Mathematical Contributions to the Theory of Evolution, 15Y 



The extraction of eleven tables from Mr. Galton's data papers I owe 

 to Miss Alice Lee, D.Sc. A twelfth is due to Mr. K. Tressler. For 

 the other three I am responsible. Of the determinations of the corre- 

 lation coefficients, I owe five to Miss Alice Lee, no less than six to 

 Mr. L. N. G. Filon, M.A., and the remaining four only are my own 

 work. The method by which the correlation coefficients have been 

 calculated will be explained and justified in another memoir ; it is a 

 novel process, which we believe to be of considerable importance, and 

 which we have already applied to a variety of attributes not capable 

 of exact quantitative measurement. The probable error of this 

 method of determining the correlation has also been ascertained, and 

 may be taken in the present cases to range from O'Ol to 0*04, so that 

 differences which are significant can be appreciated. 



Coefficients of Correlation. 



Sire and offspring : — 



Sire and all offspring 0'1775 



Sire and ^ offspring 0-2280 



Sire and ? offspring 0*1 104 



Dam and offspring : — 



Dam and all offspring 0*5239 



Dam and ^ offspring 0*5077 



Dam and ? offspring 0*5445 



Mean parental correlation pi ^ 0*3507 



Grandparent and offspring : — 



Sire's sire and all offspring 0*2144 



Sire's dam and all offspring 0*097 6 



Dam's sire and all offspring - 0*0032 



Dam's dam and all offspring 0*2215 



Mean grandparental correlation .. . p., = 0*1326 



Great grandparent and offspring : — 



All great grandparents and all offspring 0*0404 = 0*0404 



Siblings* : — 



Whole siblings from same litter 0*5084 



Whole siblings from different litters ... 0*5257 



Half siblings, dam's side 0*2222 



Half siblings, sire's side 0*1070 



* Every writer on heredity must have felt the inconvenience of our language 

 having preserved no word for either member of a pair of offspring of either or both 

 sexes from the same parent. After some hesitation, I have ventured to reintro- 

 duce a good Anglo-Saxon word with this sense. 



VOL. LXVI. O 



