o from experiments on my own mind. I find I
can deal mentally with simple sums with much less strain if I
audibly conceive the figures as on-naught, on-one, etc., and I can
both dictate and write from dictation with much less trouble when
that system or some similar one is adopted. I have little doubt that
our nomenclature is a serious though unsuspected hindrance to the
ready adoption by the public of a decimal system of weights and
measures. Three quarters of the Forms bear a duodecimal impress.

I will now give brief explanations of the Number-Forms drawn in
Plates I., II., and III., and in the two front figures in Plate IV.

DESCRIPTION OF PLATE I.

Fig. 1 is by Mr. Walter Larden, science-master of Cheltenham College,
who sent me a very interesting and elaborate account of his own case,
which by itself would make a memoir; and he has collected other
information for me. The Number-Forms of one of his colleagues and of
that gentleman's sister are given in Figs. 53, 54, Plate III. I
extract the following from Mr. Larden's letter--it is all for which
I can find space:--

[Illustration: PLATE I. _Examples of Number-Forms_.]

"All numbers are to me as images of figures in general; I see them
in ordinary Arabic type (except in some special cases), and they
have definite positions in space (as shown in the Fig.). Beyond 100
I am conscious of coming down a dotted line to the position of 1
again, and of going over the same cycle exactly as before, _e.g._
with 120 in the place of 20, and so on up to 140 or 150. With higher
numbers the imagery is less definite; thus, for 1140, I can only say
that there are no new positions, I do not see the entire number in
the place of 40; but if I think of it as 11 hundred and 40, I see 40
in its place, 11 in its place, and 100 in its place; the picture is
not single though the ideas combine. I seem to stand near 1. I have
to turn somewhat to see from 30-40, and more and more to see from
40-100; 100 lies high up to my right and behind me. I see no shading
nor colour in the figures."

Figs. 2 to 6 are from returns collected for me by the Rev. A.D. Hill,
science-master of Winchester College, who sent me replies from 135
boys of an average age of 14-15. He says, speaking of their replies
to my numerous questions on visualising generally, that they
"represent fairly those who could answer anything; the boys
certainly seemed interested in the subject; the others, who had no
such faculty ei