Page:Popular Science Monthly Volume 48.djvu/527

Rh a precise reflection of the upper. Next, let a hundred dots be counted from above downward, and let a line be drawn below them. According to the conditions, this line will stand at the height of seventy-eight inches. Using the data afforded by these two lines, it is possible by the help of the law of deviation from an average to reproduce with extraordinary closeness the entire system of dots on the board.

This law of deviation from an average is not restricted to vital phenomena, but holds true of all events which are the resultants of variable conditions, which remain the same through all the events recorded. If the marks on the board had been made by bullets fired at a horizontal line stretched in front of a target, they would have been distributed according to the same law, their average value would be constant, and the deviations of the several events from the average would be governed by the same law, which is identical with that which governs runs of luck at a gaming table.

Galton has described an apparatus which mimics in a very pretty way the conditions on which deviations from a mean depend. It is a long, shallow box set on end and glazed in front, leaving a depth of about a quarter of an inch behind the glass. Strips are placed in the upper part to act as a funnel. Below the outlet of the funnel stand a succession of rows of pins stuck squarely into the backboard, and below these again are a series of vertical compartments. A charge of small shot is inclosed. When the frame is held topsy-turvy, all the shot runs to the upper end; then when it is turned back into its working position the desired action commences.

The shot passes through the funnel and, issuing from its narrow end, scampers deviously down through the pins in a curious and interesting way: each one of them darting a step to the right or left, as the case may be, every time it strikes a pin. The pins are so placed that every descending shot strikes a pin in each successive row. The cascade issuing from the funnel broadens as it descends, and at length every shot finds itself caught in a compartment immediately after freeing itself from the last row of pins. The outline of the columns of shot that accumulate in the successive compartments approximates to the mathematical law of frequency, and is closely of the same shape, however often the experiment is repeated.

The outlines of the columns would become more nearly identical with the normal law of frequency if the rows of pins were much more numerous, the shot smaller, and the compartments narrower; also, if a larger quantity of shot were used.

The principle on which the action of the apparatus depends is that a number of small and independent accidents befall each