the millions. Any special number
of thousands returns in my mind to its position in the parallel
lines from 1 to 1000. The diagram was present in my mind from early
childhood; I remember that I learnt the multiplication table by
reference to it at the age of seven or eight. I need hardly say that
the impression is not that of perfectly straight lines, I have
therefore used no ruler in drawing it."

J.S. "The figures are about a quarter of an inch in length, and in
ordinary type. They are black on a white ground. The numeral 200
generally takes the place of 100 and obliterates it. There is no
light or shade, and the picture is invariable."

[Illustration: ]

etc. etc.
120+---------------
|
|
|110
|
30 40 50 60 70 80 90 |
/
20|
|
|
10|
|
1|

In some cases, the mental eye has to travel along the faintly-marked
and blank paths of a Form, to the place where the numeral that is
wanted is known to reside, and then the figure starts into sight. In
other cases all the numerals, as far as 100 or more, are faintly
seen at once, but the figure that is wanted grows more vivid than its
neighbours; in one of the cases there is, as it were, a chain, and
the particular link rises as if an unseen hand had lifted it. The
Forms are sometimes variously coloured, occasionally very
brilliantly (see Plate IV.). In all of these the definition and
illumination vary much in different parts. Usually the Forms fade
away into indistinctness after 100; sometimes they come to a dead
stop. The higher numbers very rarely fill so large a space in the
Forms as the lower ones, and the diminution of space occupied by
them is so increasingly rapid that I thought it not impossible they
might diminish according to some geometrical law, such as that which
governs sensitivity. I took many careful measurements and averaged
them, but the result did not justify the supposition.

It is beyond dispute that these forms originate at an early age;
they are subsequently often developed in boyhood and youth so as to
include the higher numbers, and, among mathematical students, the
negative values.

Nearly all of my correspondents speak with confidence of their Forms