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 to extract very briefly.  He says to the effect:—­

“The diagram of numerals which I usually see has roughly the shape of a horse-shoe, lying on a slightly inclined plane, with the open end towards me.  It always comes into view in front of me, a little to the left, so that the right hand branch of the horse-shoe, at the bottom of which I place 0, is in front of my left eye.  When I move my eyes without moving my head, the diagram remains fixed in space and does not follow the movement of my eye.  When I move the head the diagram unconsciously follows the movement, but I can, by an effort, keep it fixed in space as before.  I can also shift it from one part of the field to the other, and even turn it upside down.  I use the diagram as a resting-place for the memory, placing a number on it and finding it again when wanted.  A remarkable property of the diagram is a sort of elasticity which enables me to join the two ends of the horse-shoe together when I want to connect 100 with 0.  The same elasticity causes me to see that part of the diagram on which I fix my attention larger than the rest.”

Mr. Schuster makes occasional use of a simpler form of diagram, which is little more than a straight line variously divided, and which I need not describe in detail.

Fig. 22 is by Colonel Yule, C.B.; it is simpler than the others, and he has found it to become sensibly weaker in later years; it is now faint and hard to fix.

Fig. 23.  Mr. Woodd Smith:—­

“Above 200 the form becomes vague and is soon lost, except that 999 is always in a corner like 99.  My own position in regard to it is generally nearly opposite my own age, which is fifty now, at which point I can face either towards 7-12, or towards 12-20, or 20-7, but never (I think) with my back to 12-20.”

Fig. 24.  Mr. Roget.  He writes to the effect that the first twelve are clearly derived from the spots in dominoes.  After 100 there is nothing clear but 108.  The form is so deeply engraven in his mind that a strong effort of the will was required to substitute any artificial arrangement in its place.  His father, the late Dr. Roget (well known for many years as secretary of the Royal Society), had trained him in his childhood to the use of the memoria technica of Feinagle, in which each year has its special place in the walls of a particular room, and the rooms of a house represent successive centuries, but he never could locate them in that way.  They would go to what seemed their natural homes in the arrangement shown in the figure, which had come to him from some unknown source.

The remaining Figs., 25-28, in Plate I., sufficiently express themselves.  The last belongs to one of the Charterhouse boys, the others respectively to a musical critic, to a clergyman, and to a gentleman who is, I believe, now a barrister.