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Full text of "The major tactics of chess: a treatise on evolutions; the proper employment of the forces in strategic, tactical, and logistic planes"

THE MAJOR TACTICS OF CHESS 



THE ::;v-;;: :- :/. 

MAJOR TACTICS OF CHESS 

A TREATISE ON EVOLUTIONS 

THE PROPER EMPLOYMENT OF THE FORCES 

IN STRATEGIC, TACTICAL, AND 

LOGISTIC PLANES 



BY 

FRANKLIN K. YOUNG 

* 

AUTHOR OF "THE MINOR TACTICS OF CHESS" AND 
"THE GRAND TACTICS OF CHESS" 



BOSTON 

LITTLE, BROWN, AND COMPANY 
1919 






Copyright, 1898, 
BY FRANKLIN K. YOUNG. 

All rights reserved. 



Printed by 
Louis E. CROSSCUP, BOSTON, U.S.A. 



PREFACE. 



, the second volume of the Chess Strategetics 
series, may not improperly be termed a book of 
chess tricks. 

Its purpose is to elucidate those processes upon which 
every ruse, trick, artifice, and stratagem known in chess- 
play, is founded ; consequently, this treatise is devoted 
to teaching the student how to win hostile pieces, to 
queen his pawns, and to checkmate the adverse king. 

All the processes herein laid down are determinate, 
and if the opponent becomes involved in any one of them, 
he should lose the game. 

Each stratagem is illustrative of a principle of Tac- 
tics ; it takes the form of a geometric proposition, and in 
statement, setting and demonstration, is mathematically 
exact. 

The student, having once committed these plots and 
counter-plots to memory, becomes equipped with a tech- 
nique whereby he is competent to project and to execute 
any design and to detect and foil every machination of 
his antagonist. 

BOSTON, 1898. 



CONTENTS. 



PAGE 

INTRODUCTORY xv 

MAJOR TACTICS 3 

Definition of .... 3 

Grand Law of 3 

Evolutions of 3 

GEOMETRIC SYMBOLS 4 

Of the Pawn 5 

" Knight 6 

" Bishop 7 

" Rook 8 

" Queen 9 

" King 10 

SUB-GEOMETRIC SYMBOLS 11 

Of the Pawn 12 

" Knight 13 

Bishop 14 

Rook 15 

" Queen 16 

" King 17 

LOGISTIC SYMBOLS 18 

Of the Pawn 18 

" Knight 19 

Bishop 20 

Rook 21 

Queen 22 

King 23 

GEOMETRIC PLANES 24 

Tactical 25 

Logistic 26 

Strategic 27 



x CONTENTS. 

PAG* 

PLANE TOPOGRAPHY (a) 28 

Zone of Evolution 31 

Kindred Integers 32 

Hostile Integers 33 

Prime Tactical Factor 34 

Supporting Factor 35 

Auxiliary Factor 36 

Piece Exposed 37 

Disturbing Factor 38 

Primary Origin 39 

Supporting Origin 40 

Auxiliary Origin 41 

Point Material 42 

Point of Interference 43 

Tactical Front 44 

Front Offensive 45 

Front Defensive 46 

Supporting Front 47 

Front Auxiliary 48 

Front of Interference 48 

Point of Co-operation 49 

Point of Command 50 

Point Commanded 51, 52 

Prime Radius of Offence 53 

Tactical Objective 54 

Tactical Sequence 54 

TACTICAL PLANES 55 

Simple 56 

Compound 57 

Complex 58, 59 

LOGISTIC PLANES 60 

Simple 61 

Compound 62 

Complex 63 

PLANE TOPOGRAPHY (5) 64 

The Logistic Horizon 64-66 

Pawn Altitude 67 

Point of Junction 68 



CONTENTS. xi 

PLANE TOPOGRAPHY (continued'). 

Square of Progression 69 

Corresponding Knight's Octagon 70 

Point of Resistance 71 

STRATEGIC PLANES 72 

Simple 73 

Compound 74, 75 

Complex 76 

PLANE TOPOGRAPHY (c) 77 

The Objective Plane 78 

Objective Plane Commanded 79 

Point of Lodgment 80 

Point of Impenetrability 81 

Like Points 82 

Unlike Points 83 

BASIC PROPOSITIONS OF MAJOR TACTICS 84 

Proposition I 85 

II 91 

III 97 

" IV 103 

V 110 

VI Ill 

VII 112 

VIII 113 

" IX 118 

X 119 

XI 121 

XII 123 

SIMPLE TACTICAL PLANES 124 

Pawn vs. Pawn 124-127 

Pawn vs. Knight 128 

Knight vs. Knight 129 

Bishop vs. Pawn 13 

Bishop vs. Knight . . . _. 131-133 

Rook y5. Pawn i34 

Rook vs. Knight 135-137 

Queen vs. Pawn 138 

Queen vs. Knight 139-142 

King vs. Pawn 143 



Xll CONTENTS. 

SIMPLE TACTICAL PLANES (continued). 

King vs. Knight 144 

Two Pawns vs. Knight 145 

Two Pawns vs. Bishop 146 

Pawn and Knight vs. Knight 147 

Pawn and Knight vs. Bishop 148 

Pawn and Bishop vs. Bishop 149 

Pawn and Rook vs. Rook ..150 

Two Knights vs. Knight 151 

Knight and Bishop vs. Knight 152 

Knight and Rook vs. Knight 153 

Knight and Queen vs. Knight 154 

Knight and King vs. Knight 155 

Bishop and Queen vs. Knight 156 

Rook and Queen vs. Knight 157 

King and Queen vs. Knight 158 

COMPOUND TACTICAL PLANES 159 

Pawn vs. Two Knights 159 

Knight vs. Rook and Bishop 160 

Knight vs. King and Queen 161 

Bishop vs. Two Pawns 162 

Bishop vs. King and Pawn 163 

Bishop vs. King and Knight 164 

Bishop vs. Two Knights 165 

Bishop vs. King and Knight 166 

Rook vs. Two Knights 167 

Rook vs. Knight and Bishop 168, 169 

Queen vs. Knight and Bishop 170,171 

Queen us. Knight and Rook 172 

Queen us. Bishop and Rook 173 

King vs. Knight and Pawn 1 74 

King vs. Bishop and Pawn 1 75 

King vs. King and Pawn 176 

Knight vs. Three Pawns 177 

Bishop vs. Three Pawns 178 

Rook vs. Three Pawns 179 

King vs. Three Pawns 180 

Knight vs. Bishop and Pawn 181 

Bishop vs. Bishop and Pawn 187 



CONTENTS. xiii 

PAGE 

COMPLEX TACTICAL PLANES 183 

Knight and Pawn vs. King and Queen ..... 183, 184 

Bishop and Pawn vs. King and Queen 185 

Bishop and Knight vs. King and Queen 186-192 

Rook and Knight vs. King and Queen 193-195 

Queen and Bishop vs. King and Queen 196 

Queen and Rook vs. King and Queen 197 

Bishop and Pawn vs. King and Knight 198 

Bishop and Pawn vs. King and Bishoj 199 

Bishop and Pawn vs. Knight and Bishop 200 

Bishop and Pawn vs. Knight and Rook 201 

Bishop and Pawn vs. King and Queen 202 

Rook and Pawn vs. King and Bishop 203 

Rook and Pawn us. King and Rook 204 

Rook and Pawn vs. King and Queen 205 

Queen and Pawn vs. Rook and Bishop 206 

Queen and Pawn vs. Rook and Knight 207 

Queen and Pawn vs. Bishop and Knight 208 

King and Pawn vs. Bishop and Knight 209 

King and Pawn vs. Two Knights 210 

SIMPLE LOGISTIC PLANES 211 

Pawn vs. Pawn 211-213 

Pawn us. Knight 214 

Pawn vs. Bishop 215 

Pawn vs. King 216 

Knight and Pawn vs. Queen or Rook 217 

Bishop and Pawn vs. King and Rook 218 

Rook and Pawn vs. Rook 219 

Knight and Pawn vs. King 220 

Rook and Pawn vs. King 221 

Bishop and Pawn us. King and Queen 222 

COMPOUND LOGISTIC PLANES 223 

Two Pawns vs. Pawn 223, 224 

Two Pawns us. Knight 225, 226 

Two Pawns us. Bishop 227, 228 

Two Pawns us. Rook 229 

Two Pawns iw. Kins 230, 231 



xiv CONTENTS. 

PAGE 

COMPLEX LOGISTIC PLANES 23-2 

Three Pawns vs. Three Pawns .........232 

Three Pawns vs. King 233 

Three Pawns vs. Queen 234 

Three Pawns vs. King and Pawn 235 

JSIMPLE STRATEGIC PLANES 236 

Knight vs. Objective Plane 1 236 

Knight vs. Objective Plane 2 237 

Bishop vs. Objective Plane 2 ... 238 

Bishop vs. Objective Plane 3 239 

Rook vs. Objective Plane 2 240 

Rook vs. Objective Plane 3 241 

Queen vs. Objective Plane 2 242, 243 

Queen vs. Objective Plane 3 244, 245 

Queen vs. Objective Plane 4 246 

COMPOUND STRATEGIC PLANES 247 

Pawn and S. F. vs. Objective Plane 2 247 

Bishop and S. F. vs. Objective Plane 3 248, 249 

Rook and S. F. vs. Objective Plane 3 250 

Rook and S. F. vs. Objective Plane 4 251 

Rook and S. F. vs. Objective Plane 5 252 

Queen and S. F. vs. Objective Plane 7 253, 254 

COMPLEX STRATEGIC PLANES 255 

Pawn Lodgment vs. Objective Plane 8 255 

Knight Lodgment vs. Objective Plane 8 256 

Bishop Lodgment rs. Objective Plane 8 257 

Rook Lodgment vs. Objective Plane 8 258 

Pawn Lodgment vs. Objective Plane 9 259 

Bishop Lodgment vs. Objective Plane 9 260, 261 

Rook Lodgment vs. Objective Plane 9 262 

Vertical Pieces vs. Objective Plane 9 263 

Oblique et al. Pieces vs. Objective Plane 9 263 

Diagonal Pieces vs. Objective Plane 9 264 

Horizontal Pieces vs. Objective Plane 9 265 

LOGISTICS OF GEOMETRIC PLANES .... 266 



INTEODUCTORY. 



WHEN you walked into your office this morning, 
you may have noticed that your senior partner 
was even more than ordinarily out of sorts, which, of 
course, is saying a good deal. 

In fact, the prevailing condition in his vicinity was so 
perturbed that, without even waiting for a response, 
say nothing of getting any, to your very civil salutation, 
you picked up your green bag again and went into court ; 
leaving the old legal luminary, with his head drawn 
down between his shoulders like a big sea-turtle, to 
glower at the wall and fight it out with himself. 

Furthermore, you may recollect, it was in striking 
contrast that his Honor blandly regarded your arrival, 
and that it was with an emphasized but strictly judicial 
snicker that he inquired after the health of your vener- 
able associate. 

You replied in due form, of course, but being a bit 
irritated, as is natural, you did not hesitate to insin- 
uate that some kind of a blight seemed to have struck 
in your partner's neighborhood during the night ; where- 
upon you were astonished to see the judge tie himself up 
into a knot, and then with face like an owl stare straight 
before him, while the rest of his anatomy acted as if it 
had the colic. 

Were you a chess-player, you would understand all 
this very easily. But as you do not practise the game, 



xvi INTRODUCTORY. 

and this is the first book you ever read on the subject, it 
is necessary to inform you that your eminent partner 
and the judge had a sitting at chess last night, and there 
is reason to believe that your alter ego did not get all the 
satisfaction out of it that he expected. 

You have probably heard of that far-away country 
whose chief characteristics are lack of water and good 
society, and whose population is afflicted with an uncon- 
trollable chagrin. These people have their duplicates 
on earth, and your partner, about this time, is one of 
them. 

Therefore, while you are attending strictly to business 
and doing your prettiest to uphold the dignity of your 
firm, it may interest you to know what the eminent head 
of your law concern is doing. Not being a chess-player, 
you of course assume that he is still sitting in a pro- 
found reverie, racking his brains on some project to 
make more fame and more money for you both. 

But he is doing nothing of the kind. As a matter of 
fact, he still is sitting where you left him, morose and 
ugly, and engaged in frescoing the wainscoting with the 
nails in his bootheels. Yet nothing is further from his 
mind than such low dross as money and such a perish- 
able bauble as fame. At this moment he has but a 
single object in life, and that is to concoct some Mach- 
iavellian scheme by which to paralyze the judge when 
they get together this evening. This, by the way, they 
have a solemn compact to do. 

Thus your partner is out of sorts, and with reason. 
To be beaten by the judge, who (as your partner will 
tell you confidentially) never wins a game except by 
purest bull luck, is bad enough. Still, your partner, 
buoyed up by the dictates of philosophy and the near 
prospect of revenge, a revenge the very anticipation of 



INTRODUCTORY. xvil 

which makes his mouth water, could sustain even that 
load of ignominy for at least twenty-four hours. But 
what has turned loose the flood-gates of his bile is that 
lot of books on the floor beside him. You saw these and 
thought they were law books ; but they 're not, they are 
analytical treatises on chess, which are all right if your 
opponent makes the moves that are laid down for him 
to make, and all wrong if he does not. Your partner 
knows that these books are of no use to him, for the 
judge does n't know a line in any chess-book, and prides 
himself on the fact. 

It seems that the judge, when he plays chess, prefers 
to use his brains, and having of these a fair supply and 
some conception of common-sense and of simple arith- 
metic, he has the habit, a la Morphy, of making but one 
move at a time, and of paying particular attention to 
its quality. 

Thus, in order to beat the judge to-night, your partner 
realizes that he must get down to first principles in the 
art of checkmating the adverse king, of queening his 
own pawns, and of capturing hostile pieces. But in 
the analytical volumes which he has been strewing 
about the floor he can find nothing about first prin- 
ciples, or about principles of any kind for that matter. 
This makes your partner irritable, for he is one of those 
men who, when they want a thing, want it badly and 
want it quick. So if you are through with this book 
you had better send it over to him by a boy. 



MAJOR TACTICS. 



MAJOR TACTICS. 



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 combination with any of its 
kindred integers. 

An Evolution is that combination of the primary 
elements time, locality and force whereby is made 
a numerical gain ; either by the reduction of the ad- 
verse material, or by the augmentation of the kindred 
body of chess-pieces. 

In every evolution, the primary elements time, 
locality and force are determinate and the proposi- 
tion always may be mathematically demonstrated. 

The object of an evolution always is either to check- 
mate the adverse king ; or, to capture an adverse pawn 
or piece ; or to promote a kindred pawn. 

Grand Law of Major Tactics. The offensive force of a 
given piece is valid at any point against which it is 
directed ; but the defensive force of a given piece is 
valid for the support only of one point, except when 
the points required to be defended are all contained in 
the perimeter of that geometric figure which appertains 
to the supporting piece. 



GEOMETRIC SYMBOLS. 

All integers of chess force are divided into six 
classes ; the King, the Queen, the Rook, the Bishop, the 
Knight and the Pawn. 

Any one of these integers may properly be combined 
with any other and the principle upon which such com- 
bination is based governs all positions in which such 
integers are combined. "This principle always assumes 
a form similar to a geometric theorem and is susceptible 
of exact -demonstration. 

That geometric symbol which is the prime factor in 
all evolutions which contemplates the action of a Pawn 
is shown in Fig. 1. 

This figure is an inverted triangle, whose base always 
is coincident with one of the horizontals of the chess- 
board; whose sides are diagonals and whose verux 
always is that point which is occupied by the given 
pawn. 



GEOMETRIC SYMBOLS. 



GEOMETRIC SYMBOL OF THE PAWN. 
FIGURE l. 

Black. 




White. 



PRINCIPLE. 



Given a Pawn's triangle, the vertices of which are 
occupied by one or more adverse pieces, then the pawn 
may make a gain in adverse material. 



MAJOR TACTICS. 



That geometric symbol which is the prime factor in 
all evolutions that contemplate the action of a Knight is 
shown in Fig. 2. 

This figure is an octagon, the centre of which is the 
point occupied by the Knight and whose vertices are the 
extremities of the obliques which radiate from the given 
centre. 

GEOMETRIC SYMBOL OF THE KNIGHT. 
FIGURE 2. 

Black. 




White. 
PRINCIPLE. 



Given a Knight's octagon, the vertices of which are 
occupied by one or more adverse pieces, then the Knight 
may make a gain in adverse material. 



GEOMETRIC SYMBOLS. , 7 

The geometric symbol which is the prime factor in all 
evolutions which contemplate the action ef a Bishop is 
shown in Fig. 3. 

This figure is a triangle, the vertex of which always 
is that point which is occupied by the Bishop. 



GEOMETRIC SYMBOL OF THE BISHOP. 

FIGURE 3. 

Black. 




White. 



PRINCIPLE. 

Given a Bishop's triangle, the vertices of which are 
occupied by one or more adverse pieces, then the Bishop 
mav make a gain in adverse material. 



8 



MAJOR TACTICS 



That geometric symbol which is a prime factor in 
all evolutions which contemplate the action of a Rook 
is shown in Fig. 4. 

This figure is a quadrilateral, one angle of which is 
the point occupied by the Rook. 

GEOMETRIC SYMBOL OF THE BOOK. 

FIGURE 4. 
Black. 




While. 



PRINCIPLE. 

Given a Rook's quadrilateral, one of whose sides is 
occupied by two or more adverse pieces ; or two or more 
of whose sides are occupied by one or more adverse 
pieces ; then the Rook may make a gain in adverse 
material. 



GEOMETRIC SYMBOLS. 



9 



That geometric symbol which is a prime factor in all 
evolutions that contemplate the action of the Queen is 
shown in Fig. 5. 

This figure is an irregular polygon of which the Queen 
occupies the common vertex. 

GEOMETRIC SYMBOL OF THE QUEEN. 
FIGURE 5. 

Black. 




White. 



NOTE. This figure is composed of a rectangle, a 
minor triangle, a major triangle, and a quadrilateral, and 
shows that the Queen combines the offensive powers 
of the Pawn, the Bishop, the Rook and the King. 
PRINCIPLE. 

Given one or more adverse pieces situated at the 
vertices or on the sides of a Queen's polygon, then 
the Queen may make a gain in adverse material. 



10 



MAJOR TACTICS. 



That geometric symbol which is the prime factor in 
all evolutions which contemplate the action of the King, 
is shown in Fig. 6. 

This figure is a rectangle of either four, six, or 
nine squares. In the first case the King always is 
situated at one of the angles ; in the second case he 
always is situated on one of the sides and in the last 
case he always is situated in the centre of the given 
figure. 

GEOMETRIC SYMBOL OF THE KING. 

(a.) 
FIGURE 6. 



Slack. 




White. 



PRINCIPLE. 

Given one or more adverse pieces situated on the 
sides of a King's rectangle, then the King may make a 
gain in adverse material. 



GEOMETRIC SYMBOLS. 



11 



A Sub-G-eometric Symbol is that mathematical figure 
which in a given situation appertains to the Prime 
Tactical Factor, and whose centre is unoccupied by a 
kindred piece, and whose periphery is occupied by the 
given Prime Tactical Factor. 



SUB-GEOMETRIC SYMBOL OF THE PAWN. 
FIGURE 7. 




White. 



NOTE. That point which is the centre of the geo- 
metric symbol of a piece always is the centre of its 
sub-geometric symbol. 



12 



MAJOR TACTICS. 



SUB-GEOMETRIC SYMBOL OF THE PAWN. 

FIGURE 8. 

(b.) 

Black. 




White. 



NOTE. A piece always may reach the centre of its 
sub-geometric symbol in one move. 



GEOMETRIC SYMBOLS. 



13 



SUB-GEOMETRIC SYMBOL OF THE KNIGHT. 
FIGURE 9. 

Black. 




White. 



NOTE. If the piece has the move, the sub-geometric 
symbol is positive ; otherwise, it is negative. 



14 



MAJOR TACTICS. 



SUB-GEOMETRIC SYMBOL OF THE BISHOP. 
FIGURE 10. 

Black. 




White. 



NOTE. The sub-geometric symbol is the mathe- 
matical figure common to situations in which the de- 
cisive blow is preparing. 



GEOMETRIC SYMBOLS. 



15 



SUB-GEOMETRIC SYMBOL OF THE ROOK. 

FIGURE 11. 

Black. 




White. 



NOTE. The sub- geometric symbol properly should 
eventuate into the geometric symbol. 



16 



MAJOR TACTICS. 



SUB-GEOMETRIC SYMBOL OF THE QUEEN. 

FIGURE 12. 

Black. 




White. 



NOTE. A piece always moves to the centre of its 
sub-geometric symbol. 



GEOMETRIC SYMBOLS. 



17 



SUB-GEOMETRIC SYMBOL OF THE KING. 
FIGURE 13. 

Black. 




White. 



NOTE. An evolution based upon a sub-geometric 
symbol always contemplates, as the decisive stroke, the 
move which makes the sub-geometric symbol positive. 



LOGISTIC SYMBOLS. 



The Logistic Symbol of an integer of chess force 
typifies its movement over the surface of the chess- 
board and always is combined with the geometric 
symbol or with the sub-geometric symbol in the execu- 
tion of a given calculation. 

LOGISTIC SYMBOL OF THE PAWN. 

FIGURE 14. 

Slack. 




White. 



NOTE. A piece moves only in the direction of and 
to the limit of its logistic radii. 



LOGISTIC SYMBOLS. 



19 



LOGISTIC SYMBOL OF THE KNIGHT. 

FIGURE 15. 

Black. 




White. 



NOTE. A piece having the move can proceed at the 
given time along only one of its logistic radii. 



20 



MAJOR TACTICS. 



LOGISTIC SYMBOL OF THE BISHOP. 
FIGURE 16. 

Black. 




White. 



NOTE. The logistic radii of a piece all unite at the 
centre of its geometric symbol. 



LOGISTIC SYMBOLS. 



21 



LOGISTIC SYMBOL OF THE ROOK. 
FIGURE 17. 

Black. 




White. 



NOTE. The termini of the logistic radii of a piece 
always are the vertices of its geometric symbol. 



22 



MAJOR TACTICS. 



LOGISTIC SYMBOL OF THE QUEEN. 
FIGURE 18. 

Black. 




White. 



NOTE. The logistic radii of a piece always extend 
from the centre of its geometric symbol to the perimeter. 



LOGISTIC SYMBOLS. 



23 



LOGISTIC SYMBOL OF THE KING. 
FIGURE 19. 

Black. 




White. 



NOTE. The logistic radii of a piece always are 
straight lines, and always take the form of verticals, 
horizontals, diagonals, or obliques. 



GEOMETRIC PLANES. 

Whenever the geometric symbols appertaining to one 
or more kindred pieces and to one or more adverse 
pieces are combined in the same evolution ; then that 
part of the surface of the chessboard upon which such 
evolution is executed is termed in this theory a G-eo' 
metric Plane. 

Geometric Planes are divided into three classes : 

I. STRATEGIC. 
II. TACTICAL. 
III. LOGISTIC. 

Whenever the object of a given evolution is to gain 
adverse material, then that mathematical figure pro- 
duced by the combination of the geometric symbols 
appertaining to the integers of chess force thus engaged 
is termed a Tactical Plane. 



GEOMETRIC PLANES. 



25 



A TACTICAL PLANE. 
FIGURE 20. 

Black. 




White. 



White to play and win adverse material. 

NOTE. White having the move, wins by 1 P K 6 
(ck) followed by 2 Kt-K Kt 5 (ck) if Black plays 
1 QxP; and by 2 Kt Q B 5 (ck) if Black plays 
IKxP. 



26 



MAJOR TACTICS. 



Whenever the object of a given evolution is to queen 
a kindred pawn, then that mathematical figure pro- 
duced by the combination of the geometric symbols 
appertaining to the integers of chess force thus en- 
gaged is termed a Logistic Plane. 



A LOGISTIC PLANE. 

FIGURE 21. 
Slack. 




White. 



White to play and queen a kindred pawn. 

NOTE. White having the move wins by 1 P Q 6, 
followed by 2 P - Q B 6, if Black plays 1 K P x P 
and by 2 P - K 6, if Black plays 1 B P x P. 



GEOMETRIC PLANES. 



27 



Whenever the object of a given evolution is to check, 
mate tke adverse king, then that mathematical figure 
produced by the combination of the geometric symbols 
appertaining to the integers of chess force thus engaged 
is termed a Strategic Plane. 



A STRATEGIC PLANE. 
FIGURE 22. 

Black. 




White. 
White to play and checkmate the adverse king. 

NOTE. White having to move checkmates the black 
King in one move by 1 R K Kt 8 (ck). 



PLANE TOPOGRAPHY. 

Those verticals, horizontals, diagonals, and obliques, 
and the points situated thereon, which are contained in 
a given evolution, constitute, when taken collectively, 
the Topography of a given plane. 

Every plane, whether strategic, tactical, or logistic, 
always contains the following topographical features : 

1. Zone of Evolution. 14. Tactical Front. 

2. Kindred Integers. 15. Front Offensive. 

3. Hostile Integers., 16. Front Defensive. 

4. Prime Tactical Factor. 17. Supporting Front. 

5. Supporting Factor. 18. Front Auxiliary. 

6. Auxiliary Factor. 19. Front of Interference. 

7. Piece Exposed. 20. Point of Co-operation. 

8. Disturbing Integer. 21. Point of Command. 

9. Primary Origin. 22. Point Commanded. 

10. Supporting Origin. 23. Prime Radius of Offence, 

11. Auxiliary Origin. 24. Tactical Objective. 

12. Point Material. 25. The Tactical Sequence. 

13. Point of Interference. 



PLANE TOPOGRAPHY. 



29 



A COMPLEX TACTICAL PLANE. 
FIGURE 23. 

Black. 




White. 
White to play and win. 

NOTE. White wins by 1 R-K R 8 (ck), followed, 
if Black plays 1 K x R, by 2 Kt - K B 7 (ck) ; and if 
Black plays 1 K-Kt 2, by 2 R x R, for if now Black 
plays 2 Q x R, then follows 3 Kt -K 6 (ck), and White 
wins the black Q. 



MAJOR TACTICS. 



A SUB-GEOMETKIC SYMBOL POSITIVE. 
(G. S. P.) 
FIGURE 24. 

Black. 




White. 
White to move. 



NOTE. White having to move, the geometric symbol 
is positive ; had Black to move, the geometric symbol 
would be negative. 



PLANE TOPOGRAPHY. 



31 



The Zone of Evolution is composed of those verticals, 
diagonals, horizontals, and obliques which are compre- 
hended in the movements of those pieces which enter 
into a given evolution. The principal figure in any 
Zone of Evolution is that geometric symbol which ap- 
pertains to the Prime Tactical Factor. 



THE ZONE OF EVOLUTION. 

(Z. E.) 
FIGURE 25. 

Black. 




White 



NOTE. The letters A B C D E F mark the vertices 
of an octagon, which is the principal figure in this evolu- 
tion, as the Prime Tactical Factor is a Knight. 



32 



MAJOR TACTICS. 



A Kindred Integer is any co-operating piece which 
is contained in a given evolution. 



KINDRED INTEGERS. 

(K. I.) 
FIGURE 26. 

Black. 




White, 



NOTE. The kindred Integers always have the move 
in any given evolution, and always are of the same color 
-as the Prime Tactical Factor. 



PLANE TOPOGRAPHY. 



33 



A Hostile Integer is any adverse piece which is con- 
tained in a given evolution. 



HOSTILE INTEGERS. 

(H. I.) 
FIGURE 27. 

Black. 




White. 



NOTE. The Hostile Integers never have the move 
in any evolution and always are opposite in color to the 
Prime Tactical Factor. 



34 



MAJOR TACTICS. 



The Prime Tactical Factor is that kindred Pawn or 
Piece which in a given evolution either check-mates 
the adverse King, or captures adverse material, or is 
promoted to and utilized as some other kindred piece. 



THE PRIME TACTICAL FACTOR. 
(P. T. F.) 
FIGURE 28. 

Black. 




White. 



NOTE. The Prime Tactical Factor always is situated 
either at the centre or upon the periphery of the zone of 
evolution. 



PLANE TOPOGRAPHY. 



35 



The Supporting Factor is that kindred piece which 
directly co-operates in an evolution with the Prime 
Tactical Factor. 



THE SUPPORTING FACTOR. 

(S. F.) 
FIGURE 29. 

Black. 





















Wile. 



NOTE. The Supporting Factor always is situated 
upon one of the sides of the zone of evolution. 



36 



MAJOR TACTICS. 



An Auxiliary Factor is that kindred piece which 
indirectly co-operates with the Prime Tactical Factor by 
neutralizing the interference of hostile pieces not con- 
tained in the immediate evolution. 



AN AUXILIARY FACTOR. 

(A. F.) 
FIGURE 30. 

Black. 




White. 



NOTE. The Auxiliary Factor may be situated at 
any point and either within or outside of the zone of 
evolution. 



PLANE TOPOGRAPHY. 



37 



The Piece Exposed is that adverse integer of chess 
force whose capture in a given evolution may be 
mathematically demonstrated. 



THE PIECE EXPOSED. 

(P. E.) 
FIGURE 31. 

Black. 




While. 



NOTE. The Piece Exposed always is situated either 
upon one of the sides or at one of the vertices of the 
zone of evolution. 



38 



MAJOR TACTICS. 



A Disturbing Integer is an adverse piece which 
prevents the Prime Tactical Factor from occupying the 
Point of Command, or the Supporting Factor from 
occupying the Point of Co-operation. 



A DISTURBING FACTOR. 

(D. F.) 
FIGURE 32. 

Black. 




White. 



NOTE. A Disturbing Factor may or may not be situ- 
ated within the zone of evolution. 



PLANE TOPOGRAPHY. 



39 



The Primary Origin is that point which, at the 
beginning of an evolution, is occupied by the Prime 
Tactical Factor. 



THE PRIMARY ORIGIN. 

(P. 0.) 
FIGURE 33. 

Black. 




White. 



NOTE. The point A is the Primary Origin in this 
evolution, as it is the original post of the Prime Tactical 
Factor. 



40 



MAJOR TACTICS. 



The Supporting Origin is the point occupied by the 
Supporting Factor at the beginning of an evolution. 



THE SUPPORTING ORIGIN. 

(P. S.) 
FIGURE 34. 

Black. 




White. 



NOTE. The point A is the Supporting Origin in this 
evolution, as it is the original post of the Supporting 
Factor. 



PLANE TOPOGRAPHY 



41 



The Auxiliary Origin is the point occupied by the 
Auxiliary Factor at the beginning of an evolution. 



A POINT AUXILIARY. 

(P. A.) 
FIGURE 35. 

Black. 




White. 



NOTE. The Point A is the Auxiliary Origin in this 
evolution, as it is the original post of the Auxiliary 
Factor. 



42 



MAJOR TACTICS. 



The Point Material is that point which is occupied by 
the adverse piece which, in a given evolution, it is 
proposed to capture. 



POINTS MATERIAL. 
(P. M.) 

FIGURE 36. 

Slack. 




White. 



NOTE. A Point Material always is situated either 
at one of the vertices or upon one of the sides of the 
zone of evolution. 



PLANE TOPOGRAPHY. 



43 



A Point of Interference is that point which is oc- 
cupied by the Disturbing Integer. 



A POINT OF INTERFERENCE. 

(P. I.) 
FIGURE 37. 

Black. 




White. 



NOTE. The point A is the Point of Interference in 
this evolution, as it is the original post of the Disturbing 
Factor. 



44 



MAJOR TACTICS. 



The Tactical Front is composed of the Fronts Offen- 
sive, Defensive, Auxiliary, Supporting, and of Inter- 
ference. 



THE TACTICAL FRONT. 

(T. F.) 
FIGURE 38. 

Black. 




While. 

NOTE. The Front Offensive extends from White's 
K Kt 5 to K B 7 ; the Front Defensive from K Kt 1 to K 
B 2 ; the Front of Interference from Q Kt 3 to K B 7 ; 
the Front Supporting from KR7 to KR8; the Front 
Auxiliary is at QB4. 



PLANE TOPOGRAPHY. 



45 



The Front Offensive is that vertical, diagonal, hori- 
zontal, or oblique which connects the Primary Origin 
with the Point of Command. 



THE FRONT OFFENSIVE. 
FIGURE 39. 
Black. 




NOTE. The Front Offensive extends from White's 
KKt5toKB7. 



46 



MAJOR TACTICS. 



The Front Defensive is that vertical, horizontal, diag- 
onal, or oblique which extends from the Point of Com- 
mand to any point occupied by a hostile integer con- 
tained in the geometric symbol which appertains to the 
Prime Tactical Factor. 



THE FRONT DEFENSIVE. 

(F. D.) 
FIGURE 40. 

Black. 




White. 



NOTE. The Front Defensive in this evolution extends 
from black K Kt 1 to K B 2. 



PLANE TOPOGRAPHY. 



47 



TJie Supporting Front is that vertical, horizontal, di- 
agonal, and oblique which unites the Supporting Origin 
with the Point of Co-operation. 



THE SUPPORTING FRONT. 
FIGURE 41. 

Black. 




White. 



NOTE. The Front of Support in this evolution ex- 
tends from White's K R 7 to K R 8. 



MAJOR TACTICS. 



A Front Auxiliary is that vertical, horizontal, diag- 
onal, or oblique which extends from the Point Auxiliary 
to the Point of Interference ; or that point situated on 
the Front of Interference which is occupied by the Aux- 
iliary Factor. 

The Front of Interference is that vertical, horizontal, 
diagonal, or oblique which unites the Point of Inter- 
ference with the Point of Command, or with the Point 
of Co-operation. 

A FRONT OF INTERFERENCE. 

(F. I.) 
FIGURE 42. 

Black. 




White. 



NOTE. The Front of Interference in this evolution 
extends from White's Q Kt 3 to K B 7. 



PLANE TOPOGRAPHY. 



49 



The Point of Co-operation is that point which when 
occupied by the Supporting Factor enables the Prime 
Tactical Factor to occupy the Point of Command. 



THE POINT OF CO-OPERATION. 
FIGURE 43. 

Black. 




White. 



NOTE. The Point of Co-operation in this evolution 
is the white square K R 8. 



50 



MAJOR TACTICS. 



The Point of Command is the centre of that geomet- 
ric symbol which appertains to the Prime Tactical 
Factor, and which, when occupied by the latter, wins an 
adverse piece, or checkmates the adverse king, or en- 
sures the queening of a kindred pawn. 



THE POINT OF COMMAND. 

(P. C.) 
FIGURE 44. 

Slack. 




White. 



NOTE. The Point of Command in this evolution is 
the white square K B 7. 



PLANE TOPOGRAPHY. 



51 



The Point Commanded is that point at which the 
Piece Exposed is situated when the Prime Tactical 
Factor occupies the Point of Command. 



THE POINT COMMANDED. 

(C. P.) 
FIGURE 45. 

(a.) 
Black. 




White. 



NOTE. White has occupied the Point of Co-operation 
with the Supporting Factor, which latter has been cap- 
tured by the black King, thus allowing the white Knight 
to occupy the Point of Command. 



52 



MAJOR TACTICS. 



THE POINT COMMANDED. 

(C. P.) 
FIGURE 46. 

(6.) 
Black. 




White. 

NOTE. Black retired before the attack of the Sup- 
porting Factor, still defending the Point of Command. 
The Supporting Factor then captured the black Rook, 
thus opening up a new and unprotected Point of Com- 
mand, which is occupied by the white Knight. 

Those interested in military science may, perhaps, 
understand from these two diagrams why all the great 
captains, from Tamerlane to Yon Moltke, so strenuously 
recommended the study of chess to their officers. 



PLAJSE TOPOGRAPHY. 



53 



The Prime Radius of Offence is the attacking power 
radiated by the Prime Tactical Factor from the Point 
of Command against the Point Commanded. 



THE PRIME RADIUS OF OFFENCE. 

(P. R. O.) 

FIGURE 47. 

Black. 




White. 



NOTE. In this evolution the Prime Radii of Offence 
extend from the white point K B 7 to K R 8, Q 6, and 

Q8. 



54 



MAJOR TACTICS. 



The Tactical Objective is that point on the chess-board 
whose proper occupation is the immediate object of the 
initiative in any given evolution. 



THE TACTICAL OBJECTIVE. 

(T. O.) 
FIGURE 48. 

Black. 




White. 

NOTE. In this evolution the point A is the Tactical 
Objective, i.e. the initial movement in its execution is 
to occupy the Point of Co-operation with the Supporting 
Factor. 

The Tactical Sequence is that series of moves which 
comprehends the proper execution of any given 
evolution. 



TACTICAL PLANES. 

A Tactical Plane is that mathematical figure pro- 
duced by the combination of two or more kindred 
geometric symbols in an evolution whose object is gain 
of material. 

Tactical Planes are divided into three classes, viz. : 

I. SIMPLE. 
II. COMPOUND. 
III. COMPLEX. 

A Simple Tactical Plane consists of any kindred geo- 
metric symbol combined with a Point Material. 

PRINCIPLE. 

I. Whenever in a simple Tactical Plane, the Primary 
Origin and the Point Material are contained in the same 
side of that geometric symbol which appertains to the 
Prime Tactical Factor, then the latter, having the 
move, will overcome the opposing force. 

II. No evolution in a simple Tactical Plane is valid 
if the opponent has the move, or if not having the move, 
he can offer resistance to the march of the Prime Tacti- 
cal Factor along the Front Offensive. 



r >6 



MAJOR TACTICS. 



A SIMPLE TACTICAL PLANE. 
FIGURE 49. 

Black. 




White. 
White to play and win the adverse Kt in one move. 

NOTE. The decisive point is that at which the geo- 
metric and the logistic symbols appertaining to the 
Prime Tactical Factor intersect. 

A Compound Tactical Plane consists of any kindred 
geometric symbol combined with two or more Points 
Material. 

PRINCIPLE. 

Whenever in a Compound Tactical Plane the Primary 
Origin and two or more Points Material are situated at 



TACTICAL PLANES. 



57 



the vertices of that geometric symbol which appertains 
to the Prime Tactical Factor, then, if the value of each of 
the Points Material exceeds the value of the Prime Tacti- 
cal Factor ; or, if neither of the Pieces Exposed can sup- 
port the other in one move, the Prime Tactical Factor, 
having the move, will overcome the opposing force. 

II. No evolution in a Compound Tactical Plane is 
valid if the opponent can offer resistance to the Prime 
Tactical Factor. 



A COMPOUND TACTICAL PLANE. 
FIGURE 50. 

Black. 




While. 



NOTE. The decisive point is the centre of the geo- 
metric symbol which appertains to the Prime Tactical 
Factor. 



58 MAJtjtft* TACTICS. 

A Complex Tactical Plane consists of the combination 
of any two or more kindred geometric symbols with one 
or more Points Material. 

PRINCIPLE. 

I. No evolution in a Complex Tactical Plane is valid 
unless it simplifies the position, either by reducing it to 
a Compound Tactical Plane in which the opponent, even 
with the move, can offer no resistance ; or to a Simple 
Tactical Plane, in which the opponent has not the move 
nor can offer any resistance. 

II. To reduce a Complex Tactical Plane to a Com- 
pound Tactical Plane, establish the Supporting Origin 
at such a point and at such a time that, whether the 
Supporting Factor be captured or not, the Primary 
Origin and two or more of the Points Material will 
become situated on that side of the geometric figure 
which appertains to the Prime Tactical Factor, the 
latter having to move. 

III. To reduce a Complex Tactical Plane to a Simple 
Tactical Plane, eliminate all the Points Material save 
one, and all the Hostile Integers save one, and establish 
the Primary Origin and the Point Material upon the 
same side of that geometric figure which appertains to 
the Prime Tactical Factor, the latter having to move. 



TACTICAL PLANES. 



59 



A COMPLEX TACTICAL PLANE. 
FIGURE 51. 

Black. 




White. 



NOTE. This diagram is elaborated to show the student 
the Supplementary Knight's Octagon and the Supple- 
mentary Point of Command at White's K 6. 



LOGISTIC PLANES. 

A LOGISTIC PLANE is that mathematical figure pro- 
duced by the combination of two or more kindred geo- 
metric symbols in an evolution whose object is to queen 
a kindred pawn. 

A LOGISTIC PLANE is composed of a given logistic 
horizon, the adverse pawns, the adverse pawn altitudes, 
and the kindred Points of Resistance. 

Logistic Planes are divided into three classes : 

I. SIMPLE. 
II. COMPOUND. 
III. COMPLEX. 



LOGISTIC PLANES. 



61 



A simple Logistic Plane consists of a pawn altitude, 
combined adversely with that geometric figure which 
appertains to either a P, Kt, B, R, Q, or K. 

In a plane of this kind the pawn always is the Prime 
Tactical Factor. 

The following governs all logistic planes : 

PRINCIPLE. 

Whenever the number of pawn altitudes exceeds the 
number of Points of Resistance, the given pawn queens 
without capture against any adverse piece. 

A SIMPLE LOGISTIC PLANE. 

FIGURE 52. 

Black. 




White. 



White to move and queen a pawn without capture by an adverse 
piece. 



62 



MAJOR TACTICS. 



A Compound Logistic Plane is composed of two kin- 
dred pawn altitudes combined adversely with the geo- 
metric figures appertaining to one or more opposing 
integers of chess force. 



A COMPOUND LOGISTIC PLANE. 
FIGURE 53. 

Black. 




White. 



White to move and queen a pawn without capture by the adverse 
King. 

NOTE. It will be easily seen that the black King 
cannot stop both of the white Pawns. 



LOGISTIC PLANES. 



63 



A Complex Logistic Plane consists of three kindred 
pawn altitudes combined adversely with the geometric 
figures appertaining to one or more opposing integers 
of chess force. 



A COMPLEX LOGISTIC PLANE. 
FIGURE 64. 

Black. 


























White. 



White to move and queen a pawn without capture by the adverse 
pieces. 

NOTE. The black King and the black Bishop are 
each unable to stop more than one Pawn. 



64 MAJOR TACTICS. 

Plane Topography. The following topographical 
features are peculiar to Logistic Planes : - 

1. Logistic Horizon. 

2. Pawn Altitude. 

3. Point of Junction. 

4. Square of Progression. 

5. Corresponding Knights Octagon. 

6. Point of Resistance. 

The Logistic Horizon is that extremity of the chess- 
board, at which, upon arrival, a pawn may be promoted 
to the rank of any kindred piece. The Logistic Horizon 
of White always is the eighth horizontal ; that of Black 
always is the first horizontal. 



LOGISTIC PLANES. 



65 





THE LOGISTIC HORIZON. 

(White). 
FIGURE 55. 

Black. 






























White. 



NOTE. The Points of Junction are designated by 
black dots. 



66 



MAJOR TACTICS. 



THE LOGISTIC HORIZON. 
(Black.) 

FIGURE 56. 

Black. 




White. 



LOGISTIC PLANES, 



67 



A Pawn Altitude is composed of those verticals and 
diagonals along which it is possible for a pawn to 
pass to its logistic horizon. 



A PAWN ALTITUDE 

(P. A.) 
FIGURE 57. 

Black. 




White. 



68 



MAJOR TACTICS. 



A Point of Junction is that point at which an extremity 
of a pawn altitude intersects the logistic horizon, i. e. the 
queening point of a given pawn. 



A POINT OF JUNCTION. 

(P. J.) 
FIGURE 58. 

Black. 




White. 



LOGISTIC PLANES. 



69 



The Square of Progression is that part of the logistic 
Plane of which the pawn's vertical is one side and whose 
area is the square of the pawn's altitude. 



A SQUARE OF PROGRESSION. 

(S. P.) 
FIGURE 59. 

Black. 




White. 



70 



MAJOR TACTICS. 



The Corresponding Knight's Octagon is that Knight 
octagon whose centre is the queening point of the pawn, 
and whose radius consists of a number of Knight's moves 
equal to the number of moves to be made by the pawn 
in reaching its queening point. 



THE CORRESPONDING KNIGHT'S OCTAGON. 
(C. K. 0.) 

FIGURE 60. 
Black. 




White. 



NOTE. The pawn has but two moves to make in order 
to queen. The points ABODE are two Knight's moves 
from the queening point. 



LOGISTIC PLANES. 



71 



A Point of Resistance is that point on a pawn altitude 
which is commanded by a hostile integer and which is 
situated between the Primary Origin and the Point of 
Junction. 



POINT OF RESISTANCE. 
(P. R.) 

FIGURE 61. 
fcfaafc 




White. 



NOTE. In this evolution, the points A and B are 
points of resistance, as they prevent the queening of the 
Prime Tactical Factor. 



STRATEGIC PLANES. 

A STRATEGIC PLANE is that mathematical figure pro- 
duced by the combination of two or more geometric 
symbols in an evolution whose object is to checkmate 
the adverse King. 

A STRATEGIC PLANE is composed of a given Objective 
Plane and of the Origins occupied by the attacking and 
by the defending pieces. 

Strategic planes are divided into three classes : 

I. SIMPLE. 
II. COMPOUND. 
III. COMPLEX. 



STRATEGIC PLANES. 



73 



A Simple Strategic Plane is one which may be com- 
manded by the Prime Tactical Factor. 

Simple Strategic Planes are governed by the follow- 
ing 

PRINCIPLE. 

Whenever the net value of the offensive force radiated 
by a given piece is equal to the net mobility of the 
Objective Plane ; then, the given piece may checkmate 
the adverse King. 



A SIMPLE STRATEGIC PLANE. 
FIGURE 62. 

Black. 






























White. 
White to play and mate in one move. 



74 



MAJOR TACTICS. 



A Compound Strategic Plane is one which may be 
commanded by the Prime Tactical Factor with the aid 
of either the supporting or the auxiliary Factor. 

Compound Strategic Planes are governed by the 
following 

PRINCIPLE. 

Whenever the net value of the offensive force radiated 
by two kindred pieces is equal to the net mobility of the 
Objective Plane, then the given pieces may checkmate 
the adverse King. 

A COMPOUND STRATEGIC PLANE. 

(a.) 
FIGURE 63. 

Slack. 




While. 
White to play and mate in one move. 



STRATEGIC PLANES. 



75 



A COMPOUND STRAGETIC PLANE. 



FIGURE 64. 

Black. 




Whitf. 

White to play and mate in one move. 



76 



MAJOR TACTICS. 



A Complex Strategic Plane is one that can be com- 
manded by the Prime Tactical Factor only when aided 
by both the supporting and the Auxiliary Factors. 

Complex Strategic Planes are governed by the follow- 
ing 

PRINCIPLE. 

Whenever the net value of the offensive force radiated 
by three or more kindred pieces is equal to the net 
mobility of the Objective Plane, then the given kindred 
pieces may checkmate the adverse King. 

A COMPLEX STRATEGIC PLANE. 
FIGURE 65. 

Slack. 




White. 
White to play and mate in one move. 



STRATEGIC PLANES. 7? 



PLANE TOPOGRAPHY. 

The following topographical features are peculiar to 
Strategic Planes : 

1. Objective Plane. 

2. Objective Plane Commanded. 

3. Point of Lodgment. 

4. Point of Impenetrability. 

5. Like Point. 

6. Unlike Point. 



78 



MAJOR TACTICS. 



The Objective Plane is composed of the point oc- 
cupied by the adverse King, together with the imme- 
diately adjacent points. 



THE OBJECTIVE PLANE. 
FIGURE 66. 

Black. 




















White. 



NOTE. The Objective Plane is commanded when it 
contains no point open to occupation by the adverse 
King, by reason of the radii of offence operated against 
it by hostile pieces. 



STRATEGIC PLANES. 



79 



AN OBJECTIVE PLANE COMMANDED. 

FIGURE 67. 

Black. 




White. 



80 



MAJOR TACTICS. 



A Point of Lodgment is a term used to signify that a 
kindred piece other than the Prime Tactical Factor has 
become posted upon a point which is contained within 
the Objective Plane. 



A POINT OF LODGMENT. 
FIGURE 68. 
Black. 




White. 



STRATEGIC PLANES. 



81 



A Point of Impenetrability is any point in the Objec- 
tive Plane which in a given situation is occupied by an 
adverse piece other than the King. 



A POINT OF IMPENETRABILITY. 
FIGURE 69. 

Black. 




Whitr. 



82 



MAJOR TACTICS. 



A Like Point is any point in the Objective Plane of 
the same color as that upon which the adverse King is 
posted. 



LIKE POINTS. 
FIGURE 70. 

Black. 
































White. 



STRATEGIC PLANES. 



83 



An Unlike Point is any point in the Objective Plane 
of opposite color to that upon which the adverse King 
is posted. 



UNLIKE POINTS. 
FIGURE 71. 

Black. 




White. 



BASIC PROPOSITIONS OF MAJOR 
TACTICS. 

Following are the twelve basic propositions of Major 
Tactics. Upon these are founded all tactical combina- 
tions which are possible in chess play. The first four 
propositions govern all calculations whose object is to 
win adverse pieces ; the next seven govern all calcula- 
tions whose object is to queen one or more pawns ; and 
the final one governs all those calculations whose object 
is to checkmate the adverse King. 

A Geometric Symbol is positive (G. S. P.) when the 
piece to which it appertains has the right of move in 
the given situation ; otherwise it is negative (G. S. N.) 

In all situations wherein the Exposed Piece has the 
right of move the Point Material is active (P. M. A.), 
and in all other cases the Point Material is passive 
(P. M. P.). 



BASIC PROPOSITIONS. 



85 



PROPOSITION I. THEOREM. 

Given a Geometric Symbol Positive (G. S. P.) having 
one or more Points Material (P. M.), then the kindred 
Prime Tactical Factor (P. T. F.) wins an adverse piece. 



FIGURE 72. 

(a.) 

luck. 




White. 
Either to move and win a piece. 



86 



MAJOR TACTICS. 



FIGURE 73. 
(6.) 



Black. 




White. 
Either to move and win a piece. 



BASIC PROPOSITIONS. 



87 



FIGURE 74. 
(c.) 

Black. 




While. 

Either to move and win a piece. 



88 



MAJOR TACTICS. 



FIGURE 75 



Black. 




White. 
Either to move and win a piece. 



BASIC PROPOSITIONS. 



89 



FIGURE 76. 



Block. 




White. 
Either to move and win a piece. 



90 



MAJOR TACTICS. 



FIGURE 77. 



Black. 




White. 
Either to move and win a piece. 



BASIC PROPOSITIONS. 



91 



PROPOSITION II. THEOREM. 



Given a Geometric Symbol Negative (G. S. N.) hav- 
ing two or more Points Material Active (P. M. A.), then 
the kindred Prime Tactical Factor (P. T. F.) wins an 
adverse piece. 



FIGURE 78. 

(a.) 

Black. 




White. 
Black to move, white to win a piece. 

NOTE Black, even with the move, can vacate only 
one of the vertices of the white geometric symbol. 
Therefore the remaining black piece is lost, according to 
Prop. I. 



92 



MAJOR TACTICS. 



FIGURE 79. 

(6.) 
Black. 




White. 
Black to move, white to win a piece. 

NOTE. Black, even with the move, cannot vacate 
the perimeter of the white Knight's octagon ; conse- 
quently the remaining black piece is lost, according to 
Prop. I. 



BASIC PROPOSITIONS. 



93 



FIGURE 80. 



Black. 




White. 



Black to move, white to win a piece. 

NOTE. Black, even with the move, cannot vacate 
the side of the white Bishop's triangle ; consequently 
the remaining black piece is lost, according to Prop. I. 



MAJOR TACTICS. 



FIGURE 81. 
(d.) 
Black. 




White. 

Black to move, white to win a piece. 

NOTE. The Knight cannot in one move support the 
Bishop, neither can the Bishop occupy its K 2 or K 8 to 
support the Knight, as these points are commanded by 
the white Rook. 



BASIC PROPOSITIONS. 



95 



FIGURE 82. 



Black. 




White. 
Black to move, white to win a piece. 

NOTE. Obviously all those points to which the black 
Knight can move are commanded by the white Queen. 



MAJOR TACTICS. 



FIGURE 83. 



Black. 




White. 
Black to move, white to win a piece. 

NOTE. The Bishop cannot support the Rook, neither 
can the Rook occupy K B 4 in support of the Bishop, as 
that point is commanded by the white King. 



BASIC PROPOSITIONS. 



97 



PROPOSITION III. THEOREM. 

Given a Sub-Geometric Symbol Positive (S. G. S. P.) 
having two or more Points Material Passive (P. M. P.), 
then the kindred Prime Tactical Factor (P. T. F.) wins 
an adverse piece. 

FIGURE 84. 
(a.) 
Black. 




White. 

White to move and win a piece. 



NOTE. The p awn? having the move, advances along 
its Front Offensive to that point where its logistic sym- 
hr.j niul its frt'ometric symbol intersect. 



98 



MAJOR TACTICS. 



FIGURE 85. 

w 

Black. 




White. 
White to move and win a piece. 



NOTE. The Point of Command is that centre or 
vertex where the logistic symbol and the geometric 
symbol intersect. 



BASIC PROPOSITIONS. 



FIGURE 86. 



Black. 




White. 
White to move and win a piece. 



NOTE. The diagram illustrative of any position al- 
ways should contain the logistic symbol and the geo- 
metric symbol appertaining to the Prime Tactical 
Factor. 



100 



MAJOR TACTICS. 



FIGURE 87. 

w 

Black. 




White. 
White to move and win a piece. 

NOTE. The Point of Command and the points mate- 
rial are all contained in the same sides of the Rook's 
quadrilateral. 



BASIC PROPOSITIONS. 



101 



FIGURE 88. 

M 

Black. 




White. 
White to move and win a piece. 

NOTE. The Point of Command is White's Q 5 as the 
logistic radii at Q R 4 do not intersect the centre or a 
vertex of the geometric symbol. 



102 



MAJOR TACTICS. 



FIGURE 89. 



Slack. 




White. 
White to move and win a piece. 



NOTE. The white King cannot move to Q 4 nor to 
K 3, on account of the resistance of the black pieces. 
But White wins, as the latter do not command K 4. 



BASIC PROPOSITIONS. 



103 



PROPOSITION IV. THEOREM. 

Given a piece which is both attacked and supported, 
to determine whether the given piece is defended. 

DEFENDED PIECE. 

FIGURE 90. 

(a.) 

Black. 



S/s/S/SSSSJ 'S/S'S"S'SS */SSSS"SSSi ,*"*"*"* 

m, w n. HI 





NOTE. With or without the move the white Q B P is 
defended. (See Eule page 109.) 



104 MAJOR TACTICS. 



SOLUTION. 

X = Any piece employed in the 

given evolution. 
Y = Piece attacked. 
B+R+R+Q= Attacking Pieces. 
B+R+R+Q= Supporting Pieces. 

B+R+R+Q=B+R+R+Q= Construction of the inequality. 

4 X = Number of terms contained in 

left side. 
4 X = Number of terms contained in 

right side. 
(B-l-R + R + Q) (B + R + R + Q) = Value of unlike terms. 



Thus, the given piece is defended, as the number of 
terms and the sum of their potential complements are 
equal. 



BASIC PROPOSITIONS. 



105 



DEFENDED PIECE. 

FIGURE 91. 

(b.) 

Black. 







White. 

NOTE. With or without the move the white Q B P 

is defended. 

SOLUTION. 

X = Any piece employed in the given 

evolution. 

Y = Piece attacked. 
B+R+Q+R= Attacking Pieces. 

B + R -f R = Supporting Pieces. 
B + R + Q+R>B-|-R + R = Construction of the inequality. 

4 X = Number of terms contained in left side. 
3 X = Number of terms contained in right 

side. 

4 x 3 X = Excess of left-side terms. 
(B + R) - (B + R) = Value of like terms. 

Q - R = Value of first unlike term. ? 



106 



MAJOR TACTICS. 



Thus the given piece is defended, for, although the 
number of terms contained in the left side of the in- 
equality exceeds by one the number of terms contained 
in the right side, the third term of the inequality is an 
unlike term, of which the initial contained in the left 
side is greater than the initial contained in the right 
side. 



UNDEFENDED PIECE. 

FIGURE 92. 

(a.) 

Black. 




White. 



NOTE. Without the move the white Q B P is unde- 
fended. 



BASIC PROPOSITIONS. '107 



SOLUTION. 

X = Any piece employed in the 

given evolution. 
Y = Piece attacked. 
B+R+R+Q= Attacking Pieces. 
B + R + R = Supporting Pieces. 

B+R+R+Q>B+R+R= Construction of the inequality. 
4 X = Number of terms contained in 

left side. 
3 X = Number of terms contained in 

right side. 

4 X 3 X = Excess of left-side terms. 
(B + R + R) - (B + R -|- R) = Value of unlike terms. 

Thus, there being no unlike terms, and the number of 
pieces contained in the left side exceeding the number 
of pieces contained in the right side, the given piece is 
undefended. 



108 



MAJOR TACTICS. 



UNDEFENDED PIECE. 

FIGURE 93. 

(b.) 
Black. 











White. 

NOTE. Without the move the white Q B P is un- 
defended. 

SOLUTION. 

X = Any piece employed in the 

given evolution. 
Y = Piece attacked. 
B+R+Q+R= Attacking Pieces. 

B + R = Supporting Pieces. 
Q-fR>B + R = Construction of the inequality. 
4 X = Number of terms contained in 

left side. 
2 X = Number of terms contained in 

right side. 

4 X - 2 X = Excess of left-side terms. 
(B + R) - (B + R) = Value of unlike terms. 



BASIC PROPOSITIONS. 109 

Thus the given piece is undefended as there are no 
unlike terms, and the number of terms on the left side 
exceeds the number of terms on the right side. 

RULE. 

I. Construct an algebraic inequality having on the 
left side the initials of the attacking pieces arranged 
in the order of their potential complements from left to 
right; and on the right side the initials of the Support- 
ing Pieces arranged in the order of their potential com- 
plements, and also from left to right ; then, 

If the sum of any number of terms taken in order 
from left to right on the left side of this inequality is 
not greater than the sum of the same number of terms 
taken in order from left to right on the right side, and if 
none of the terms contained in the left side are less 
than the like terms contained in the right side, the 
given piece is defended. 

II. In all cases wherein two or more of the Attacking 
Pieces operate coincident radfi of offence, or two or 
more of the Supporting Pieces operate coincident radii 
of defence, those pieces must be arranged in the con- 
struction of the inequality, not in the order of their 
potential complements, but in the order of their proxim- 
ity to the given piece. This applies only to the position 
of their initials with respect to each other; the pieces 
need not necessarily lie in sequence; but in all cases 
the initial of that piece of highest potential complement 
should be placed as far to the right on either side of the 
equality as possible. 



110 



MAJOR TACTICS. 



PROPOSITION V. THEOREM. 

Given a Square of Progression (S. P.) whose net 
area is equal to the net area of the adverse square of 
Progression, then, if the Primary Origins (P. 0.) are 
situated neither upon the same nor adjacent verticals, 
and if the Points of Junction are situated not upon 
the same diagonal, the kindred Prime Tactical Factor 
(P. T. F.) queens against an adverse pawn. 



FIGURE 94. 

Black. 




White. 
Either to move and queen a pawn. 



BASIC PROPOSITIONS. 



Ill 



PROPOSITION VI. THEOREM. 

Given a Square of Progression Positive (S. P. P.) 
whose net area is greater by not more than one hori- 
zontal than the net area of the adverse Square of Pro- 
gression Negative (S. P. N.), then, if the Primary Origins 
(P. 0.) are situated neither upon the same nor adjacent 
verticals, and the points of junction are situated not 
upon the same diagonals, the kindred Prime Tactical 
Factor (P. T. F.) queens against an adverse pawn. 



FIGURE 95. 

Slack. 




White. 
White to move, both to queen a pawn. 



112 



MAJOR TACTICS. 



PROPOSITION VII. THEOREM. 

Given a Square of Progression Positive (S. P. P.) 
whose net area is less by one horizontal than the net 
area of the adverse Square of Progression Negative 
(S. P. N.), then, if the Primary Origins (P. 0.) are situ- 
ated not upon the same nor adjacent verticals, the kin- 
dred Prime Tactical Factor (P. T. F.) will queen and 
will prevent the adverse pawn from queening. 

FIGURE 96. 

Black. 




White. 



White to move and queen a pawn and prevent the adverse pawn 
from queening. 



BASIC PROPOSITIONS. 



113 



PROPOSITION VIII. THEOREM. 

Given a Square of Progression Positive (S. P. P.) 
opposed to a knight's octagon, then, if the Disturbing 
Factor (D. F.) is situated without the corresponding 
Knight's octagon, or within the corresponding Knight's 
octagon, but without the Knight's octagon of next lower 
radius and on a square of opposite color to the square 
occupied by the kindred pawn, the Prime Tactical Factor 
{P. T. F.) queens against the adverse Knight. 



FIGURE 97. 

(a.) 
Black. 




White. 

White to move and queen a pawn. 



114 



MAJOR TACTICS. 



FIGURE 98. 

(60 
Slack. 




White. 
White to move and queen a pawn. 

DEMONSTRATION. A pawn queens without capture 
against an adverse Knight, if, in general, the Knight 
is situated (1) without the corresponding Knight's octa- 
gon, or (2) within the corresponding Knight's octagon, 
but without the Knight's octagon of next lower radius 
and on a square of opposite color to the square occupied 
by the pawn. 

In diagram No. 97, take the queening point (o) of 
the pawn as a centre, and make a Knight's move to B, 



BASIC PROPOSITIONS. 115 

C, D, and E; connect these points by straight lines and 
draw the vertical lines B A and E F ; then the figure 
A B C D E F (or 1-1) is part of an eight-sided figure, 
which may be called, for brevity's sake, a Knight's 
octagon of single radius. 

Similarly, describe the figure G H I J K (or 2-2) 
whose sides are parallel to those of the figure 1-1, but 
whose vertices are two Knight's moves distance from 
the point o ; this figure may be called a Knight's octagon 
of double radius. 

Now, if the pawn has the first move it will be seen, 
first, that a Knight situated anywhere within the octagon 
1-1, provided it be not en prise of the pawn (an assump- 
tion common to all situations), nor at K B 8 nor Q 8 (an 
exception peculiar to this situation), will be able to stop 
the pawn, either by preventing it from queening or by 
capturing it after it has queened ; secondly, that a 
Knight situated anywhere without the octagon 2-2 will 
be unable to stop the pawn ; and thirdly, that a Knight 
situated anywhere between the octagon 1-1 and 2-2, 
will be able to stop the pawn if it starts from a square 
of the same color as that occupied by the pawn (white, 
in this instance), but unable to do so if it starts from 
a square of the opposite color (in this instance, black). 

From diagram No. 98, it is apparent that four 
Knight's diagrams can be drawn on the surface of the 
chess-board, and the perimeter of a fifth may be con- 
sidered as passing through the lower left-hand corner. 
In this diagram the white pawn is supposed to start 
from a point on the King's Rook's file. 

If the pawn starts from K R 6, a black square, and 
having two moves to make in reaching the queening 
point, the Knight must be situated as in Fig. No. 98, 
within the octagon of single radius, or on a black square 



116 MAJOR TACTICS. 

between the octagon of single radius and the octagon of 
double radius. 

If the pawn starts from K R 5, a white square, and 
having three moves to make, the Knight must be situated 
within the octagon of double radius, or on a white 
square between the octagon of double radius and the 
octagon of triple radius (3-3). 

If the pawn starts from K R 4, a black square, and 
having four moves to make, the Knight must be situated 
within the octagon of triple radius, or in a black square 
between the octagon of triple radius and the octagon of 
quadruple radius (4-4). 

If the pawn starts from K R 3, a white square, having 
five moves to make, the Knight must be situated within 
the octagon of quadruple radius, or on a white square 
between the octagon of quadruple radius and the 
octagon of quintuple radius (5). In this last case it 
appears that the only square from whence the Knight 
can stop the pawn is Black's Q R 8. 

If the pawn starts from K R 2, it may advance two 
squares on the first move, and precisely the same con- 
ditions exist as if it started from K R 3. 

Still another octagon may be imagined to exist on the 
board, namely, the octagon of null radius, or simply 
the queening point (o), which is the centre of each of 
the other octagons. This being understood, it follows 
that if the pawn starts from KR 7, a white square, and 
having one move to make, the Knight must be situated 
within the octagon of null radius (o), i. e. at White's 
K R 8, or, on a white square between the octagon of 
null radius and the octagon of single radius, i. e. at K 
Kt 6 or at K B 7. 

From these data a general law may be deduced. In 
order to abbreviate the enunciation of this law, it is well 



BASIC PROPOSITIONS. 117 

to lay down these definitions : By " the Knight's octagon 
corresponding to a pawn," is meant that Knight's 
octagon whose centre is the queening point of the pawn, 
and whose radius consists of a number of Knight's 
moves equal to the number of moves to be made by 
the pawn in reaching its queening point ; and by " the 
Knight's octagon of next lower radius," is meant that 
Knight's octagon whose centre is the queening point of 
the pawn, and whose radius consists of a number of 
Knight's moves one less than the number of moves to be 
made by the pawn, in reaching its queening point. The 
law, then, is as follows : 

A Knight can stop a pawn that has the move and is 
advancing to queen, if the Knight is situated between 
the Knight's octagon corresponding to the pawn and the 
Knight's octagon of next lower radius, and on a square 
of the same color as that occupied by the pawn, or if 
the Knight is situated within the Knight's octagon of 
next lower radius ; provided, that the Knight be not en 
prise to the pawn, nor (if the pawn is at its sixth square) 
en prise to the pawn after the latter's first move. 



118 



MAJOR TACTICS. 



PROPOSITION IX. THEOREM. 

Given a Square of Progression Positive (S. P. P.) 
opposed to a Bishop's triangle, then, if the given square 
of progression is the smallest or the smallest but one, 
and if the Point of Junction is a square of opposite color 
to that occupied by the hostile integer, the kindred Prime 
Tactical Factor (P. T. F.) queens without capture against 
the adverse Bishop. 

FIGURE 99. 



Black. 




White. 
"White to move and queen a pawn. 



BASIC PROPOSITIONS. 



119 



PROPOSITION X. THEOREM. 

Given a Square of Progression Positive (S. P. P.) 
opposed to a Rook's quadrilateral or to a Queen's poly- 
gon, then, if the square of progression is the smallest 
possible, and if the hostile integer does not command 
the Point of Junction, the kindred Prime Tactical Factor 
queens without capture against the adverse Rook or 
Queen. 

FIGURE 100. 
(a.) 




White. 
White to move and queen a pawn. 



120 



MAJOR TACTICS. 



FIGURE 101. 
(6.) 

Slack. 




White. 
White to move and queen a pawn. 



BASIC PROPOSITIONS. 



121 



PROPOSITION XI. 

Given a Square of Progression Positive (S. P. P.) op- 
posed to a King's rectangle ; then, if the given King is 
not posted on a point within the given square of pro- 
gression, the given pawn queens without capture against 
the adverse King. 

FlGUEE 102. 
(a.) 
Black. 




White to move and.queen a pawn. 

*"* 



122 



MAJOR TACTICS. 



FIGURE 103. 
(6.) 

Black. 




White. 
White to move and queen a pawn. 



BASIC PROPOSITIONS. 



123 



PROPOSITION XII. THEOREM. 

Given a Geometric Symbol Positive (G. S. P.) or a 
combination of Geometric Symbols Positive which is 
coincident with the Objective Plane ; then, if the Prime 
Tactical Factor (P. T. F.) can be posted at the Point of 
Command, the adverse King may be checkmated. 



FIGURE 104. 

Black. 




WMts. 

White to play and mate in one move. 



SIMPLE TACTICAL PLANES. 



EVOLUTION No. 1. 

FIGURE 105. 
Pawn vs. Pawn. 

Black. 




White. 



When two opposing pawns are situated on adjacent 
verticals and each on its Primary Base Line, that side 
which has not the move wins the adverse pawn. 



SIMPLE TACTICAL PLANES. 



125 



EVOLUTION No. 2. 
FIGURE 106. 
Pawn vs. Pawn. 
Black. 




White. 



A pawn posted at its Primary Base Line and either 
with or without the move, wins an adverse pawn situated 
at the intersection of an adjacent vertical with the sixth 
horizontal. 



126 



MAJOR TACTICS. 



EVOLUTION No. 3. 

FIGURE 107. 
Pawn vs. Pawn. 

Black. 















4 




















TFMe. 



When the number of horizontals between two opposing 
pawns situated on adjacent verticals is even, that pawn 
which has the move wins the adverse pawn. 



SIMPLE TACTICAL PLANES. 



127 



EVOLUTION No. 4. 

FIGURE 108. 

Pawn vs. Pawn. 

Black. 




White 



When the number of horizontals between two opposing 
pawns situated on adjacent verticals, is odd, that pawn 
which has not to move wins the adverse pawn ; provided 
the position is not that of Evolution No. 2. 



w 



128 



MAJOR TACTICS. 



EVOLUTION No. 5. 

FIGURE 109. 
Pawn vs. Knight. 

Slack. 




























White. 



Whenever a pawn altitude is intersected by the per- 
iphery of an adverse Knight's octagon, then, if the pawn 
has not crossed the point of intersection, the adverse 
Knight wins the given pawn. 



SIMPLE TACTICAL PLANES. 



129 



EVOLUTION No. 6. 
FIGURE 110. 

Knight vs. Knight. 




White. 



A Knight posted at R 1 or R 8, and having to move, 
is lost if all the points on its periphery are contained in 
an adverse Knight's octagon. 



130 



MAJOR TACTICS. 



EVOLUTION No. 7. 

FIGURE 111. 
Bishop vs. Pawn. 

Black. 



























White. 



Whenever a pawn's altitude intersects a Bishop's 
triangle, then, if the pawn has not crossed the point of 
intersection, the adverse Bishop wins the given pawn. 



SIMPLE TACTICAL PLANES. 



131 



EVOLUTION No. 8. 

FIGURE 112. 
Bishop vs. Knight. 

Black. 




White. 



A Knight posted at R 1 or R 8, and with or without 
the move, is lost if all the points on its periphery are 
contained in the same side of the Bishop's triangle. 

NOTE. The B will equally win if posted at Q 8. 



132 



MAJOR TACTICS. 



EVOLUTION No. 9. 

FIGURE 113. 

Bishop vs. Knight. 

Black. 




White. 



A Knight posted at R 2, R 7, Kt 1, or Kt 8, and having 
to move, is lost, if all the points on its periphery are 
contained in the sides of an adverse Bishop's triangle. 



SIMPLE TACTICAL PLACES. 



133 



EVOLUTION No. 10. 

FIGURE 114. 
Bishop vs. Knight. 

Black. 




White. 



A Knight posted at R 4, R 5, K 1, K 8, Q 1, or Q 8, 
and having the move, is lost if all the points on its 
periphery are contained in the sides of an adverse 
Bishop's triangle. 



134 



MAJOR TACTICS. 






EVOLUTION No. 11. 

FIGURE 115. 

Rook vs. Pawn. 

Black. 






















White. 



Whenever a pawn altitude intersects a Rook's quad- 
rilateral, then, if the pawn has not crossed the point of 
intersection, the adverse Rook wins the given pawn. 

NOTE Obviously, whenever a pawn altitude is coin- 
cident with one side of a Rook's quadrilateral, all the 
points are points of intersection and the pawn is liable 
to capture when crossing each one. 



SIMPLE TACTICAL PLANES. 



135 



EVOLUTION No. 12. 

FIGURE 116. 
Rook vs. Knight. 

Black. 




A Knight posted at R 1 or R 8, and having to move, 
is lost if all the points on its perimeter are contained in 
the sides of an adverse Rook's quadrilateral. 

NOTE. Obviously the R would equally win if posted 
-at Q B 6. 



136 



MAJOR TACTICS. 



EVOLUTION No. 13 
FIGURE 117. 
Rook vs. Knight. 
Black. 

































White. 



A Knight posted at R 2, R 7, Kt 1, or Kt 8, and having 
to move, is lost if all the points on its periphery are con- 
tained in the sides of an adverse Rook's quadrilateral. 



SIMPLE TACTICAL PLANES. 



137 



EVOLUTION No. 14. 

FIGURE 118. 

Rook vs. Knight. 

Black. 




While. 



A Knight posted at Kt 2, or Kt 7, and having to move, 
is lost if all the points on its perimeter are contained 
in the sides of an adverse Rook's quadrilateral. 



138 



MAJOR TACTICS. 



EVOLUTION No. 15. 

FIGURE 119. 
Queen vs. Pawn. 

Black 




White. 

Whenever a pawn altitude intercepts an adverse 
Queen's polygon, then, if the pawn has not crossed the 
point of intersection, the adverse Queen wins the given 
pawn. 

NOTE. The Q will equally win if posted at Q B 1, Q 
R 1, K 1, K B 1, K Kt 1, K R 1, K 3, K B 4, K Kt 5, K R 
6, Q B 3, Q Kt 2, Q R 3, Q B 4, Q B 5, Q B 6, Q B 7, or 
Q B 8. 



SIMPLE TACTICAL PLANES. 



139 



EVOLUTION No. 16. 

FIGURE 120. 
Queen vs. Knight. 

Black. 




White. 



A Knight posted at R 1 or R 8, and having to move, is 
lost if all the points in its perimeter are contained in 
the sides of an adverse Queen's polygon. 

NOTE. The Q will equally win if posted at Q R 5, 
Q R 7, Q Kt 8, Q B 6, Q B 5 or Q 8. 



140 



MAJOR TACTICS. 



EVOLUTION No. 17. 
FIGURE 121. 

Queen vs. Knight. 
Black. 




White. 



A Knight posted at R 2, R 7, Kt 1, or Kt 8, and having 
to move, is lost if all the points on its perimeter are 
contained in the sides of an adverse Queen's polygon. 

NOTE. The Q will equally win if posted at Q 7, K 8, 
or Q B 5. 



SIMPLE TACTICAL PLANES. 



141 



EVOLUTION No. 18. 

FIGURE 122. 

Queen vs. Knight. 

Black. 




White. 



A Knight posted at R 4, R 5, K 1, K 8, Q 1, or Q 8, and 
having to move, is lost if all the points on its perimeter 
are contained in the sides of an adverse Queen's polygon. 

NOTE. The Q will equally win if posted at Q 5. 



142 



MAJOR TACTICS. 



EVOLUTION No. 19. 

FIGURE 123. 

Queen vs. Knight. 

Black. 




White. 



A Knight posted at Kt 2 or Kt 7, and having to move, 
is lost if all the points on its periphery are contained in 
the sides of an adverse Queen's polygon. 



SIMPLE TACTICAL PLANES. 



143 



EVOLUTION No. 20. 

FIGURE 124. 

King vs. Pawn. 

Black. 




White. 

Whenever the centre of a King's rectangle is con- 
tained in the square of progression of a pawn; then 
the adverse King wins the given pawn. 

NOTE. Obviously the King would equally win if 
posted on any square from the first to the third hori- 
zontal inclusive, the King's Rook's file excepted. 



144 



MAJOR TACTICS. 



EVOLUTION No. 21. 

FIGURE 125. 

King vs. Knight. 

Black. 

























While. 





A Knight posted at El or E, 8, and having to move, 
is lost if all the points on its periphery are contained in 
the sides of an adverse King's rectangle. 

NOTE. The K would equally win if posted at Q B 6. 



SIMPLE TACTICAL PLANES. 



145 



EVOLUTION No. 22. 

FIGURE 126. 

Two Pawns vs. Knight. 

Black. 




Whitt. 



A Knight situated at R 1, and having to move, is lost 
if all the points on its perimeter are contained in two 
adverse pawn triangles. 

NOTE. The pawns will equally win if posted at Q 6 
and Q B 5 ; or at Q R 5 and Q Kt 6. 



MAJOR TACTICS. 



EVOLUTION No. 23. 

FIGURE 127. 

Two Pawns vs. Bishop. 

Black. 




A Bishop posted at R 1, and with or without the move, 
is lost if the point which it occupies is one of the verti- 
ces of a pawn's triangle. 

NOTE. The pawns equally win if posted at QB6 
and Q Kt 7. 



SIMPLE TACTICAL PLANES. 



147 



EVOLUTION No. 24. 

FIGURE 128. 

Pawn and Knight vs. Knight. 
Black. 




Whenever a point of junction is the vertex of a mathe- 
matical figure formed by the union of the logistic 
symbol of a pawn with an oblique, diagonal, horizontal, 
or vertical from the logistic symbol of any kindred 
piece ; then the given combination of two kindred pieces 
wins any given adverse piece. 

NOTE. Obviously it is immaterial what the kindred 
piece may be, so long as it operates a radius of attack 
against the point Q 8 ; nor what the adverse piece may 
be, nor what its position, so long as it does not attack 
the white pawn at Q 7. 



148 



MAJOR TACTICS. 



EVOLUTION No. 25. 

FIGURE 129. 

Pawn and Knight vs. Bishop. 
Black. 




White. 

Whenever a piece defending a hostile point of junc- 
tion is attacked, then, if the point of junction and all 
points on the periphery of the given piece wherefrom it 
defends the point of junction, are contained in the 
geometric symbol which appertains to the adverse piece, 
the piece defending a hostile point of junction is lost. 



SIMPLE TACTICAL PLANES. 



149 



EVOLUTION No. 26. 

FIGURE 130. 

Bishop and Pawn vs. Bishop. 
Black. 




White. 

Whenever an adjacent Point of Junction is com- 
manded by a kindred piece, the adverse defending piece 
is lost. 

NOTE. Obviously, it is immaterial what may be 
either the kindred piece or the adverse piece ; the white 
pawn queens by force, and the kindred piece wins the 
adverse piece, which, of course, is compelled to capture 
the newly made Queen. 



150 



MAJOR TACTICS. 



EVOLUTION No. 27. 

FIGUKB 131. 

Eook and Pawn vs. Rook. 
Black. 




? M 

* ...,y / ' /// " // ',. 
























White. 



NOTE. White wins easily by R to K 7 supporting the 
kindred pawn ; followed by R to K 8 upon the removal of 
the black Rook from Q 1. 



SIMPLE TACTICAL PLANES. 



151 



EVOLUTION No. 28. 

FIGURE 132. 
Two Knights vs. Knight. 

Black. 




White. 



A Knight having to move is lost if all the points in its 
periphery are commanded by adverse pieces. 



152 



MAJOR TACTICS. 



EVOLUTION No. 29. 

FIGURE 133. 

Knight and Bishop vs. Knight. 
Black. 



















White. 



NOTE. White wins by Kt to Q 6, or Kt to K 7, thus 
preventing the escape of the adverse Knight via Q B 1. 



SIMPLE TACTICAL PLANES. 



153 



EVOLUTION No. 30. 

FIGURE 134. 

Rook and Knight vs. Knight. 
Black. 




White 



NOTE. White wins by Kt to K 5, thus preventing the 
escape of the adverse Knight via Q B 3 and Q B 5. 



154 



MAJOR TACTICS. 



EVOLUTION No. 31. 

FIGURE 135. 

Queen and Knight vs. Knight. 
Black. 




White. 



NOTE. White wins if Black has to move. 



SIMPLE TACTICAL PLANES. 



155 



EVOLUTION No. 32. 

FIGURE 136. 

King and Knight vs. Knight. 
Black. 




White. 



NOTE. White wins if Black has to move. 



156 



MAJOR TACTICS. 



EVOLUTION No. 33. 

FIGURE 137. 
Queen and Bishop VB. Knight. 

Black. 





























White. 



NOTE. White wins either with or without the move. 



SIMPLE TACTICAL PLANES 



157 



EVOLUTION No. 34. 

FIGURE 138. 

Queen and Rook rs. Knight. 
Black. 




White. 



NOTE. White wins either with or without the move. 



158 



MAJOR TACTICS. 



EVOLUTION No. 35. 

FIGURE 139. 

King and Queen vs. Knight. 
Black, 




















White. 



NOTE. White wins either with or without the move. 



COMPOUND TACTICAL PLANES. 



EVOLUTION No. 36. 

FIGURE 140. 
Pawn vs. Two Knights. 

Black. 




VTiite. 

Whenever two adverse pieces are posted on the verti- 
ces of a pawn's triangle and on the same horizontal, 
then if neither piece commands the remaining vertex, 
the given pawn, having to move, wins one of the adverse 
pieces. 

NOTE. White wins by P to K 4. The pawn would 
equally win if posted at K 3. 



160 



MAJOR TACTICS. 



EVOLUTION No. 37. 

FIGURE 141. 

Knight vs. Rook and Bishop. 
Black. 




White. 



Whenever two adverse pieces are situated on the 
perimeter of a Knight's octagon, then if neither piece 
commands the centre point nor can support the other 
only by occupying another point on the perimeter of the 
said octagon, the given Knight, having to move, wins one 
of the adverse pieces. 



COMPOUND TACTICAL PLANES. 



161 



EVOLUTION No. 38. 

FIGURE 142. 

Knight rs. King and Queen. 
Black. 




WhUf. 



Whenever the adverse King is situated on the perime- 
ter of any opposing geometric symbol, another point on 
which is occupied by an unsupported adverse piece which 
the King cannot defend by a single move, or by another 
adverse piece superior in value to the attacking piece, 
then the given attacking piece makes a gain in adverse 
material. 

NOTE. For after the check the white Knight takes 
an adverse Queen or Rook, regardless of the fact that 
itself is thereby lost. 



162 



MAJOR TACTICS. 



EVOLUTION No. 39. 

FIGURE 143. 
Bishop vs. Two Pawns. 

Black. 




White. 



NOTE. White wins either with or without the move. 



COMPOUND TACTICAL PLANES. 



163 



EVOLUTION No. 40. 

FIGURE 144. 
Bishop vs. King and Pawn. 

Black. 




White. 



NOTE. White wins by checking at Q Kt 3, for the 
black King is not able to defend the pawn in one move. 



164 



MAJOR TACTICS. 



EVOLUTION No. 41. 

FIGURE 145. 

Bishop vs. King and Knight. 
Black. 




White. 



NOTE. White wins by B to Q Kt 3 for Black is un- 
able to defend the Knight in one move. 



COMPOUND TACTICAL PLANES. 



165 



EVOLUTION No. 42. 

FIGURE 146. 
Bishop vs. Two Knights. 

Black. 




White. 



NOTE. White wins by B to Q 5 as neither of the ad- 
verse pieces are able to support the other in a single 
move. 



166 



MAJOR TACTICS. 



EVOLUTION No. 43. 

FIGURE 147. 

Bishop vs. King and Knight. 
Black. 




White. 



NOTE. White wins by B to Q B 4 (ck), for the ad- 
verse King is unable to support the black Knight in a 
single move. 



COMPOUND TACTICAL PLANES. 



167 



EVOLUTION No. 44. 

FIGURE 148. 

Rook vs. Two Knights. 

Black. 




Whenever two Knights are simultaneously attacked 
by an adverse piece, then if one of the Knights has to 
move, the adverse piece wins one of the given Knights. 



168 



MAJOR TACTICS. 



EVOLUTION No. 45. 

FIGURE 149. 
Rook vs. Knight and Bishop. 

Black. 




White. 



Whenever a Knight and a Bishop occupying squares 
opposite in color, or of like color but unable to support 
each other in one move, are simultaneously attacked, 
then, either with or without the move, the adverse piece 
wins the given Bishop or the given Knight. 



COMPOUND TACTICAL PLANES. 



169 



EVOLUTION No. 46. 

FIGURE 150. 

Rook vs. Knight and Bishop. 
Black. 




White. 



NOTE. White wins either with or without the move. 



170 



MAJOR TACTICS. 



EVOLUTION No. 47. 

FIGURE 151. 

Queen vs. Knight and Bishop. 
Black. 




White. 



NOTE. White wins either with or without the move. 



COMPOUND TACTICAL PLANES. 



171 



EVOLUTION No. 48. 

FIGURE 152. 

Queen vs. Knight and Bishop. 
Black. 




White 



NOTE. White wins either with or without the move. 



172 



MAJOR TACTICS. 



EVOLUTION No. 49. 

FIGURE 153. 
Queen vs. Rook and Knight. 

Black. 




White. 



NOTE. White wins either with or without the move. 



COMPOUND TACTICAL PLANES. 



173 



EVOLUTION No. 50. 

FIGURE 154. 
Queen vs. Rook and Bishop. 

Black. 




White. 



NOTE. White wins either with or without the move. 



174 



MAJOR TACTICS. 



EVOLUTION No. 51. 
FIGURE 155. 

King vs. Knight and Pawn. 
Slack. 





























White. 



NOTE. White wins either with or without the move. 



COMPOUND TACTICAL PLANES. 175 

4% 




DEVOLUTION No. 52. 



FIGURE 156. 



King vs. Bishop and Pawn. 
Black. 




White. 



NOTE. White wins either with or without the move. 







c^f-s 



176 



MAJOR TACTICS. 



EVOLUTION No. 53. 

FIGURE 157. 

King vs. King and Pawn. 
Black. 

























!JL 







White. 



NOTE. White loses if he has to move, and wm& &e , 
if he has not to move. 



COMPOUND TACTICAL PLANES. 



Ill 



EVOLUTION No. 54 

FIGURE 158. 
Knight vs. Three Pawns. 

Black. 




White. 



NOTE. White, if he has not to move, will win all the 
adverse pawns. 



178 



MAJOR TACTICS. 



EVOLUTION No. 55. 

FIGURE 159. 
Bishop vs. Three Pawns. 

Black. 

























White. 



NOTE. White, if he has not to move, wins all the ad- 
verse pawns. 



COMPOUND TACTICAL PLANES. 



179 



EVOLUTION No. 56. 

FIGURE 160. 
Rook vs. Three Pawns. 

Slack. 




While. 



NOTE. White, if he has not to move, will win all 
the adverse pawns, ^^ W4t> *<rv* *w< ^- fcKf /, 

/ ' 



130 



MAJOR TACTICS. 



EVOLUTION No. 57. 

FIGURE 161. 
King vs. Three Pawns. 

Black. 




White. 



NOTE. White, if he has not to move, will win all 
the adverse pawns. 



COMPOUND TACTICAL PLANES. 



181 



EVOLUTION No. 68. 

FIGURE 162. 
Knight vs. Bishop and Pawn. 

Slack. 




Wftitf. 



<*' 



. 



NOTE. White, with the move, wins' by Kt to K B 8, 
as both the black pieces are simultaneously attacked 
and will not mutually support each other after Black's 
next move. 



182 



MAJOR TACTICS. 



EVOLUTION No. 59. 

FIGURE 163. 

Bishop vs. Bishop and Pawn. 
Black. 




White. 



NOTE. White wins either with or without the move. 



COMPLEX TACTICAL PLANES. 



EVOLUTION No. 60. 

FIGURE 164. 

Knight and Pawn vs. King and Queen. 
Black. 




White. 



NOTE. By the sacrifice of the pawn by P to Q 5 (ck) 
all the pieces become posted on the perimeter of the 
same Knight's octagon, and White, having the move, 
v. : n, in accordance with Prop. IV. 



184 



MAJOR TACTICS. 



EVOLUTION No. 61. 

FIGURE 165. 

Knight and Pawn vs. King and Queen. 
Slack. 




White. 



NOTE. White, having the move, wins by P to Kt 8 
(queening), followed by Kt to K B 6 (ck). 



COMPLEX TACTICAL PLANES 



185 



EVOLUTION No. 62. 

FIGURE 166. 
Bishop and Pawn vs. King and Queen 

Black. 




White. 



NOTE. White, having the move, wins by sacrificing 
the pawn by P to Q B 4 (ck) and thus bringing all the 
pieces on the perimeter of the same Bishop's triangle. 



186 



MAJOR TACTICS. 



EVOLUTION No 63. 

FIGURE 167. 
Knight and Bishop vs. King and Queen. 

Slack. 













vULf 












White. 



NOTE. White, having the move, wins by B to K B 7 
(ck). 



COMPLEX TACTICAL PLANES. 



187 



EVOLUTION No. 64. 

FIGURE 168. 
Bishop and Knight vs. King and Queen. 

Black. 




White. 



NOTE. White, having the move, wins by B to Q 5 
(ck), followed by Kt to K B 6 (ck). 



188 



MAJOR TACTICS. 



EVOLUTION No. 65. 

FIGURE 169. 

Knight and Bishop vs. King and Queen. 
Slack. 




White. 



NOTE. White, having the move, wins by B to Q 5, 
followed by Kt to K B 6 (ck). 



COMPLEX TACTICAL PLANES. 



189 



EVOLUTION No. 66. 

FIGUKE 170. 

Knight and Bishop vs. King and Queen. 
Black. 




While. 



NOTE. White, having the move, wins by B to K Kt 7 
(ck), followed by Kt to K B 5 (ck). 



190 



MAJOR TACTICS. 



EVOLUTION No. 67. 
FIGURE 171. 

Knight and Bishop vs. King and Queen. 
Slack. 
























White. 



NOTE. White, having to move, wins by B to Q 6 (ck), 
followed, if K x B, by Kt to K 4 (ck), and if Q x B, by 
Kt to K B 5 (ck). 



COMPLEX TACTICAL PLANES. 



191 



EVOLUTION No, 68. 
FIGURE 172. 

Knight and Bishop vs. King and Queen. 

Black. 




White. 



NOTE. White, having to move, wins by Kt to K Kt 5 
(ck). 



192 



MAJOR TACTICS. 



EVOLUTION No. 69. 

FIGURE 173. 

Knight and Bishop vs. King and Queen. 
Black, 




White. 



NOTE. White, having to move, wins by either Kt to 
K B 2 or Kt to Q 5. 



COMPLEX TACTICAL PLANES. 



193 



EVOLUTION No. 70. 

FIGURE 174. 
Knight and Rook vs. King and Queen. 

Black. 




White. 



NOTE. White, having to move, wins by R to Q Kt 5, 
followed by Kt to Q 4 (ck). 



194 



MAJOR TACTICS. 



EVOLUTION No. 71. 

FIGURE 175. 
Rook and Knight vs. King and Queen. 

Black. 
























White. 



NOTE. White, having to move, wins by B, to Q 8 (ck), 
followed by Kt to K 6 (ck). 



COMPLEX TACTICAL PLANES. 



195 



EVOLUTION No. 72. 

FIGURE 176. 

Rook and Knight vs. King and Queen. 
Black. 






























White. 



NOTE. White, having to move, wins by R to K B 5 
(ck), followed by Kt to Q 4 (ck). 



196 



MAJOR TACTICS. 



EVOLUTION No. 73. 

FIGURE 177. 

Queen and Bishop vs. King and Queen, 
Black. 




White. 



NOTE. White, having to move, wins by B to K Kt 4 
(ck). 



COMPLEX TACTICAL PLANES. 



197 



EVOLUTION No. 74. 

FIGURE 178. 
Queen and Rook vs. King and Queen. 

Black. 




White. 



NOTE. White, having to move, wins by R to K B 6 
(ck). 



198 



MAJOR TACTICS. 



EVOLUTION No. 75. 

FIGURE 179. 

Bishop and Pawn vs. King and Knight. 
Black. 




White. 



NOTE. White, having to move, wins by P to Q 8 
(queening), followed by B to K 7 (ck). 



COMPLEX TACTICAL PLANES. 



199 



EVOLUTION No. 76. 

FIGURE 180. 
Bishop and Pawn vs. King and Bishop. 

Black. 




White. 



NOTE. White, having to move, wins by B to K B 
(ck), followed by P to Q B 8 (queening). 



200 



MAJOR TACTICS. 



EVOLUTION No. 77. 

FIGURE 181. 
Bishop and Pawn vs. Bishop and Knight. 

Black. 




White. 



NOTE. White, having to move, wins material by P 
to Q 8 (queening). 



COMPLEX TACTICAL PLANES. 



201 



EVOLUTION No. 78. 

FIGURE 182. 
Bishop and Pawn vs. Rook and Knight. 

Black. 



























While. 



NOTE. White, having to move, wins material by P 
to K 8 (queening), followed by B to Q 7. 



202 



MAJOR TACTICS. 



EVOLUTION No. 79. 

FIGURE 183. 

Bishop and Pawn us. King and Queen. 
Black. 




White. 



NOTE. White, having to move, wins by P to K B 8 
(queening), followed by B to Q Kt 4 (ck). 



COMPLEX TACTICAL PLANES. 



203 



EVOLUTION No. 80. 

FIGURE 184. 
Hook and Pawn vs. King and Bishop. 

Black. 




White. 



NOTE. White, having to move, wins by P to K 7, fol- 
lowed, if B x P, by R to K 8. Otherwise, the pawn 
queens and wins. 



204 



MAJOR TACTICS. 



EVOLUTION No. 81. 

FIGUBE 185. 

Rook and Pawn vs. King and Rook. 
Black. 




White. 



NOTE. White, having to move, wins by P to K 8 
(queening), and followed, if K X Q, by R to R 8 (ck) and 
RtoRT (ck). 



COMPLEX TACTICAL PLANES. 



205 



EVOLUTION No. 82. 

FIGURE 186. 

Rook and Pawn r*. King and Queen. 
Black. 




White. 



NOTE. White, having to move, wins by Rto K B 8 
(ck), followed by P to Q 8 (queening). 



206 



MAJOR TACTICS. 



EVOLUTION No. 83. 
FIGURE 187. 

Queen and Pawn vs. Rook and Bishop. 
Black. 
















t m 








White. 



NOTE. White, having to move, wins by P to Q 8 
(queening), followed, if B x Q, by Q to Q 7. 



COMPLEX TACTICAL PLANES. 



207 



EVOLUTION No. 84. 

FIGURE 188. 

Queen and Pawn vs. Rook and Knight. 
Black. 




White. 



NOTE. White, having to move, wins by P to R 8 
(queening), followed, if R x Q, by Q to K Kt 7. 






208 



MAJOR TACTICS. 



EVOLUTION No. 85. 
FIGURE 189. 

Queen and Pawn vs. Bishop and Knight. 

Black. 




NOTE. White, having to move, wins by P to K 6, 
followed, if Kt x P, by either Q to K 4 or Q to K 8. 



COMPLEX TACTICAL PLANES. 



209 



EVOLUTION No. 86. 

FIGURE 190. 
King and Pawn vs. Bishop and Knight. 

Black. 




White. 



NOTE. White, having to move, wins by P to Q 8 
(queening), followed, if B x Q, by K x Kt. 



210 



MAJOR TACTICS. 



EVOLUTION No. 87. 
FIGURE 191. 

King and Pawn vs. Two Knights. 
Black. 





White. 



NOTE. White, having to move, wins by P to Q 8 
(queening). 



SIMPLE LOGISTIC PLANES. 



EVOLUTION No. 88. 
FIGURE 192. 

Pawn vs. Pawn. 
Black. 




White. 



NOTE. Either to move and queen without capture. 



212 



MAJOR TACTICS. 



EVOLUTION No. 89. 

FIGURE 193. 

Pawn vs. Pawn. 

Black. 










. 

'//////////s. dH^ 

















White. 



NOTE. White, having to move, wins, first queening 
his pawn and then with the newly made queen captur- 
ing the adverse pawn. If white has not the move, the 
black pawn queens without capture. 



SIMPLE LOGISTIC PLANES. 



213 



EVOLUTION No. 90. 

FIGURE 194. 
Pawn vs. Pawn. 
Black. 




White. 



XOTE. White, either with or without the move, 
queens and captures the adverse pawn. 



214 



MAJOR TACTICS. 




EVOLUTION No. 91. 

Fioure 195. 
Pawn vs. Knight. 
Black. 



























White. 



NOTE. White, having to move, queens without 
capture. 



SIMPLE LOGISTIC PLANES. 



215 



EVOLUTION No. 92. 

FIGURE 196. 
Pawn vs. Bishop. 

Black. 

























White. 



NOTE. White, either with or without the move, 
queens without capture. 



MAJOR TACTICS. 



EVOLUTION No. 93. 

FIGURE 197. 

Pawn vs. King. 

Black. 




White. 



NOTE. White, having to move, queens without 
capture. 



SIMPLE LOGISTIC PLANES. 



217 



EVOLUTION No. 94. 

FIGURE 198. 
Pawn and Knight vs. Queen or Rook. 

Black. 




White. 

Whenever a Queen or Rook defending a hostile Point 
of Junction has not the move, then if an adverse piece 
can be in one move posted on the adjacent vertex of the 
pawn's triangle, the given pawn queens without capture. 

XOTE. It is, of course, immaterial what the kin- 
dred piece may be, so long as it can occupy the point 
K 8 ; or what the position of the defending piece, if it 
does not attack the pawn at Q 7. 



218 



MAJOR TACTICS. 



EVOLUTION No. 95. 

FIGURE 199. 
Bishop and Pawn vs. King and Rook. 

Slack. 




White. 



NOTE. White, having to move, wins by B to K R 3 
(ck), followed by B to Q B 8. 



SIMPLE LOGISTIC PLANES. 



219 



EVOLUTION No. 96. 

FIGURE 200. 
Rook and Pawn vs. Rook. 

White. 




White. 



NOTE. White wins, either with or without the more. 



220 



MAJOR TACTICS. 



EVOLUTION No. 97. 

FIGURE 201. 

Knight and Pawn vs. King. 
Black. 

























White. 



NOTE. White, either with or without, wins, as 
the black King cannot gain command of the Point 
of Junction. 



SIMPLE LOGISTIC PLANES. 



221 



EVOLUTION No. 98. 

FIGURE 202. 

Rook and Pawn vs. King. 
Black. 























W/. 











White. 



NOTE. White wins, either with or without the move, 
as the adverse King cannot attack any point on the kin- 
dred pawn's altitude. 



222 



MAJOR TACTICS. 



EVOLUTION No. 99. 

FIGURE 203. 
Bishop and Pawn vs. King and Queen. 

Black. 






















White. 



NOTE. White, having the move, wins by P to Q 8, 
queening and disclosing check from the kindred Bishop. 



COMPOUND LOGISTIC PLANES. 



EVOLUTION No. 100. 

FIGURE 204. 

Two Pawns vs. Pawn. 

Black. 






Hi 































White. 



NOTE. White wins, either with or without the move, 
by eliminating the adverse Point of Resistance by 
P to Q 6, or by P to Q Kt 6 ; clearing the vertical of 
one or the other of the kindred pawns. 



224 



MAJOR TACTICS. 



EVOLUTION No. 101. 

FIGURE 205. 
Two Pawns vs. Pawn. 

Black. 






















White. 



NOTE. White wins, either with or without the move. 



COMPOUND LOGISTIC PLANES. 



EVOLUTION No. 102. 

FIGURE 206. 
Two Pawns vs. Knight. 

Black. 




White. 



NOTE. White, having the move, will queen one of 
the pawns without capture by the adverse Knight. 



226 



MAJOR TACTICS. 



EVOLUTION No. 103. 

FIGURE 207. 
Two Pawns vs. Knight. 

Black. 




White. 



NOTE. White, either with or without the move, will 
queen one of the pawns without capture by the adverse 
Knight. 



COMPOUND LOGISTIC PLANES. 



227 



EVOLUTION No. 104. 

FIGURE 208. 
Two Pawns vs. Bishop. 




White. 



NOTE. White, either with or without the move, will 
queen one of the pawns without capture by the adverse 
Bishop. 



228 



MAJOR TACTICS. 



EVOLUTION No. 105. 
FIGURE 209. 

Two Pawns vs. Bishop. 
Slack. 




White. 



NOTE. White, either with or without the move, will 
queen one of the pawns without capture by the adverse 
Bishop. 



COMPOUND LOGISTIC PLANES. 



229 



EVOLUTION No. 106. 

FIGURE 210. 
Two Pawns vs. Rook 

Black. 




White. 



NOTE. White, either with or without the move, will 
queen one of the pawns without capture by the adverse 
Rook. 



230 



MAJOR TACTICS. 



EVOLUTION No. 107. 

FIGURE 211. 
Two Pawns vs. King. 

Black. 




White. 



NOTE. White, either with or without the move, will 
queen one of the pawns without capture by the adverse 
King. 



COMPOUND LOGISTIC PLANES. 



231 



EVOLUTION No. 108. 

FIGURE 212. 

Two Pawns vs. King. 

Black. 






























While. 



NOTE. White, either with or without the move, will 
queen one of the pawns without capture by the adverse 
King. 



COMPLEX LOGISTIC PLANES. 




EVOLUTION No. 109. 

FIGURE 213. 

Three Pawns vs. Three Pawns. 
Black. 




White. 



NOTE. White, having to move, will queen a pawn 
without capture by T'to Q 6^ followed, if K P x P, by P to 
Q B 6 ; and if B P x P, by Pto K 6. 



COMPLEX LOGISTIC PLANES. 



233 



EVOLUTION No. 110. 

FIGURE 214. 

Three Pawns vs. King. 
Black. 




White 



NOTE. If White moves, Black wins all the pawns 
by moving the King in front of that pawn which ad- 
vances ; but if Black has to move, one of the pawns 
will queen without capture against the adverse King. 

The key of the position is the posting of the King in 
front of the middle pawn, with one point intervening, 
when all are in a line and when it is the turn of the 
pawns to move. Then the King must play to the point 



in frnr.1. nf 



Tinxvn <l-nt 



234 



MAJOR TACTICS. 



EVOLUTION No. 111. 

FIGURE 215. 
Three Pawns vs. Queen. 

Black. 






















White. 





NOTE Black wins, either with or without the move. 
The key of this position is that the black Queen wins 
if she is posted on any square opposite in color to those 
occupied by the pawns, from whence she commands 
the adjacent Point of Junction. 



COMPLEX LOGISTIC PLANES. 



235 



EVOLUTION No. 112. 

FIGURE 216. 

Three Pawns vs. King and Pawn. 
Black. 




White. 



NOTE. White wins, either with or without the move. 



SIMPLE STRATEGIC PLANES. 



EVOLUTION No. 113. 

FIGURE 217. 
Knight vs. Objective Plane of Single Radius. 

Black. 



























White. 



NOTE. The Front Offensive always is an oblique, and 
the Point of Command of unlike color to the Point 
Material, and the radius a point on the perimeter of the 
adverse Knight's octagon. 



SIMPLE STRATEGIC PLANES. 



237 



EVOLUTION No. 114. 

FIGURE 218. 

Knight vs. Objective Plane of Two Radius. 
Black. 




NOTE. The Front Offensive always is an oblique ; 
the Point of Command of unlike color to the Point 
Material, and the radius is a section of two points on 
the adverse Knight's octagon. 



238 



MAJOR TACTICS. 



EVOLUTION No. 115. 

FIGURE 219. 
Bishop vs. Objective Plane of Two Radius. 

Black. 




White. 



NOTE. The Front Offensive always is a diagonal; 
the Point of Command and the radius are of like color 
to the Point Material, and the latter is situated on the 
same side of the Bishop's triangle as the Point of 
Command. 



SIMPLE STRATEGIC PLANES, 



239 



EVOLUTION No. 116. 
FIGURE 220. 

Bishop vs. Objective Plane of Three Radius. 




White 



XOTE. The Front Offensive always is a diagonal ; 
the Point of Command and the radius are of like color 
to the Point Material, and the latter is situated on 
the same side of the Bishop's triangle as the Point of 
Command. 



240 



MAJOR TACTICS. 



EVOLUTION No. 117. 

FIGURE 221. 

Rook vs. Objective Plane of Two Radius. 
Slack. 




White. 



NOTE. The Front Offensive is a vertical or hori- 
zontal; the radius is composed of one like and one 
unlike point, and situated on one side of the adverse 
Rook's quadrilateral. The Point of Command may be 
either a like or an unlike point. 



SIMPLE STRATEGIC PLANES. 



241 



EVOLUTION No. 118. 

FIGURE 222. 
Rook vs. Objective Plane of Three Radius. 

Black. 



























White. 



NOTE. The Front Offensive is a vertical or hori- 
zontal ; the radius is composed of one like and two 
unlike points and situated on one side of the adverse 
Rook's quadrilateral. The Point of Command may be 
either a like or an unlike point. 



242 



MAJOR TACTICS. 



EVOLUTION No. 119. 

FIGURE 223. 
Queen vs. Objective Plane of Two Kadius. 

Black. 




White. 



NOTE. The Front Offensive is a diagonal ; the radius 
is composed of two like points situated on the same side 
of the adverse Queen's polygon. The Point of Com- 
mand and the Point Material are like points. 



SIMPLE STRATEGIC PLANES. 



243 



EVOLUTION No. 120. 

FIGDBE 224. 
Queen vs. Objective Plane of Two Radius. 

Black. 




White. 



NOTE. The Front Offensive is a vertical or a hori- 
zontal ; the radius is composed of one like and one un- 
like point, contained in the same side of the adverse 
Queen's polygon. The Point of Command may be either 
a like or an unlike point. 



MAJOR TACTICS. 



EVOLUTION No. 121. 

FIGURE 225. 

Queen us. Objective Plane of Three Radius. 
Black. 




White. 



NOTE. The Front Offensive is a diagonal ; the radius 
is composed of like points, contained in the same side 
of the adverse Queen's polygon. The Point of Com- 
mand and the Point Material are like points. 



SIMPLE STRATEGIC PLANES. 



245 



EVOLUTION No. 122. 

FIGURE 226. 

Queen vs. Objective Plane of Three Radius. 
Black. 










iHi 





















White. 



NOTE. The Front Offensive is a vertical or hori- 
zontal ; the radius is composed of one like and two un- 
like points, contained in the same side of the adverse 
Queen's polygon. The Point of Command may be 
either a like or an unlike point. 



246 



MAJOR TACTICS. 



EVOLUTION No. 123. 

* FIGURE 227. 

Queen vs. Objective Plane of Four Radius. 
Black. 




White. 



NOTE. The Front Offensive is a vertical or hori- 
zontal combined with a diagonal ; the radius is com- 
posed of " two like and two unlike points, and these are 
coincident with given sides of the Queen's polygon. 
The Point of Command and the Point Material are like 
points. 



COMPOUND STRATEGIC PLANES. 



EVOLUTION No. 124. 

FIGURE 228. 
Pawn and Supporting Factor vs. Objective Plane of Two Radius. 

Black. 







* 

* 



























White. 

NOTE. A single Pawn cannot command any Ob- 
jective Plane. In this situation, the Front Offensive is 
a diagonal ; the radius is composed of two like points 
and contained on the same side of the adverse Pawn's 
triangle. The Point of Command and the Point Mate- 
rial are like Points. 



248 



MAJOR TACTICS. 



EVOLUTION No. 125. 

FIGURE 229. 
Bishop and Supporting Factor vs. Objective Plane of Three Radius 

Black. 




NOTE. The Front Offensive is a diagonal ; the radius 
is composed of two like points, contained in the same 
side of the adverse Bishop's triangle, and one unlike 
point contained in the perimeter of the supporting 
Factor. The Point of Command is a like point. 



COMPOUND STRATEGIC PLANES. 



249 



EVOLUTION No. 126. 

FIGURE 230. 

Bishop and Supporting Factor vs. Objective Plane of Three Radius. 

Block. 




While. 



NOTE. The Front Offensive is made up of a diago- 
nal and an oblique ; the radius is composed of three 
like points, all of which are contained in the adverse 
diagonal. The Point of Command is a like point. 



250 



MAJOR TACTICS. 



EVOLUTION No. 127. 

FIGURE 231. 

Rook and Supporting Factor vs. Objective Plane of Three Radius. 

Slack. 




While. 

NOTE. The Front Offensive is made up of a vertical 
or horizontal and an oblique ; the radius is composed of 
two like and one unlike point, two of which are contained 
in one side of the adverse Rook's quadrilateral and the 
other in the perimeter of the adverse Knight's octagon. 
The Point of Command may be either a like or an 
unlike point, and situated upon either the horizontal 
or vertical. 



COMPOUND STRATEGIC PLANES 



251 



EVOLUTION No. 128. 

FIGURE 232. 
Rook and Supporting Factor vs. Objective Plane of Four Radius. 

Black. 




White. 

NOTE. The Front Offensive consists of a vertical or 
horizontal and an oblique ; the radius is composed of two 
like and two unlike points, two of which, both unlike, 
are situated on the perimeter of an adverse Knight's 
octagon, and one like and one unlike are situated on 
one side of the adverse Rook's quadrilateral. The Point 
of Command is an unlike point, and is that point in the 
Objective Plane at which the given octagon and quadri- 
lateral intersect. 



252 



MAJOR TACTICS. 



EVOLUTION No. 129i 

FIGUKE 233. 
Rook and Supporting Factor vs. Objective Plane of Five Radius. 

Slack. 




White. 

NOTE. The Offensive Front consists of a vertical, a 
horizontal, and an oblique. The radius is composed of 
two like and of three unlike points, two like and one 
unlike points being contained in the horizontal, one 
like and two unlike points being contained in the hori- 
zontal, and one unlike point in the oblique. The Point 
of Command is an unlike point, and is that point at 
which the adverse quadrilateral and octagon intersect. 



COMPOUND STRATEGIC PLANES. 



253 



EVOLUTION No. 130. 

FIGURE 234. 

Queen and Supporting Factor vs. Objective Plane of Seven Radius. 

Black. 




White. 



NOTE. The Front Offensive consists of a horizontal, 
a vertical, two diagonals, and two obliques. The radius 
is composed of three like and four unlike points ; three 
unlike points are contained in the diagonals, two unlike 
and one like points in the vertical, one unlike and two 
like points in the horizontal, and two unlike points in 
the obliques. The Point of Command is an unlike point, 
and is that point at which the adverse polygon and 
octagon intersect. 



254 



MAJOR TACTICS. 



EVOLUTION No. 131. 

FIGURE 235. 
Queen and Supporting Factor vs. Objective Plane of Seven Radius 

Black. 





















White. 

NOTE. The Front Offensive consists of a vertical, a 
horizontal, a diagonal, and an oblique. The radius is 
composed of five like points and two unlike points, one 
like and two unlike points, and contained in both the 
vertical and the horizontal, three like points in the 
diagonal, and one in the oblique. The Point of Com- 
mand is a like point, and is that point at which the 
adverse polygon and octagon intersect. 



COMPLEX STRATEGIC PLANES. 



255 



COMPLEX STRATEGIC PLANES. 



EVOLUTION No. 132. 
FIGURE 236. 

A Pawn Lodgment in an Objective Plane of Eight Radius. 
Black. 




White. 



NOTE. The Queen never occupies a Point of Lodg- 
ment, and consequently she can only enter the Objec- 
tive Plane as a Prime Tactical Factor. 



256 



MAJOR TACTICS. 



EVOLUTION No. 183. 
FIGURE 237. 

A Knight Lodgment in an Objective Plane of Eight Radius. 
Black. 
























White. 



NOTE. In evolutions combining a Knight lodg- 
ment, the Supporting Factor always must be defended 
by an Auxiliary Factor. 



COMPLEX STRATEGIC PLANES 



257 



EVOLUTION No. 134. 
FIGURE 238. 

A Bishop Lodgment in an Objective Plane of Eight Radius. 
Black. 




White. 



NOTE. The Point of Lodgment must always be sup- 
ported whenever it is established in any Objective Plane. 



258 



MAJOR TACTICS. 



EVOLUTION No. 135. 

FIGURE 239. 

A Rook Lodgment in an Objective Plane of Eight Radius. 
Black. 

























White. 



NOTE. This is the only manner by which the 0. P. 8 
can be commanded by two pieces. 



COMPLEX STRATEGIC PLANES 



259 



EVOLUTION No. 136. 

FIGURE 240. 

A Pawn Lodgment in Objective Plane of Nine Radius. 
Black. 































White. 



NOTE. The union of the kindred King with a pawn 
lodgment is the most effective combination against an 
Objective Plane of nine radii which does not contain 
the Queen. 



260 



MAJOR TACTICS. 



EVOLUTION No. 137. 
FIGURE 241. 

A Knight Lodgment in an Objective Plane of Nine Radius. 
Black. 




White. 



NOTE. The above position is suggestive of a very 
pretty allegory. 



COMPLEX STRATEGIC PLANES. 



261 



EVOLUTION No. 138. 

FIGURE 242. 
A Bishop Lodgment in an Objective Plane of Nine Radius. 

Black. 




White. 



NOTE This is the only manner in which this com- 
bination of force can command the Objective Plane of 
nine radii. 



262 



MAJOR TACTICS. 



EVOLUTION No. 139. 
FIGURE 243. 

A Rook Lodgment in an Objective Plane of Nine Radius. 
Black. 




NOTE. In an evolution against the 0. P. 9, and 
whenever the kindred Queen is not present, three pieces 
are necessary to effect checkmate. 



COMPLEX STRATEGIC PLANES. 



263 



EVOLUTION No. 140. 
FIGURE 244. 

Command of an Objective Plane of Nine Radius by minor Diagonals 
and Obliques. 

Black. 




White. 

NOTE. The student should observe that the power 
of the white force is derived from the presence of the 
pawn's diagonals. The white King is passive and un- 
available for offence against the black King, and with 
both Knights but without the pawns the Objective Plane 
cannot be commanded. 



264 



MAJOR TACTICS. 



EVOLUTION No. 141. 

FIGURE 245. 
Command of an Objective Plane of Nine Radius by Diagonals. 

Black. 




White. 



NOTE. In any combination of the diagonal pieces 
against the 0. P. 9, the Queen is always the Prime 
Tactical Factor. 



COMPLEX STRATEGIC PLANES. 



265 



EVOLUTION No. 142. 
FIGURE 246. 

Command of an Objective Plane of Nine Radius by Verticals and 
Horizontals. 

Black. 




White. 



NOTE. The 0. P. 9 never can be commanded by less 
than three pieces. 



LOGISTICS OF GEOMETRIC PLANES. 

In each of the foregoing evolutions, there is depicted 
one of the basic ideas of Tactics ; the motif of which is 
either the capture of an opposing piece, the queening of 
a kindred pawn, or the checkmate of the hostile King. 

The material manifestation of each idea is given by 
formations of opposing forces, upon specified points ; 
and the execution of the plan i. e. the practical ap- 
plication of this basic idea in the art of chess-play is 
illustrated by the movements of the given forces, from 
the given points to other given points, in given times. 

Upon these movements, or evolutions, are based all 
those combinations in chess-play wherein a given piece 
co-operates with one or more kindred pieces, for the 
purpose of reducing the adverse material, or of aug- 
menting its own force, or of gaining command of the 
Objective Plane ; and there is no combination of forces 
for the producing of either or all of these results pos- 
sible on the chess-board, in which one or more of these 
basic ideas is not contained. 

Furthermore, the opposing forces, the points at which 
each is posted, and the result of the given evolution 
being determinate, it follows that the movements of 
the given forces equally are determinate, and that the 
points to which the forces move and the verticals, hori- 
zontals, diagonals, and obliques over which they move, 
may be specified and described. 

As the reader has seen, the movements of the pieces 
in every evolution take the form of straight lines, ex- 



LOGISTICS OF GEOMETRIC PLANES. 267 

tending from originally specified points to other neces- 
sary points ; which latter constitute the vertices of 
properly described octagons, quadrilaterals, rectangles, 
and triangles. 

The validity of an evolution, i. e. its adaptability to 
a given situation, once established, the execution is 
purely mechanical, and its practical application in chess- 
play is simple and easy ; but to determine the validity 
of an evolution in any given situation is the test of 
one's understanding of the true theory of the game. 

The secret of Major Tactics 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 first axiom of Major Tactics is : 

A piece exerts no force for the defence of the point 
upon which it stands. 

Consequently, so far as the occupying piece is con- 
cerned, the point upon which a piece is posted is ab j 
solutely defenceless. 

The second axiom of Major Tactics is : 

A piece exerts no force for the defence of any verti- 
cal, horizontal, diagonal, or oblique, along which it does 
not operate a radius of offence. 

Hence it is obvious that a pawn defends only a minor 
diagonal ; that it does not defend a vertical, a horizon- 
tal, a major diagonal, nor an oblique ; that a Knight 
defends an oblique, but not a vertical, a horizontal, nor 
a diagonal ; that a Rook defends a vertical and a hori- 
zontal, but not a diagonal nor an oblique ; that a Queen 
defends a vertical, a horizontal, and a diagonal, but not 
an oblique, and that a King defends only a minor verti- 
cal, a minor horizontal, and a minor diagonal, and does 
not defend a major vertical, a major horizontal, a major 
diagonal, nor an oblique. 



268 MAJOR TACTICS. 

It also is evident that an attacking movement for the 
purpose of capturing a hostile piece always should take 
the direction of the point upon which the hostile piece 
stands ; and that the attacking force should be directed 
along that vertical, horizontal, diagonal, or oblique, 
which is not defended by the piece it is proposed to 
capture. 

That is to say : the simple interpretation of Major 
Tactics is that you creep up behind a man's back while 
he is not looking, and before he can move, and while he 
is utterly defenceless you off with his head. 

This, of course, is the crude process. But it does not 
appertain to savages alone ; in fact, it is the process 
usually followed by so-called educated and civilized folk, 
whether chess-players or soldiers ; furthermore, the 
final situation of the uplifted sword and the unsuspect- 
ing and defenceless victim is the invariable climax of 
every evolution of Major Tactics, whether the latter be- 
longs to war or to chess. 

It is admitted that men, whether soldiers or chess- 
players, have eyes in their heads, and that it is not 
supposable that they would permit an enemy thus to 
take them unawares and by such a simple and un- 
sophisticated process. Nevertheless there is another 
process which leads to the same result; and this pro- 
cess is the quintessence of science, whether of war or 
of chess. 

These two methods, one the crudest and one the most 
scientific possible, unite at the point at which the sword 
is lifted to the full height over the head of the unsus- 
pecting and defenceless enemy. From thence they act 
as unity, for it needs no talent to cut off a man's head 
who is incapable of resistance, to massacre an army 
that is hopelessly routed, nor to checkmate the adverse 



LOGISTICS OF GEOMETRIC PLANES. 269 

King in one move. In such a circumstance a butcher 
is equal to Arbuthnot ; a Zulu chief to Napoleon ; and 
the merest tyro at chess to Paul Morphy. 

To attack and capture an enemy who can neither fight 
nor run is very elementary and not particularly edify- 
ing strategetics ; but to attack simultaneously two hos- 
tile bodies, at a time and at points whereat they cannot 
be simultaneously defended, is the acme of chess and of 
war. In either case the result is identical, and success 
is attained by the same means. But the second process, 
as compared with the first process, is transcendental; 
for it consists in surprising and out-manoeuvring two 
adversaries who have their eyes wide open. 

The means by which success is attained in Major 
Tactics is the proper use of time. 

" He who gains time gains everything ! " is the dictum 
of Frederic the Great, a man who, as a major tac- 
tician, has no equal in history. 

To illustrate the truth of this maxim, the attention of 
the student is called to the simple fact that if, at the 
beginning of a game of chess, White had the privilege of 
making four moves in succession and before Black 
touched a piece, the first player would checkmate the 
adverse King by making one move each with the K P 
and the K B and two moves with the Q. 

Again, in any subsequent situation, if either player 
had the privilege of making two moves in succession, it 
is evident that he would have no difficulty in winning 
the game. To gain this one move, with all due de- 
ference to the shade of Philidor, and not the play of 
the pawns, is the soul of chess. 

But it is easy to see that gain of time can be of little 
advantage to a man who does not understand the proper 
use of time ; and it is equally easy to see, if time is 



270 MAJOR TACTICS. 

to be properly utilized in an evolution of Major Tactics, 
that a thorough knowledge of the forces and points con- 
tained in the given evolution, and of their relative values 
and relations to each other, is imperative. 

Hence the student of Major Tactics should be en- 
tirely familiar with these facts : 

Whatever the geometric plane, whether strategic, 
tactical, or logistic, no evolution is valid unless there 
exists in the adverse position what is termed in " The 
Grand Tactics of Chess " a strategetic weakness. 

Assuming, however, that such a defect exists in the 
opposing force, and that an evolution is valid, it is 
then necessary to determine the line of operations. 
(See " Grand Tactics," p. 318.) If the object of the 
latter is to checkmate the adverse King, it is a strategic 
line of operations ; if its object is to queen a kindred 
pawn, it is a logistic line of operations ; if its object is 
to capture a hostile piece, it is a tactical line of 
operations. 

The line of operations being determined, it only re- 
mains to indicate the initial evolution and the geometric 
plane appertaining thereto. 

Whatever may be the nature of the geometric plane 
upon the surface of which it is required in any given 
situation to execute an evolution, the following condi- 
tions always exist : 

The Prime Tactical Factor always is that kindred 
pawn or piece which captures the adverse Piece Ex- 
posed ; or which becomes a Queen or any other desired 
kindred piece by occupying the Point of Junction; or 
which checkmates the adverse King. The Prime Tacti- 
cal Factor always makes the final move in an evolution; 
it always is posted either on the central point or on the 
perimeter of its own geometric symbol, and its objective 



LOGISTICS OF GEOMETRIC PLANES. 271 

always is the Point of Command, which latter always is 
the central point of the geometric symbol appertaining 
to the Prime Tactical Factor. 

The Prime Radii of Offence always extend from the 
Point of Command, as a common centre, to the perimeter 
of the geometric symbol appertaining to the Prime 
Tactical Factor, and upon the vertices of this geometric 
symbol are to be found the Points Material in every 
valid evolution. 

The Point of Co-operation always is either coincident 
with a Point Material or is a point on the perimeter of 
that geometric symbol appertaining to the Prime Tacti- 
cal Factor of which the Point of Command is the central 
point ; it always is an extremity of the Supporting 
Front, and it always is united, either by a vertical, a 
horizontal, a diagonal, or an oblique, with the Support- 
ing Origin. 

The nature of a Geometric Plane always is determined 
by the nature of the existing tactical defect ; the nature 
of the Geometric Plane determines the selection of the 
Prime Tactical Factor, and the character of the geo- 
metric symbol of the Prime Tactical Factor determines 
the nature of the evolution. 

The student, therefore, has only to locate a tactical 
defect in the adverse position and to proceed as follows 



RULES OF MAJOR TACTICS. 

Whenever a tactical defect exists in the adverse 
position : 

I. Locate the Piece Exposed and the Prime Tactical 
Factor. 

II. Indicate the Primary Origin and the Points Mate- 
rial and describe that geometric symbol which apper- 



272 MAJOR TACTICS. 

tains to the Prime Tactical Factor and upon the 
perimeter of which the Points Material are situated. 

III. Taking the Primary Origin, then indicate the 
Point of Command and describe the Front Offensive. 

IV. Taking the Point of Command as the centre and 
the Points Material as the vertices of that logistic sym- 
bol which appertains to the Prime Tactical Factor, 
describe the Front Defensive and the Prime Radii of 
Offence. 

V. Locate the Supporting Factor, then indicate the 
Point of Co-operation and the Supporting Origin, and 
describe the Supporting Front. 

VI. Locate the Disturbing Factors, then indicate 
the Points of Interference and describe the Front of 
Interference. 

VII. Taking the Fronts of Interference, locate the 
Auxiliary Factors ; then indicate the Auxiliary Origins 
and describe the Auxiliary Fronts. 

VIII. Taking the Front Offensive, the Front Defen- 
sive, the Supporting Front, the Fronts Auxiliary, and 
the Fronts of Interference, describe the Tactical Front. 

Then, if the number of kindred radii of offence which 
are directly or indirectly attacking the Point of Com- 
mand, exceed the number of adverse radii of defence 
which directly or indirectly are defending the Point of 
Command, the Prime Tactical Factor may occupy the 
Point of Command without capture, which latter is the 
end and aim of every evolution of Major Tactics. 



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