ten in all the numbers up to 30; the others are
not added merely for want of space; they appear in their
corresponding positions. You will see that 21 is curiously placed,
probably to get a fresh start for the next 10. The loops gradually
diminish in size as the numbers rise, and it seems rather curious
that the numbers from 100 to 120 resemble in form those from 1 to 20.
Beyond 144 the arrangement is less marked, and beyond 200 they
entirely vanish, although there is some hazy recollection of a
futile attempt to learn the multiplication table up to 20 times 20."

[Illustration: PLATE II. _Examples of Number Forms_.]

"Neither my mother nor my sister is conscious of any mental
arrangement of numerals. I have not found any idea of this kind
among any of my colleagues to whom I have spoken on the subject, and
several of them have ridiculed the notion, and possibly think me a
lunatic for having any such feeling. I was showing the scheme to G.,
shortly after your first article appeared, on the piece of paper I
enclose, and he changed the diagram to a sea-serpent [most amusingly
and grotesquely drawn.--F. G.], with the remark, 'If you were a rich
man, and I knew I was mentioned in your will, I should destroy that
piece of paper, in case it should be brought forward as an evidence
of insanity!' I mention this in connection with a paragraph in your
article."

Fig. 40 is, I think, the most complicated form I possess. It was
communicated to me by Mr. Woodd Smith as that of Miss L. K., a lady
who was governess in a family, whom he had closely questioned both
with inquiries of his own and by submitting others subsequently sent
by myself. It is impossible to convey its full meaning briefly, and
I am not sure that I understand much of the principle of it myself.
A shows part only (I have not room for more) of the series 2, 3, 5, 7,
10, 11, 13, 14, 17, 18, 19, each as two sides of a square,--that is,
larger or smaller according to the magnitude of the number; 1 does
not appear anywhere. C similarly shows part of the series (all
divisible by 3) of 6, 9, 15, 21, 27, 30, 33, 39, 60, 63, 66, 69, 90,
93, 96. B shows the way in which most numbers divisible by 4 appear.
D shows the form of the numbers 17, 18, 19, 21, 22, 23, 25, 26, 27,
29, 41, 42-49, 81-83, 85-87, 89, 101-103, 105-107, and 109. E shows
that of 31, 33-35, 37-39. The other numbers are not clear, viz. 50,
51, 53-55, 57-59. Beyond 100 the arrangement becomes hazy, except
t