37 



Distribution of individual variations within the 

 species. 



(i) The normal curves of variations. 



Galton's observations on the English people. 



{See Galton, Natural Inheritance, pp. 35-70.) 



The curve of distribution. 



The curve of frequency. 



Relations of these curves. 



The curve of frequency of error. 



Mechanical illustration of the cause of the 

 curve of frequency. 



Weldon's observations on Crangon and Car- 

 ciniis. 

 (Proc. Roy. Soc, Vol. 47, p. 445, and Vol. 54, p. 318). 



(2) The correlation of variations. 



(See Darwin, Animals and Plants under Domestication, 

 Vol. 2, pp. 311-332 ; and Brooks, Heredity, p. 157.) 



Correlation between associated parts. 

 Correlation between homologous parts. 



Galton's function (See Galton, Proc. Roy. 

 Soc, Vol. 45, p. 135 ; Weldon, /. c, Vol. 



55» P- 234)- 



M^ mean, Q = "probable error." 



Qa. = the Q of organ A. 



Qb = the Q of organ B. 



V =z any deviation of organ A from its M. 

 Xm = mean associated deviation of organ 



B from its M. 

 X = any deviation of organ B from its M. 

 Ym = mean associated deviation of organ 

 A from its M. 



X». ^ Qb Y,n ^Qa 



^=: -— = r, a constant, 



Y -^Qa X -^Q, 



