hat the hundreds and thousands go on again in complete, consecutive,
and proportional squares indefinitely. The groups of figures are not
seen together, but one or other starts up as the number is thought of.
The form has no background, and is always seen _in front_. No Arabic
or other figures are seen with it. Experiments were made as to the
time required to get these images well in the mental view, by
reading to the lady a series of numbers as fast as she could
visualise them. The first series consisted of twenty numbers of two
figures each--thus, 17, 28, 13, 52, etc.; these were gone through on
the first trial in 22 seconds, on the second in 16, and on the third
in 26. The second series was more varied, containing numbers of one,
two, and three figures--thus 121, 117, 345, 187, 13, 6, 25, etc.,
and these were gone through in three trials in 25, 25, and 22 seconds
respectively, forming a general result of 23 seconds for twenty
numbers, or 2-1/3 seconds per number. A noticeable feature in this
case is the strict accordance of the scale of the image with the
magnitude of the number, and the geometric regularity of the figures.
Some that I drew, and sent for the lady to see, did not at all
satisfy her eye as to their correctness.

I should say that not a few mental calculators work by bulks rather
than by numerals; they arrange concrete magnitudes symmetrically in
rank and file like battalions, and march these about. I have one
case where each number in a Form seems to bear its own _weight_.

Fig. 45 is a curious instance of a French Member of the Institute,
communicated to me by M. Antoine d'Abbadie (whose own Number-Form is
shown in Fig. 44):--

"He was asked, why he puts 4 in so conspicuous a place; he replied,
'You see that such a part of my name (which he wishes to withhold)
means 4 in the south of France, which is the cradle of my family;
consequently _quatre est ma raison d'etre_.'"

Subsequently, in 1880, M. d'Abbadie wrote:--

"I mentioned the case of a philosopher whose, 4, 14, 24, etc., all
step out of the rank in his mind's eye. He had a haze in his mind
from 60, I believe [it was 50.--F.G.], up to 80; but latterly 80 has
sprung out, not like the sergeants 4, 14, 24, but like a captain,
farther out still, and five or six times as large as the privates 1,
2, 3, 5, 6, etc. 'Were I superstitious,' said he, 'I should
conclude that my death would occur in the 80th year of the century.'
The growth of 80 was _