21(5 



The Law of Ancestral HerccUty 



Yet since the publication of Francis Galton 's Natural Inheritance in 1889 mach 

 progi-css has been niade in tlie theory of multiple coirelation, and also in cur 

 treatment of characters not quantitatively mcasurablo, but which we may rcason- 

 ably suppose to be based on quantitative factors, — as the degi-ee of yellow pigment 

 in the human eye. Further larger scries of observatii>ns have been collected 

 and reduced, and we are much clearcr than we were ten years ago on the nature 

 of regression and ' blend.' 



Giveu t«o relatives P and Q the- general theory of statistics teils us how 

 to dress a table froui which we can read off at once the most probable character 

 of P when we know the character of Q. Therc is no biological theory in this, 

 it is merely an arraiigenient of Statistical information iuto classes. Such classes 

 may be arranged on au actual (juantitative scale, or as in the case of eye or liair 

 colour on a (|ualitative scalc, wiiich with a high degree of ])robability coricsponds 

 to a true (piaiititative scale in sonie ouo or other piguieut, whose amount cauuot 

 be actually determined. In both cases the methods of statistics allow us to 

 determine : 



(a) The variability in character of both P and Q in terms of the ränge 

 of one of thesc arbitrary classes. 



{b) The average variability in the same teruis of an array of P's corre- 

 sponding to a given Q, or of an array of Q's corresponding to a given P. 



(c) The first two terms of the dosest linear function which c.xpresses 

 the probable character of P or Q in terms of the known character of Q or P. 



hiheritance of Cubit. 

 21 



20 



S 19 



o 



.~ 18 



17 



16 



OI2]«SG7S9iO 



16 17 18 19 20 



Cuhit of Ftitlier in Iitclies. 



21 



22 



Probable value of cubit of son Q, for a known cubit in father P. A marked deviation from linearity 

 only ocours in the extreme casc of father's cubit, where theru were ouly a few instances to base the 

 Bon's mean upon. 



