Chapter 40

_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.] pg040 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. pg041 (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.

pg042 TABLE IV.

·-----------------------------------------------· | Adjunct | | | of | Compartments, or Cells, assigned | | Classes. | 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 " | | xy'm' | " " " Outer " | | x'ym | South-West " Inner " | | x'ym' | " " " Outer " | | x'y'm | " East " Inner " | | x'y'm' | " " " Outer " | ·-----------------------------------------------·

pg043