K. Pearson 227 



i.e. befoi-e ([tiantitative analysis, not .sUite whuthor tlie total ainouiits they will 

 contributc to the predicate will or will iidt indicate a biological regression *. 



((]) The law of aiiccstial hcicdity as a i)iiio Statistical statement has been 

 suppleinunted by liypotheses which iiecd verification aiid are semi-biological. These 

 niay (i) eitlier bu liypotheses as to the multiple regression coefficieiits, or (ii) as to 

 the individual coefficieiits of correlatioii. 



Mr Galton has assuniod tliat the fornier are the geometrical series ^, i, ^ 



I have assuined that the medii correlation coefficients for each ancestral generation 

 form soine geometrical series. It foUows from my assumption that the regression 

 coefficients would also form a geometrical series, but not necessarily Mr Galtou's. 



(e) In eye-coloiir in mau and coat-colour in horses the mean ancestral 

 coefficients of regression form within the liniits of errors of random sampling a 

 geometrical series, but it is not Mr Galtou's series : 



•5000, -2500, -1200, -0625..., 

 but more uearly : 



•6244, -1988, •0630, •0202.... 



In other words actual statistics sliow that in man and horse the parents are much 

 more and the grandparents and higher ancestry less influential thau on Mr Galton's 

 hypothesis. 



Thus the law of ancestral heredity (by which we are to understand the theory 

 of multiple correlation together with the hypothesis that the mean ancestral 

 correlations or tlie regression coefficients form a geometrical series) fits the data 

 for horse and man remarkably well. 



(/') In man and horse we find the means of each generation differ, and 

 further the variabilities of each generation differ. It is au assumption to suppose 

 under these circumstances that the suiu of the regression coefficients (or rather that 

 part of them which we have represented by J^, J„, J,, ...) is unity. 



Any geometrical series for the regression coefficients which satisfies the con- 

 dition e = \— p (like Mr Galton's does) would give ou the suppositiou of eqnal 

 means and variabilities for each generation no regression whutever after a stock 

 began to in-breed. 



If we may apply (which is very doubtful) our values for the J's in mau and 

 horse to cases in which the means and variabilities of each generation remained 

 the same, there would result the following principle : 



Two or three generations of selection would produce a stock of upwards of 90 

 per Cent, of the selected character, but uo amouut of selection, unless of a greater 



* It is curious that the original nunibers selected by Mr üalton for the regression coefficients 

 i, i, \, etc. indicate no regression whatever towards the predicate mean, after the first generation, if 

 the stock in-breeds or breeds with ita likes. It is characteristic of how conceptions are misunderstood, 

 that this point of " regi-casion " is what the majority of biologists have seized as the one easily 

 comprehended principle out of the whole of Mr Galton's work 1 



29—2 



