Mathematical_Recreations-Kraitchik-2e

122 Mathematical Recreations
marks off on the x-axis of a co-ordinate system equally
spaced points for the possible readings (say one for each .0001
inch in the vicinity of the expected value), and takes as or
dinate at each such point the number of times the corresponding
reading has occurred, the greater the total number
of readings the more closely will the ordinates corne to as~
surning the shape of the error curve when they have been
FIGURE 19.
The Error Curve: y "" Ae- bz •• •
joined by a smooth curve. The constants A and b permit one
to adjust the steepness of the curve to fit varying conditions.
Halton's apparatus (illustrated in Figure 20) enables one,
to find the curve mechanically. It consists of an inclined
board into which have been fixed a great many pins as obstacles.
At the top is a reservoir of shot with a hole at the
middle of its lower edge. When the hole is opened the shot
roll down the board, hitting the nails as they pass. At the
bottom of the board are narrow straight-sided compartments,
• From Mathematics for the Million, by Lancelot T. Hogben, published
by W. "\V. Norton & Company, Inc., New York.