STATISTICAL METHODS 313 



statement by an experienced statistician, Mr. G. Udny Yule 

 (1902, p. 196) : 



" A series of measurements is made of some one variable 

 character, e.g. a length, in parents and in their offspring, noting 

 the individual families (the more the better) and not merely 

 measuring the first generation as a whole and then their offspring 

 as a whole. From these measurements an equation is derived, 

 giving, as nearly as may be, the mean character of the offspring 

 in terms of the character of the parent. Supposing X to be the 

 character in the parent, Y the mean character in the offspring, 

 then the simplest form of such equation is :. 



Y=A 4- BX, 



where A is a dimension of the same order as X or Y, and B is a 

 number that will vary from case to case. We have for instance, 

 from the data collected by Mr. Galton for inheritance of stature 

 in man, reduced by Prof. Pearson, the equation relating mean 

 stature of sons and stature of father : 



Y =31-10 + '45 X, 



i.e. the mean stature of sons is 31 # i inches, together with nine- 

 twentieths of the stature of the father (also in inches, of course). 

 The father's stature is thus some guide to the stature of his 

 offspring ; it enables us to form a closer estimate of their stature 

 than we could from a mere knowledge of the mean characters 

 of the race, and we may therefore say that stature is an inherited 

 character. The sons do diverge from the race-mean in the 

 same direction as their parent. Quite generally, the statistician 

 speaks of a character as inherited whenever the number or 

 " constant " B is greater than zero ; if it does not differ sensibly 

 from zero the character is held to be non-heritable, quite apart 

 from the question whether the mean is more or less constant 

 from one generation to the next, a consideration which does 

 not affect the conception of individual heredity." 



