26o THE POPULAR SCIENCE MONTHLY. 



A person who was described as a raatlicmatical astronomer, of rapidly- 

 rising reputation, saw the numbers in a straight row, while he would 

 be standing a little on one side. They went away in the distance, so 

 that 100 was the farthest number be could see distinctly. The row 

 was dusky-gray, and paler near to the observer. The tens were 

 marked by a kind of fleecy lumps, 



M. d'Abbadie made a communication on the peculiarities of nu- 

 merical vision to the Anthropological Society of Paris, and this led 

 ]M. Jaqucs Bertillon to relate his experiences in the matter, beginning 

 with the time when he learned to count. " I connected," he says, 

 "each of the numbers as it was taught me with some object in our 

 garden, so that when I went over the series I would in imagination 

 walk along an alley that led from the house to the end of the garden. 

 Thus, an indestructible association of ideas arose between the figures 

 and the plants in the garden : the figure 1 became attached to a 

 chestnut-tree that marked the beginning of the walk, the figure 5 to a 

 bench near it, the figure 7 to a tub farther on, the number 14 to a 

 little laurel ; 30 and the following figures were lost in a dark avenue 

 of trees that terminated the walk ; while beyond 40 the numbers 

 ceased to be associated with any object, probably because I had not 

 learned to count further when I made the i:.leasant associations. If I 

 wished to add 14 and 5, I would in fancy go to the place (the laurel- 

 bush) that 14 occupied in the garden, and go some steps farther to 19. 

 The puerile work was wholly involuntary ; and I well recollect when 

 my tendency to proceed thus was almost invincible. I had another 

 process for fractions : the idea of ^, for example, was directly associ- 

 ated with the idea of a quarter of an hour marked on the clock ; and 

 if I had to add \ and \, I imagined the hand pushed forward twenty 

 minutes, or one third of an hour, and I immediately had the result, -^. 

 I was not able, however, to calculate any fractions in this way the de- 

 nominators of which were not factors of 60." 



A professor of mathematics in Geneva saw the numbers in a zig- 

 zag line which made turns at 10 and at GO, up to IIG, and no further, 

 and added to his description that when young he likened some sounds 

 to colors : a grave sound was black, a less grave one, red ; an acute 

 sound, yellow ; a very acute one, bright yellow. 



Another correspondent saw the numbers arranged in their regular 

 orders in a system of lines — the first 10 in a horizontal line, the next 

 10 in a line perpendicular to it, the third 10 in a line running diag- 

 onally from right to left, the numbers from 30 to 90 in a perpendicu- 

 lar line parallel to the line of the second series, and the larger num- 

 bers to 1,000 in a line running from right to left parallel with the first 

 one. The vision stopped at 1,000. 



To another correspondent of M. Bertillon's the numbers presented 

 themselves — not very clearly distinct from one another — in a descend- 

 ing column, quite narrow down to 10, where it doubled in width ; 



