Complete Works of Lewis Carroll (148 page)

CHAPTER I.

SYMBOLS AND CELLS.

First, let us suppose that the above
left
-hand Diagram is the Biliteral Diagram that we have been using in Book III., and that we change it into a
Triliteral
Diagram by drawing an
Inner Square
, so as to divide each of its 4 Cells into 2 portions, thus making 8 Cells altogether.
The
right
-hand Diagram shows the result.

[The Reader is strongly advised, in reading this Chapter,
not
to refer to the above Diagrams, but to make a large copy of the right-hand one for himself,
without any letters
, and to have it by him while he reads, and keep his finger on that particular
part
of it, about which he is reading.]

Secondly, let us suppose that we have selected a certain Adjunct, which we may call “
m
”, and have subdivided the
xy
-Class into the two Classes whose Differentiæ are
m
and
m
′
, and that we have assigned the N.W.
Inner
Cell to the one (which we may call “the Class of
xym
-Things”, or “the
xym
-Class”), and the N.W.
Outer
Cell to the other (which we may call “the Class of
xym
′
-Things”, or “the
xym
′
-Class”).

[Thus, in the “books” example, we might say “Let
m
mean ‘bound’, so that
m
′
will mean ‘unbound’”, and we might suppose that we had subdivided the Class “old English books” into the two Classes, “old English bound books” and “old English unbound books”, and had assigned the N.W.
Inner
Cell to the one, and the N.W.
Outer
Cell to the other.]

Thirdly, let us suppose that we have subdivided the
xy
′
-Class, the
x
′y
-Class, and the
x
′y′
-Class in the same manner, and have, in each case, assigned the
Inner
Cell to the Class possessing the Attribute
m
, and the
Outer
Cell to the Class possessing the Attribute
m
′
.

[Thus, in the “books” example, we might suppose that we had subdivided the “new English books” into the two Classes, “new English bound books” and “new English unbound books”, and had assigned the S.W.
Inner
Cell to the one, and the S.W.
Outer
Cell to the other.]

It is evident that we have now assigned the
Inner Square
to the
m
-Class, and the
Outer Border
to the
m
′
-Class.

[Thus, in the “books” example, we have assigned the
Inner Square
to “bound books” and the
Outer Border
to “unbound books”.]

When the Reader has made himself familiar with this Diagram, he ought to be able to find, in a moment, the Compartment assigned to a particular
pair
of Attributes, or the Cell assigned to a particular
trio
of Attributes.
The following Rules will help him in doing this:—

(1) Arrange the Attributes in the order
x
,
y
,
m
.

 (2) Take the
first
of them and find the Compartment assigned to it.

(3) Then take the
second
, and find what
portion
of that compartment is assigned to it.

(4) Treat the
third
, if there is one, in the same way.

[For example, suppose we have to find the Compartment assigned to
ym
.
We say to ourselves “
y
has the
West
Half; and
m
has the
Inner
portion of that West Half.”

Again, suppose we have to find the Cell assigned to
x
′ym′
.
We say to ourselves “
x
′
has the
South
Half;
y
has the
West
portion of that South Half, i.e.
has the
South-West Quarter
; and
m
′
has the
Outer
portion of that South-West Quarter.”]

The Reader should now get his genial friend to question him on the Table given on the next page, in the style of the following specimen-Dialogue.

Q.

Adjunct for South Half, Inner Portion?

A.

x
′m
.

Q.

Compartment for
m
′
?

A.

The Outer Border.

Q.

Adjunct for North-East Quarter, Outer Portion?

A.

xy
′m′
.

Q.

Compartment for
ym
?

A.

West Half, Inner Portion.

Q.

Adjunct for South Half?

A.

x
′
.

Q.

Compartment for
x
′y′m
?

A.

South-East Quarter, Inner Portion.

&c.
&c.

TABLE IV.

 Adjunct 

 of 

 Classes. 

 Compartments, 

 or Cells, 

 assigned to them. 

 
x

 North

Half. 

 
x
′

 South

〃
 

 
y

 West

〃
 

 
y
′

 East

〃
 

 
m

 Inner

Square. 

 
m
′

 Outer

Border. 

 
xy

 North-

West

Quarter. 

 
xy
′

〃

East

〃
 

 
x
′y

 South-

West

〃
 

 
x
′y′

〃

East

〃
 

 
xm

 North

Half,

Inner

Portion. 

 
xm
′

〃

〃
 

Outer

〃
 

 
x
′m

 South

〃
 

Inner

〃
 

 
x
′m′

〃

〃
 

Outer

〃
 

 
ym

 West

〃
 

Inner

〃
 

 
ym
′

〃

〃
 

Outer

〃
 

 
y
′m

 East

〃
 

Inner

〃
 

 
y
′m′

〃
 

〃
 

Outer

〃
 

 
xym

 North-

West

Quarter, 

Inner

Portion. 

 
xym
′

〃

〃
 

〃
 

Outer

〃
 

 
xy
′m

〃

East

〃
 

Inner

〃