K. I'karson and A. JjKK 



:}(i!) 



Tli(j rolliiwiiiy is thc 'l'ablf f'or foira.nii in Kons. 

 Fureariii in Smis. Il.")(i Cnscs. .lAnn/ = 1S"'Ö2, StandanI l>ei!iiitwn = "'dH'3. 



This Table as well as thc pn-vions one snggests that a sniall Imt sensible 

 element of skewness in the foreann as well as tlie (jutlying group coutribtites to 

 the divcrgcncc from norinalitv- 



It will be seen that onr present data justities Mr Galtun's original use f'or 

 stature of tlio uornial curvo and the normal surface, i.e. 



1 i:^_2^^]n 



(where zB.>'?>ij is the fre<juency of a grouji of relative pairs having characters with 

 deviations from their nieans lying between .'-,// and .c +&/■,?/ + S^ ; N being the 

 total number of pairs, a^, o",, being the Standard deviations, and r the c-oetficient 

 of correlatiou of thc two characters: see Phil. Trans. Vol. 1X7, A, p. 2(34 et seq.). 

 It also is fully justified for span and even for forearm (if we remember that there 

 exists a small group of " outliers "). The norniality of the distribution adds little, 

 however, to our investigation, as long as we can show that the regression is 

 practically linear (see Diagrani III.). The pnictical value of normality arises 

 chiefly when we pass from measurable characters in man to those that are not 

 capable of exact quantitative measurement, for here every excej)tion to normality 

 weakens our gencral iDosition. 



The general linearity of our regression lines enables us in the present case to 

 apply a simple theory, as soon as we have calculated the means, the Standard 

 deviations, and the correlations of the various characters. 



These will enable us, by using the formulae of simple or multiple correlation, 

 which depend simply on linearity, to predict the probable character in any 

 individual from a knowledge of one or more parents or brethren (" siblings," = 

 brothers or sisters). But without further assuniption they do not enable us to 

 test the effect of long-continued selection in cstablishing Stocks ; for we have 

 no ancestral correlations, beyond the parental, for the characters dealt with. 

 Ancestral correlations be^'ond the parental are, however, kiiown for man in eye- 

 colour inheritance (up to great-grandparents), for horses in coat-colo<ir (up to 

 great-great grandpareuts), and for dogs in coat-colour (up to grandparents). 

 Hence, if the parental correlations for men, horses and dogs are sensibly the same, 



