1903.] 



to the Theory of Evolution. 



293 



line, until the range of data is very largely extended, 

 sion is sensibly linear. 



Table IIIa and Table IIIb give the following results :— 



The 



^egres- 



Mean age of elder brother . . = 14 '1249 

 S.D. of elder brother's age. . = 2 '5124 

 Mean bead -length, younger 



brother =183-8578 



S.D. of head -length, younger 



brother = 7 -2806 



Correlation of age of elder and 



head-length of younger . . = '396,598 



Mean age of younger brother = 11 "7149 



S.D. of younger brother's age = 2 "7221 

 Mean head -length, elder 



brother =186 '6515 



S.D. of head-length, elder 



brother = 7 '5005 



Correlation of age of younger 



and head -length of elder . = '379,326 



We see accordingly that within the limits of the probable error, the 

 correlation between younger brother's head-length and eider brother's 

 age is the same as that between elder brother's head-length and 

 younger brother's age. This result might, to some extent, have been 

 anticipated, but actual proof of this type of cross-relation is of value. 

 In Table IV we have the correlation between ages of brothers giving 

 the constants : — 



Mean age of elder brother = 14*1508 



Mean age of younger brother == 11 '7487 



S.D. of elder brother's age = 2-5080 



S.D. of younger brother's age = 2 • 7220 



Correlation of brothers' ages = 0*884,186 



The first four results are in good agreement with those of Tables 

 IIIa and IIIb. The last result shows how nearly there is an approxi- 

 mation to a constant difference in age between brothers in schools. 

 Very closely we have — 



Probable age of younger brother = 0*96 x (age of elder brother) - 1*83, 



When the elder brother is 6, his younger brother is probably 2*1 years 

 younger than he is ; when the elder brother is 12, the younger brother 

 is probably 2 '3 years younger, and when he is 18, 2*6 years younger. 

 The explanation of this is that when the elder brother is very young 

 only his near or second brother will, as a rule, be at the same school, 

 but in the secondary schools, which he reaches at a much later age, it 

 is possible for a much younger brother to be at the same school. 



Now let us substitute the correlation values, found in equations (i) 

 to (iii), of page 290. We have 



r xy = 0*601,654, r hh = 0' 884,186 



r xh = r yh - 0-453,496, 



r xti = 0-379,326, r yh = 0' 396,598. 



