VARIATION AND HEREDITY 25 



that the laws of heredity can, in general, only be applied 

 to foretell the average results in large numbers of cases. 

 We cannot predict whether any one chick with two 

 blue Andalusian parents will be black, white, or blue. 

 All that we know is that, of large numbers of such 

 chicks, half will be blue and one quarter each black and 

 white. In general, heredity cannot deal with indi- 

 viduals, but only with large groups of individuals, 

 statistically and in the aggregate. 



Statistical methods indeed were applied to biological 

 problems by Quetelet in 1845, before Darwin published 

 The Origin of Species, before Mendel's work was done, 

 and long before its importance was recognized. Quetelet 

 pointed out, in a series of letters to the Grand Duke of 

 Saxe-Coburg and Gotha, that the mathematical theory 

 of chance and probability might be applied to many 

 biometrical problems, and thus throw light on some 

 departments of sociology. 



A typical example of the action of chance is the 

 falling of a number of coins with " head " or " tail " 

 upwards when the coins are tossed. If we have two 

 coins, the possibilities are that we may get (i) head, 

 head ; (2) head, tail ; (3) tail, head ; (4) tail, tail. 

 But of these cases (2) and (3) are essentially identical. 

 Each combination is as probable as any of the others, 

 and thus the chances of obtaining two heads, one head 

 and one tail, or two tails, are as i : 2 : i . If we had 

 ten coins, and made 1024 trials, tossing all the coins 

 each time, calculation shows that the probable relative 

 frequency would be in accordance with the following 

 numbers : 



