158 THE FOUNDATIONS OF ZOOLOGY 



between seventy-one and seventy-two inches, between seventy-two 

 and seventy-three, and so on. Now, at this point, the law of 

 deviation from an average steps in. It shows that the number 

 per million, whose heights range between seventy-one and seventy- 

 two inches, or between any other limits we please to name, could 

 be predicted from the previous datum of the average, and of any 

 other one fact, such as that of one hundred per million exceeding 

 seventy-eight inches. 



Suppose a million of the men to stand in turn with their 

 backs against a vertical board of sufficient height, and their 

 heights to be dotted off upon it. The line of average height is 

 that which divides the dots into two equal parts, and stands, in 

 the case we have assumed, at the height of sixty-six inches. The 

 dots will be found to be ranged so symmetrically on either side 

 of the line of average that the lower half of the board will be 

 almost a precise reflection of the upper. Next, let a hundred 

 dots be counted from above downwards, 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 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 stands a succession of rows of pins 

 stuck fairly into the backboard, and below these, again, are a 

 series of vertical compartments. A charge of small shot is 



