K. PkARSON AM) A. JiKK 3!)5 



thc ränge of iiew problenm wliich suggcst tliciiisolvos for Solution. Yct I tliink 

 eacli lai'Lfe niass of rnatcrial Statistical ly rrdiiccd placos a further Stratum nt liini 

 grounil bi'ni'adi ns. In |iarticular, tliis tirst, papcr <iii iiihciitancc of tlie jjh^'sioal 

 characters in man, iias, 1 hold, cnabled us to rcach some vcry definitiv rcsults. 

 Jndccd, I bi'licve tlu'ui sutKcicnt i-('|iaynK'nt for the years spont by my hclpers in 

 measiu'ing u]i\vard.s of a thousand familics and tabling and rcducing th<' data*. 

 Of the special result.s obtained I would refcr in parlicidai' to the foUowing. 



(i) We have very definite evidenee that: the n(jrnia.l eurve sullice.s to describe 

 within the liniits of randoni sanipling the distribution of the chief physical 

 characters in man. 



This eontinns the conclusions of Galton, Macdoneli, Fawcctt and othcr workers 

 in anthroponietry, and is of special value wheii we come to e.xtend our results to 

 the inheritance of characters not quantitatively measurablo. 



(ü) The regression eurve between pairs of blood rehitions, wliethcr we deal 

 with direct or cross-heredity, is within the liniits of random .sanipling linedv. This 

 had been already suggested by Galton on the basis of the theory of normal 

 distribution, and confirmed by bis researches on stature. I tliink we mar safely 

 assume in future that the diniensions of the human body give linear regrcssion- 

 linesf. 



(iii) There is an appanMit cliange in type going on in man, especially 

 evidenced in the feniale, but also sensible in the male. The young adidt differs 

 in magnitude, variability and correlation froni the old adult and the difference 

 appears to be signitieantly beyond growth ehanges. 



We cannot at present determine whether this change is : 



(Vf) Environmental, due to change in physical training and food between the 

 j'ouiig and old generatious. 



(6) Due to natural selectiou, the young adults being reduced nearer to the 

 old adult type by deaths of a selective character in the intervening 20 to 30 years. 

 If the change of type is due to a selective death rate, it may be either periodic, 

 occurring in each generation, or secular, i.e., a progressive change. 



(c) Due to reproductive selection, out of young adults a certain class have a 

 differential fertilit}' and beeomc in bulk the parents of adult offspriiig. 



But although we are not in a position to etfectually discriminate at present 

 between the amount of change due to (a), (6) and (t), our results irauiensely 

 emphaiäise the view that even in apparently unessential characters mankind is, even 

 at the present day, not in a stable ccjndition, but that a change of type is very 

 probably taking place owing to natural or reproductive selection or environmental 



* When it is remembered that the whole work of nieasurement was done by volunteer aid, and without 

 assistance from any public ('und, I think other workers may take heart, who imagine that probloms in 

 heredity are neces.sarily confined to extensive breeding experiments of an expensive nature. 



t This is really a very important point. In a forthcoming memoir on skew oorrelatiou, I deal with 

 non-linear regression and show how fairly frequent it is and how coniplex it renders the treatment of 

 correlation. 



