280 Prof. Karl Pearson. 



1-0832,* while the ratios of 0*4374 to 0-4281 and 0*4488 to 0*4427, 

 are only T0219 and 1*0139 respectively, thus there is still a slight 

 prepotency of paternal influence on stature to be recorded. (See 



(4) (ii).) 



Confining our attention to the differences in stature for fathers and 

 sons corresponding to all mothers whatsoever, we have, if D e f be the 

 difference in stature between father and corresponding fraternity of 

 elder sons, D^ between father and fraternity of younger sons : 



D ef = 0-5754-0-5719^. 

 D yf = 0-6208- 0-5573 h f . 



Hence the difference betwen the father and fraternity of younger 

 sons will be greater than the difference between the father and the 

 corresponding fraternity of elder sons unless the father be 3'110 

 inches less, or 1*059 more than the average. But 3*11 is about 1*2 

 and 1*059 about 0*415 times the standard deviation of the stature of 

 fathers, or, fraternities of younger sons are nearer in stature to their 

 father than fraternities of elder sons in about 46 per cent, of cases. 



Similarly if D gnt , ~D ym represent the differences of stature of mothers 

 and fraternities of elder and younger sons respectively, we have in 

 inches 



D em = 5*8416- 0-5626/4. 



-D yrn = 5-8870-0-5512A OT . 



Thus fraternities of younger sons are always more divergent than 

 fraternities of elder sons from the stature of their mothers, unless the 

 mother be 3*982 inches less, or 10*53 inches more than the average. 

 These are 1'6 and 4*24 times the standard deviation in stature of 

 mothers ; or, only in about 5*5 per cent, of cases are fraternities of 

 younger sons nearer in stature to their mothers than elder sons. 



Now, it is difficult to read into these results any evidence for a 

 steady telegenic influence. It is true that the case of younger sons 

 being more like their parents than elder sons occurs in eight times as 

 many cases with the father as with the mother, but the broad fact 

 remains that in more than half the cases, judged by difference of 

 stature, the elder son is more like the father than the younger son. 

 In fact, examined in this way by difference of stature not an un- 

 . natural manner of first approaching the problem the true closeness 

 of parent and offspring appears to be quite obscured by some secular, 

 or, at any rate, periodic (see 3) evolution in stature between 

 successive generations an evolution which even makes itself felt in 

 the interval between younger and elder sons. 



* 13/12 = 1*0833; thus these returns again confirm Mr. Galton's selection of 

 this fraction for the sexual ratio for stature. 



