G ALTON AND STATISTICAL STUDY OF INHERITANCE 157 



adhere pretty closely, while other members of the group may 

 be more abnormal, showing marked deviation from the mean. 

 The deviation of these abnormal individuals from the mean is 

 not accidental or due to "chance," for it is part of the orderly 

 system of nature. If the cases tabulated are numerous enough, 

 the individuals will conform, so far as this quality is concerned, 

 to what is known in statistical science as the law of frequency 

 of error. This agreement will be so close, when great numbers of 

 individuals are compared, that the number which depart from the 

 mean to any specified degree may be computed mathematically. 



For example, the chest measurements of 5738 soldiers gave 

 the following results : 



If the number of events had been five 

 hundred thousand or five million instead of 

 five thousand, the agreement between the 

 computed and observed frequency of each 

 degree of departure from the mean would 

 have been very much closer. When the 

 number of cases is unlimited, the agree- 

 ment is perfect. 



Galton gives the following illustration 

 of the significance of a type: Suppose 

 a large island inhabited by a single race, 

 who intermarry freely and have lived for 

 many generations under constant condi- 

 tions, then the average heiglit of the adult 

 male of that population will undoubtedly 



be the same year after year. Also still arguing from the expe- 

 rience of modern statistics, which are found to give constant results 

 in far less carefully guarded examples we should undoubtedly 

 find year after year the same proportion maintained between the 

 number of men of different heights. I mean if the average stature 

 were found to be sixty-six inches, and if it were also found in any 

 one year that one hundred per million exceeded seventy-eight 

 inches, the same proportion of one hundred per million would be 

 closely maintained in all other years. 



An equal constancy of proportion would be maintained 

 between any other limits of height we please to specify, as 



