1903.] 



to the Theory of Evolution. 



291 



A few remarks must be made on these tables. 



Table I gives the following values of the constants : — 



Mean length of head of elder brother = 186 "7508 in mm. 



„ „ younger = 183-8296 „ 



Standard deviation of elder brother = 7*5027 „ 

 „ younger „ = 7*3536 „ 



The correlation is, then, found to be 0*601,751,* and the regression, 

 younger on elder brother, 0*5897. These give the intensity of heredity, 

 uncorrected, for the growth factor. 



Now, the most noteworthy part of this result is, as we shall see later,, 

 that taking brothers at different ages tends to exaggerate the apparent intensity 

 of heredity. If we were to take pairs of boys at ages from 4 to 19, each 

 pair having no hereditary relationship, but being, on the average, 

 within a year or so of the same age, we should find a spurious correlation 

 due to the mixture of material, each pair having approximately-like 

 head-lengths because the members of it were, approximately, of like 

 age. On the other hand, if the boys were blood relations of very 

 different ages, their apparent relationship would be weakened, because? 

 we should be correlating the same organ at different stages of its- 

 growth. We have thus two factors : one tending to exaggerate, and! 

 the other to weaken the apparent strength of hereditary resemblance. 

 It is of great interest to note that the former factor in the present 

 case is the more effective. 



In Table II we have what I term a growth table, i.e., a correlation 

 table between period of growth and the quantitative measure of a 

 character. The constants of this table are as follows : — 



Mean age of boy = 13 * 0394 years. 



Standard deviation of age = 2*8207 „ 



Mean head-length = 185*4516 mm. 



Standard deviation of head-length = 7' 4991 ,, 



Correlation of age and head-length = 0*453,496 



The regression coefficient for head-length on age = 1*205676, and 

 we have the probable head-length Hp for observed age A given by 



Hp = 169*7303 + 1*2057 A (e.) 



Thus, on the average, boys' heads grow in length 1*2 mm. a year. 



My results are based on 1637 cases entirely taken off the brother- 

 brother data papers. Dr. Alice Lee at an earlier stage also worked out 

 a growth table. We had not then so many brother-brother data 

 papers filled in. She used in addition all the brother measurements 

 on the brother-sister papers, and so reached 1856 boys, of which, I 



* Six figures have been kept in the correlation coefficients, as we require to- 

 calculate the regression coefficients from the differences of products and powers. 



