do not think there is much
room for correction on either head. Neither do I think it requisite
to make much allowance for inaccurate answers, as the tone of the
replies is simple and straightforward. Those from Princeton, where
the students are older and had been specially warned, are remarkable
for indications of self-restraint. The result of personal inquiries
among adults, quite independent of and prior to these, gave me the
proportion of 1 in 30 as a provisional result for adults. This is as
well confirmed by the present returns of 1 in 21 among boys and
youths as I could have expected.

I have not a sufficient number of returns from girls for useful
comparison with the above, though I am much indebted to Miss Lewis
for 33 reports, to Miss Cooper of Edgbaston for 10 reports from the
female teachers at her school, and to a few other schoolmistresses,
such as Miss Stones of Carmarthen, whose returns I have utilised in
other ways. The tendency to see Number-Forms is certainly higher in
girls than in boys.

Fig. 20 is the Form of Mr. George Bidder, Q.C.; it is of much
interest to myself, because it was, as I have already mentioned,
through the receipt of it and an accompanying explanation that my
attention was first drawn to the subject. Mr. G. Bidder is son of
the late well-known engineer, the famous "calculating boy" of the
bygone generation, whose marvellous feats in mental arithmetic were
a standing wonder. The faculty is hereditary. Mr. G. Bidder himself
has multiplied mentally fifteen figures by another fifteen figures,
but with less facility than his father. It has been again transmitted,
though in an again reduced degree, to the third generation. He says:
--

"One of the most curious peculiarities in my own case is the
arrangement of the arithmetical numerals. I have sketched this to
the best of my ability. Every number (at least within the first
thousand, and afterwards thousands take the place of units) is
always thought of by me in its own definite place in the series,
where it has, if I may say so, a home and an individuality. I should,
however, qualify this by saying that when I am multiplying together
two large numbers, my mind is engrossed in the operation, and the
idea of locality in the series for the moment sinks out of prominence."

Fig. 21 is that of Prof. Schuster, F.R.S., whose visualising powers
are of a very high order, and who has given me valuable information,
but want of space compels me