;.) STATISTICS OF SEX 



The computation of the formula (5) is shown in the following table. 

 To enable the essential numbers of this table to be understood without 

 the necessity of going through all the mathematical formulas, I shall 

 state their significance and application. On the left are found certain 

 possible values of n, the number of children in a family from 2 to 12 

 inclusive. Each block of numbers connected with a single value of n 

 relates solely to families of that number of children. 



In the next column are given all possible distributions between the 

 two sexes which the family can have. Complementary families as re- 

 gards sex are combined. For example, a family of three children must 

 consist either of three children of one sex, whether male or female, and 

 none of the other; or it comprises two of one sex, whichever it may be, 

 and one of the other. The two lines correspond to these cases. 



The three following columns contain numbers employed in comput- 

 ing the probabilities as found in the expression on the right. The 

 denominators of the fractions which enter into these probabilities are 

 written after the sign -=- of division, and, in each set relating to one 

 value of n, the fractions are reduced to the least common denominator, 

 but not to their lowest terms. This form of expression is used for 

 convenience in tracing the law of the numbers and continuing the table. 

 The probability is expressed as the sum of two terms : one a pure num- 

 ber; the other a coefficient of the factor ha. The purely numerical 

 term shows what the respective probabilities of the division of sexes 

 found in the second column will be in case of no unisexual tendency. 

 For example, in a family of four children there will then be one chance 

 of all four being of one sex, three chances of one being of one sex and 

 one of the other, and three chances of an equal division, making eight 

 chances in all. Hence, in a great mass of such families, we shall have 

 one-eighth all of the same sex, four-eighths, or one-half, with a pre- 

 ponderance 3 to 1, and three-eighths with an equal division. 



The next term shows how this probability is modified in case of a 

 unisexual tendency. The symbol In expresses the fraction of the whole 

 number of parents which have such a tendency. The tendency in one- 

 half of this fraction of cases will be in the male, in the other in the 

 female direction. The symbol a is the unknown amount of this ten- 

 dency. 



These expressions for the probability are rigorous when n is 2 or 3. 

 But, when n has a greater value, terms in the higher powers of a 

 really exist, the highest power being n, or n - - 1, according as n is even 

 or odd, but, as a must always be a rather small factor, these high powers 

 may be neglected. 



