certain parts, especially where 1 emerges, and about 20.  How I get from 100 to 120 I hardly know, though if I could require these figures a few times without thinking of them on purpose, I should soon notice.  About 200 I lose all framework.  I do not see the actual figures very distinctly, but what there is of them is distinguished from the dark by a thin whitish tracing.  It is the place they take and the shape they make collectively which is invariable.  Nothing more definitely takes its place than a person’s age.  The person is usually there so long as his age is in mind.”

[Footnote 8:  The engraver took much pains to interpret the meaning of the rather faint but carefully made drawing, by strengthening some of the shades.  The result was very very satisfactory, judging from the author’s own view of it, which is as follows:—­“Certainly if the engraver has been as successful with all the other representations as with that of my shape and its accompaniments, your article must be entirely correct.”]

T. M.  “The representation I carry in my mind of the numerical series is quite distinct to me, so much so that I cannot think of any number but I at once see it (as it were) in its peculiar place in the diagram.  My remembrance of dates is also nearly entirely dependent on a clear mental vision of their loci in the diagram.  This, as nearly as I can draw it, is the following:—­”

[Illustration:  ]

“It is only approximately correct (if the term ‘correct’ be at all applicable).  The numbers seem to approach more closely as I ascend from 10 to 20, 30, 40, etc.  The lines embracing a hundred numbers also seem to approach as I go on to 400, 500, to 1000.  Beyond 1000 I have only the sense of an infinite line in the direction of the arrow, losing itself in darkness towards 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