defect in some other part of the adverse position. PLANS OF CAMPAIGN. Any given plan of campaign may endure for many moves, or it may become vitiated after a few moves, or it may be changed at every move ; but in all cases the true plan of campaign is governed by the following : SIXTEENTH LAW OF THE ART OF CHESSPLAY. I. In every true jjilan of campaign, the Prime Logistic Operation ahuays emanates from that Kindred Prime Strategetic Factor ivhich dominates the given situation and always takes direction towards the natural objective of the given Kindred Prime Strategetic Factor. II. In all cases ivherein the given situation is domi- nated hy an adverse Prime Strategetic Factor, the Prime Logistic operation cdivays emanates from that Kiyidred Primie Strategetic Factor ivhich at the given time is best calculated to reduce the dominant adverse Prime Strate- getic Factor to a Factor Subordinate. III. A true plan of campaign never contemplates a Prime Logistic Operation by a Factor Subordinate. By means of this law the student readily sees that every true plan of campaign changes as the relative value of the opposing^ Prime Strategetic Factors changes, nnd that the duration of any plan of campaign, there- fore, is indeterminate and may be altered with each succeedino; move. PLANS OF CAMPAIGN. 235 Hence, obviously it is imperative that, at every turn to move, the entire situation be exactly reconnoitred. This is done in the following manner, viz. : — RULES FOR MAKING A RECONNOISSANCE ON THE CHESSBOARD. (a) Compare the opposing columns of manoeuvre, and note that one which has the advantage. (6) Specify in what this advantage consists. (c) Compare the opposing columns of support, and note that one which has tiie advantage. {d) Specify in what this advantage consists. (e) Compare the opposing columns of attack, and note that one which has the advantage. (/) Specify in what this advantage consists. At every turn to move, the plan of campaign should be either strategetically offensive or strategically defen- sive. (a) If offensive, it should combine those measures whereby that column in which the kindred force lias the advantage may be made the Predominant Prime Tactical Factor in the given situation. (^) If defensive, it should combine those measures whereby that column in which the adverse force has the advantage may be reduced to a subordinate Prime Tactical Factor in the given situation. A plan of campaign should be offensive whenever the kindred force has the advantage : — 1. With the column of attack, with the column of support, and with the column of manoeuvre. 2. Both with the column of attack and with the column of support. 23G CHESS STRATEGETICS. 3. Both with the column of attack and with tlie column of manoeuvre. 4. Both with the column of support and with the column of manoeuvre. 5. With the column of attack, no offsetting advan- tage appertaining to the adverse column of support. 6. With the column of support, no offsetting advan- tage appertaining to the adverse column of attack. A plan of campaign should be defensive whenever the opponent has the advantage : — 1. Both with the column of attack and with the column of support. 2. With the column of attack, no offsetting advan- tage appertaining to the kindred column of support. 3. With the column of support, no offsetting ad- vantage appertaining to the kindred column of at- tack. PRIME LOGISTIC OPERATIONS. Having decided on the plan of campaign, the logistic operation will either be a line of manoeuvre or a line of operation ; each of which may or may not combine with itself a line of mobilization or a line of development. Whenever the logistic operation takes the form of a line of manoeuvre, the latter always is either : — 1. Simple, 2. Compound, or 3. Complex. The simple line of manoeuvre always should be adopted whenever an exact reconnoissance of the entire situation at any given turn to move shows no strategetic weakness in the adverse position. A simple line of manoeuvre preferably should com- bine with itself a line of mobilization or a line of development ; in direction it should be coincident with the dominant Kindred Prime Tactical Factor, and at every move it should either occupy the topographical key, or attack simultaneously the topographical key and one or more tactical keys in the adverse position. The compound line of manoeuvre always should be adopted whenever an exact reconnoissance of the entire situation at any given turn to move shows a true strat- egetic horizon whose vertices constitute an adverse strategetic weakness of either Class lY., V., YI., or YIL, in a direction coincident with the dominant kin- dred Prime Tactical Factor. 238 CHESS STRATEGETICS. A compound line of manoeuvre preferably should combine with itself a line of mobilization or a line of development ; in direction it should be coincident with the dominant Kindred Prime Tactical Factor, and at every move it should attack simultaneously two or more tactical keys in the adverse position. A complex line of manoeuvre always should be adopted whenever an exact reconnoissance of the entire situation at any given turn to move shows a true strategetic horizon whose vertices constitute an adverse strategetic weakness of Classes I., II., and III., in a direction coincident with the dominant Kindred Prime Strategetic Factor. A complex line of manoeuvre preferably should com- bine with itself either a line of mobilization or a line of development ; in direction it should be coincident with the dominant Kindred Prime Strategetic Factor, and at every move it should attack simultaneously two or more tactical keys in the adverse position. Whenever the logistic movement takes the form of a line of operation the latter always is either I. Strategic. 11. Tactical. III. Logistic. When the line of operation is strategic, it is coin- cident with the kindred column of attack and always takes direction towards the objective plane. The tac- tical key always is that point from which the Prime Tactical Factor may command the ultimate objective plane, and the Prime Tactical Factor always is that Corps Offensive whose exponent of force is equal to the net mobility of the adverse king. When the line of operation is logistic, it is coincident with the kindred column of support and always takes PRIME LOGISTIC OPERATIONS. 239 direction towards the kindred logistic horizon. The tactical key always is a point of junction, and the Prime Tactical Factor always is a kindred pawn. When the line of operation is tactical, it may be coin- cident either with the column of attack, or with the column of support, or with the column of manoeuvre. The tactical key always is a point occupied by an adverse piece, and the Prime Tactical Factor alw^ays is a kindred piece posted on the centre of its own geo- metric symbol at a time when the tactical key is a point on the perimeter of the same geometric symbol. Whether the line of operations be strategic, tactical, or logistic, every move of a Corps Offensive should simul- taneously attack two or more inadequately defended tac- tical keys^ both of which are not situated in the same topographical horizon. ORDERS OF BATTLE. Having determined whether the balance of advantage is with the kindred or with the adverse force, and whether, in consequence, the kindred plan of campaign is to be strategetically offensive or strategetically defen- sive ; and having designated the Prime Logistic Opera- tion and determined the true strategetic horizon, the true tactical evolution, and the true tactical sequence of moves appertaining to the corps offensive ; the next step is to depict the correct order in which the corps offensive shall be brought into action against the strategic vertices, — if a strategetic weakness exists in the adverse position, or against the topographical key, if no strategetic weakness exists in the adverse position, — or how the corps de- fensive shall be brought into action in order to neutral- ize the dominant adverse prime strategetic factor. It is thus easy to see that all orders of battle neces- sarily are divided into two classes : — I. Offensive. IT. Defensive. Offensive orders of battle are of three kinds : — (a) Those in which the corps offensive are manoeu- vred according to the first tactical sequence. (5) Tliose in which the corps offensive are manoeu- vred according to the second tactical sequence. {c) Those in which the corps offensive are manoeu- vred according to the third tactical sequence. The fundamental idea of strategetics, whether of war or of chess, is that the strategetic offensive always wins, ORDERS OF BATTLE. 241 and the strategetic defensive alwaj-s loses. Consequently, it is obvious that no valid system of defensive tactics is possible — since any defensive system must lose — and equally so it is only by assuming the offensive strateget- ically that the chessplayer, or the military commander, can hope to achieve, or even to deserve, victory. But of course situations will necessarily and fre- quently arise, both in warfare and in chessplay, wherein even the greatest master and the greatest captain will find himself, for reasons beyond his control, at least temporarily compelled to act on the strategetic defensive. According to all writers on strategetics, the defending party admittedly is in a bad pickle, and all these writers invariably have left him in that condition. For the first time by any author, the basic law of defensive tactics was announced on page 349 of " The Grand Tactics of Chess," viz. : — ''The nature of the offensive is constructive, and the nature of the defensive is destructive, and the prime ener- gies of the defence always must be devoted to destroying those formations which the attack labors to erect." Hence, it is clear that the defensive order of battle must absolutely conform to the adverse offensive order of battle^ and that its prime object must be to reduce the dominant adverse prime tactical factor to a subordinate factor^ viz. : — 1. By eliminating the adverse corps offensive. 2. By commanding the adverse points offensive. 3. By obstructing the adverse logistic radii. Thus it is that these special duties of detail appertain particularly to the defending force, viz. : — (a) To adequately cover, support, and sustain all kindred tactical keys. 16 242 CHESS STRATEGETICS. (b) To maintain a point of impenetrability on every adverse pawn altitude. (c) To permit no corps defensive to be outfronted^ outflanked, commanded, outnumbered, surrounded, or surprised. (*Erlon destroys the Dutch and Belgian Contingent, 20. P X Kt. Guyot destroys the Dutch and Belgian troops under Bylandt. 20. P X P. Ziethen repulses Guyot's division and attacks the French artillery. 21. Q-K2. The French artillery falls back before Ziethen. THE BATTLE OF WATERLOO. 265 21. P-Q4. English and Germans covering the advance of Biilow against Planchenoit. 22. QR-Ql. Reille's reserves moving to tlie attack of Hougoumont. 22. Q _ Q R 4. Biilow attacking the French right in force. 23. B-Q2. Lobau's corps again concentrated at Planchenoit to oppose Biilow. 23. P-QKt5. Biilow marching on Planchenoit. 266 THE BATTLE OE WATERLOO. POSITION ATTEE 'WHITE'S TWEXTT-THIPwD MO^'E. (About 5 P M.) The Fee>-ch- % Vyh:7T//A tt M, ms> %^A ^ i A H ^ ^^ • ^ Fa^ ^# ^ ■^M Cl H .^. y/z/y/zM, . .. . ^^^^^ Wyy:/z>yy. i^^^„ fti ^H e^ IS ■ A- m The Allies. Biiloiv assaulting FlancheJioit. 24. Kr - (J E 4, Milhaud covering the French right wing against Blilow. 24. K E - Q 1. English resailars supporting Ziethen on the centre. 25. B ~ Q B 1. Lobau covering the rear of the French armv against Biilow. THE BATTLE OF WATERLOO. 267 25. B-QB3. English cavalry co-operating with BUlow against Milhaud. 2Q. Kt — Kt2. Milhaud manoeuvring in support of Lobau's corps and covering the rear of the French army against Billow. 2Q. Q X R P. Billow overthrows Gen. Teste's infantry division and turns the right flank of the French army. POSITION AFTER WHITE'S TWENTY-SIXTH MOVE. (About 5.15 p. M.) The Erench. Sdl^'^ ^1^'^ mi m y/^^^^ '^r77f}777 >/ . ^^y^//y. 1 km.i- m ^ ^hM ■ isi^ ,^. in. m,. i ^ ^^ The Allies. SUlow turns the French Right Flanh, 268 THE BATTLE OF WATERLOO. 27. Kt-K5. Kellerman's cuirassiers charging the English on Mont St. Jean. 27. B - Q Kt 4. f English cavalry co-operating with Btilow in the attack of Planchenoit. .28. Kt-KB7. Kellerman breaks the English centre and establishes the French cavalry on the crest of Mont St. Jean. 28. E-Kl. English infantry moving to the support of Welling- ton's centre. 29. E-Q4. Reille's reserves marching to the attack of Hougou- mont. 29. B-QB4. English cavalry covering Wellington's left wing. 30. E - K E 4. Reille's corps massed against Hougoumont. 30. P-QKt6. Billow attacking Lobau's corps at Planchenoit in force. 31. B-Ql. Lobau falling back before Btilow. 31. P - Q B 6. Billow driving before him the entire French right THE BATTLE OF WATERLOO. 32. E X K R P. 269 Reille's corps attempting to take Hougoumont by storm. POSITION AFTER BLACK'S THIRTY-SECOKD MOVE. (About 5.30 P.M.) The French. m^ %^^A 11 'm . K X P. Destruction of the Imperial Guard under Gen. Friant. If 57. B X P, Kt - K 6, mate. 57. Q X P (ck). French artillery, almost devoid of infantry support, still keeping up the battle. 57. K-Ql. THE BATTLE OF WATERLOO. 281 Wellington forming a second line of battle. bS. Q X Kt (ck). Last effort of the French to restore the battle. bS, K - B 1. English rallying by the left. 59. Q - K 6. French artillery taking post to cover the flight of the surviving French. 59. B-Q2. English cavalry charging the French artillery. 60. Q - Kt 8 (ek). French artillery retreating toward Nivelles road. 60. K-Kt2. Wellington completes his second line of battle. 61. R - Q Kt 3 (ck). Imperial Guard under Morand opposing the junction of Bliicher's and Wellington's forces. The only resource to avert immediate mate by 62. Q - K R 8, etc. 282 THE BATTLE OF WATERLOO. POSITION AFTEE BLACKS SIXTY-FIRST MOVE. (Abouc 9 P.M. I The Fee>"CH. i ^, mm U777.. ,.,^/y^y^. '///////////, V////^////} W'. mm. mm. 11 1 m '-Wm '^ ^^^ m. 9k ra ^i ^ The Allies. Destruction of the Old Guard. 61. E X E. MorancVs Infantrv of the Imperial Guard destroyed near Planchenoit. 62. Kt - K 4. Kellerman's cuirassiers coverins- the centre of the French army. To prevent 63. R — K Kt 6 (ck). followed hy 64. Q - K Kt 8. mate. THE BATTLE OF WATERLOO. 283 62. E X B P (ck). Billow storms La Belle Alliance and captures the artillery of tlie Imperial Guard. . 63. Kt X Pv. Kellerman checks Billow and covers tlie French right against Bliicher. If 63. K X R, White mates in two moves by Q — K 6 (ck), etc. 63. R - K Kt 6 (ck). English regulars cliarging on La Belle Alliance. 64. Q X P. Temporary repulse of the English infantry by the French artillery of the line. 64. B X Q. Capture of the entire French artillery by the English cavalry. Q>o. Kt (R 6) - Kt 4. Milhaud unites with Kellerman at La Belle Alliance to cover the flight of the surviving French. 28-i THE BATTLE OE WATERLOO. PuSniOX AFTER BLACK'S SIXTY-FIFTH MOVE. (About 9.30 P.M.) Thz FKi:>XH. mm ^ 'mm ,^,,, y..M WM-R-WM. ^^^^^^^' W/m, 'WE% w^M ^ w^^.^ 1 m. m._ mm ^£. ^M, 'WMi „„ ,.W/>M- 1 fei • % The Allies Milhaud's and KeJlerinan's Cuirassiers covering the FfigJit of the French. 1\ A D 7.5. ^ ' •V' ,-t°.c ^. ... .'.«i&.'. ^.^^/ ,^^„^ ^^^^^. V' si ;V ^ ■ft.' -^^ ^^ ^^rr.-^ .^^ \ ^Ov\ .0 ^^^^ . ^o-n^. %. h* ^o.