Extension and Connection with Numbers.

By extending the letter sequence it is of course possible to name a larger field. By using the limit names the corners of each square can be named.

Thus “en sen,” “an sen,” etc., will be the names of the points nearest the origin in “en” and in “an.”

A field of points of which each one is indefinitely small is given by the names written below.

The squares are shown in dotted lines, the names denote the points. These points are not mathematical points, but really minute areas.

Instead of starting with a set of squares and naming them, we can start with a set of points.

By an easily remembered convention we can give names to such a region of points.

Let the space names with a final “e” added denote the mathematical points at the corner of each square nearest the origin. We have then

for the set of mathematical points indicated. This system is really completely independent of the area system and is connected with it merely for the purpose of facilitating the memory processes. The word “ene” is pronounced like “eny,” with just sufficient attention to the final vowel to distinguish it from the word “en.”

Now, connecting the numbers 0, 1, 2 with the sequence e, a, i, and also with the sequence n, t, l, we have a set of points named as with numbers in a co-ordinate system. Thus “ene” is (0, 0) “ate” is (1, 1) “ite” is (2, 1). To pass to the area system the rule is that the name of the square is formed from the name of its point nearest to the origin by dropping the final e.

By using a notation analogous to the decimal system a larger field of points can be named. It remains to assign a letter sequence to the numbers from positive 0 to positive 9, and from negative 0 to negative 9, to obtain a system which can be used to denote both the usual co-ordinate system of mapping and a system of named squares. The names denoting the points all end with e. Those that denote squares end with a consonant.

There are many considerations which must be attended to in extending the sequences to be used, such as uniqueness in the meaning of the words formed, ease of pronunciation, avoidance of awkward combinations.

I drop “s” altogether from the consonant series and short “u” from the vowel series. It is convenient to have unsignificant letters at disposal. A double consonant like “st” for instance can be referred to without giving it a local significance by calling it “ust.” I increase the number of vowels by considering a sound like “ra” to be a vowel, using, that is, the letter “r” as forming a compound vowel.

The series is as follows:—

Consonants.
	0	1	2	3	4	5	6	7	8	9
positive	n	t	l	p	f	sh	k	ch	nt	st
negative	z	d	th	b	v	m	g	j	nd	sp
Vowels.
	0	1	2	3	4	5	6	7	8	9
positive	e	a	i	ee	ae	ai	ar	ra	ri	ree
negative	er	o	oo	io	oe	iu	or	ro	roo	rio

Pronunciation.—e as in men; a as in man; i as in in; ee as in between; ae as ay in may; ai as i in mine; ar as in art; er as ear in earth; o as in on; oo as oo in soon; io as in clarion; oe as oa in oat; iu pronounced like yew.

To name a point such as (23, 41) it is considered as (3, 1) on from (20, 40) and is called “ifeete.” It is the initial point of the square ifeet of the area system.

The preceding amplification of a space language has been introduced merely for the sake of completeness. As has already been said nine words and their combinations, applied to a few simple models suffice for the purposes of our present enquiry.

Printed by Hazell, Watson & Viney, Ld., London and Aylesbury.