K. Pkarson 219 



(/)) //^, , /(,, , hj,^ ... aiv (lcvi;itii)iis f'roin tlie type of eacli geiieratiDn. I hcive 

 ncver foiiml tlic type« of oach griici-atinn idcntieal. Thcy ofteii dillVr very 

 scnsibly. 



(c) Eaeh inrlividiial ancestor contributes oiil}- a fraction of his doviation 

 froin t^'pe to the ])iobal)l(! deviatioii in type uf the off'spriiif^. Bat if tho aiicestry 

 bo maintained for two or thioe f,a'iiürations at a given deviatioii froiii type 

 the ooiitributioiis of the differciit terms of (i) provide a probable deviatioii in type 

 of otüspriiij; which inay be e(|ual to or iiiay even exceed that of the ancestry. 



This point is over and over again forgotteu when biologists talk of regressioii 

 as if it were a persistent retrogres.sive factor. 



As a matter of fact with the numbers we ah'eady have for man, breeding true 

 for three or four generations gives a value of p,^ vvithin a small peicentage of the 

 selected hp, and this is only slowiy moditied, if the stock continues to bieed true 

 to itself Therc is no such tliiiig in Statistical theory as a necessary regression if 

 the selected stock pair with selected stock. The rapid establishment of brecds is 

 not evidencc therefore against the present view of heredity. On the coutrary 

 it rtows at oncc fi'om it. 



(4) So far there is practically no assuniption in our treatineiit of heredity, 

 wliich has not been justified by ample experience, e.g. the closc liiiearity in 

 distribution of the probable valne of a character in onc relative for a kiiown 

 value of a character in a second. Further it enables us to prcdict probable values 

 from any group of kiiown relatives. When however we predict from dircct 

 ancestors only we state more particidarly the law of aiicestral heredity. If we are 

 content with parcnts, or possibly in somc cases with graudparents also, we have 

 material for making a lairly close prediction, but if we want to deal with wholc 

 lines of ance.stry, we are met at once by the difficulty of collecting Statistical 

 material for the correlation of the offspring's character with that of the higher ante- 

 cedents. In man few observations or measurements have been made on a higher 

 thaii the grandparental generation, and even in pedigree animals, where we can go 

 much further back, the characters recorded are never quantitative, but concern 

 colour or markings. To get over this absence of material Mr Galton originally 

 proposed that we should correlate not with each individual ancestor but with 

 the mean of each ancostral generation, females being rediiced to a male Standard. 

 There is no assumption in this because, of course, correlation can statistically 

 be worked for any such group of ancestry. But as we do not know the values of 

 the correlation coeflficients of the higher groups, Mr Galton suggested that we 

 should take the /,, J,, J3,... of equation (i) on p. 217 equal to i, |, i ... respec- 

 tively. This was undoubtedly an assumption, although not an unreasonable one 

 ä priori. That the iutensity of ancestral heredit}' diminishes as we go backwards 

 is demonstrated by both exporiment and Observation ; and a geometrical series 

 naturally first arises as a measure of such diminishing influence. But the law 

 could only be demonstrated on the base of the first few terms of the /-series, and 



28—2 



