line turns abruptly to the right, passes into a pleasanter region where grass grows, and so continues up to 20.  At 20 the line turns to the left, and passes up the before-described incline to 100.  This figure will help you in understanding my ridiculous notions.  The asterisk (*) marks the place where I commonly seem to myself to stand and view the line.  At times I take other positions, but never any position to the left of the (*), nor to the right of the line from 20 upwards.  I do not associate colours with numbers, but there is a great difference in the illumination which different numbers receive.  If a traveller should start at 1 and walk to 100, he would be in an intolerable glare of light until near 9 or 10.  But at 11 he would go into a land of darkness and would have to feel his way.  At 12 light breaks in again, a pleasant sunshine, which continues up to 19 or 20, where there is a sort of twilight.  From here to 40 the illumination is feeble, but still there is considerable light.  At 40 things light up, and until one reaches 56 or 57 there is broad daylight.  Indeed the tract from 48 to 50 is almost as bad as that from 1 to 9.  Beyond 60 there is a fair amount of light up to about 97, From this point to 100 it is rather cloudy.”

In a subsequent letter he adds:—­

“I enclose a picture in perspective and colour of my ‘form.’  I have taken great pains with this, but am far from satisfied with it.  I know nothing about drawing, and consequently am unable to put upon the paper just what I see.  The faults which I find with the picture are these.  The rectangles stand out too distinctly, as something lying on the plane instead of being, as they ought, a part of the plane.  The view is taken of necessity from an unnatural stand-point, and some way or other the region 1-12 does not look right.  The landscape is altogether too distinct in its features.  I rather know that there is grass, and that there are trees in the distance, than see them.  But the grass within a few feet of the line I see distinctly.  I cannot make the hill at the right slope down to the plane as it ought.  It is too steep.  I have had my poor success in indicating my notion of the darkness which overhangs the region of eleven.  In reality it is not a cloud at all, but a darkness.

“My sister, a married lady, thirty-eight years of age, sees numerals much as I do, but very indistinctly.  She cannot draw a figure which is not by far too distinct.”

Most of those who associate colours with numerals do so in a vague way, impossible to convey with truth in a painting.  Of the few who see them with more objectivity, many are unable to paint or are unwilling to take the trouble required to match the precise colours of their fancies.  A slight error in hue or tint always dissatisfies them with their work.