PEARL— SEX RATIO IN DOMESTIC FOWL. 427 



The striking fact which this table brings out is the great reduc- 

 tion in the variation of the sex ratio from mating to mating as the 

 progeny from the individual mating becomes more numerous. 



Even with the large families, however, the amount of variation 

 in the sex ratio is large, absolutely and relatively. Taking families 

 of 10 the percentage of the standard deviation in the mean is 



27-53- 



This is of roughly the same order of magnitude as the coeffi- 

 cients of variation of such physiological characters as fecundity ,'^° 

 etc. There can be no question that the sex ratio is relatively a much 

 more variable character than stature, skull form, and most other 

 morphological characters of animals. In view of this fact, there 

 would seem to be need of vastly more caution than is commonly 

 exercised by writers on the sex ratio in drawing far-reaching con- 

 clusions from very small numbers. 



The values for the standard deviation of the sex-ratio here ob- 

 tained for poultry are of the same general order of magnitude as 

 those of Heron^^ for man and horse, and of Weldon^- for mice. 



The form of the normal sex-ratio variation curve is of interest. 

 In order to deal with this adequately, we must resort to the ana- 

 lytical methods of Pearson. ^^ 



The case presents some difficulties from the standpoint of graph- 

 ical representation, because of the fact pointed out above, that we 

 have dealt with the actual centers of gravity of each piece of area 

 standing over a unit on the abscissal axis, and have not assumed as 

 is usually done, that the center of gravity of each strip was at its 

 mid-point. The conventional histogram does not give any repre- 

 sentation of this distorted concentration, and hence the correct fitted 

 curve does not seem to give so true a representation of the facts as 

 an incorrect one, as will presently appear. 



10 Cf. Pearl, R., Science, Vol. 37, p. 228, 1913. 



11 Heron, D., Biometrika, Vol. V., pp. 79-85, 1906. 



12 " On Heredity in Mice from the Records of the Late W. F. R. Weldon. 

 Part I. On the Inheritance of the Sex-ratio and of the Size of Litter," Bio- 

 metrika, Vol. v., pp. 437-449, 1907. 



13 Pearson, K., Phil. Trans., Vol. 86 A, pp. 343-414, 10 pls.„ 1895, ibid.. 

 Vol. 197 A, pp. 443-459. 1901- 



