84 



POPULAR SCIENCE MONTHLY. 



DISCUSSION AND COEEESPONDENCE. 



PROFESSOR PEARSON ON THE 

 DISTRIBUTION OF FERTILITY. 

 In a note concerning the question 

 of the birth rate in the April number 

 of the Monthly, you quote Professor 

 Karl Pearson's distributions of fertil- 

 ity and also refer to his measurements 

 of the resemblance between mother and 

 daughter in fertility. The skewness of 

 the distribution of fertility in the case 

 of the Quaker families probably repre- 

 sents no real condition, but is due to 

 a statistical procedure, namely, to the 

 combination in one distribution of 

 groups of individuals of a number of 

 different generations. As I show in an 

 article in this number of the Monthly, 

 the distribution of natural fertility in 



I 1 3 H S' 6 7 M 10 /I n /3 



any one decade is approximately nor- 

 mal, there being no pronounced skew- 

 ness save that due in late decades to 

 the undistributed zeros. But if I com- 

 l)ino all my results from Middlebury 

 College, using thus families of men 

 born from 1780 to 1850, I get a curve, 

 as shown in tlio diagram, like Professor 

 Pearson's in its pronounced positive 

 skewness. If wo suppose, as I am sure 

 we must, that in Professor Pearson's 



Quaker families, the families are of 

 larger and larger size as we go back 

 in time and that also the number of 

 families examined is fewer and fewer 

 as we go back in time, we must con- 

 clude that even if the distribution were 

 perfectly normal at any one period the 

 total score would give just such skew- 

 ness as he found. The abnormality of 

 his distribution is thus a sign of the 

 statistical mixture of species, not of 

 any essential physiological character- 

 istic. Of the Copenhagen records I 

 can not speak assuredly as I do not 

 know how the individuals were dis- 

 tributed in time. The occurrence in 

 Professor Pearson's records of families 

 of 13-22, higher that is than any that 

 I have found in over 2,000 families of 

 the last century, would seem to show 

 that the beginning of the decadence of 

 the American stock dates back beyond 

 the nineteenth century. 



It is possible too that the resem- 

 blance in fertility between mother and 

 daughter which Professor Pearson has 

 measured, and naturally enough at- 

 tributed to heredity, may be really due 

 to the necessary nearness in time of 

 a mother and her daughter. If, for 

 instance, in five generations fertility 

 dropped steadily from 10 to 2, and we 

 calculated a coefficient of filial correla- 

 tion for a group of mother-daughter 

 pairs distributed throughout the five 

 generations, we shouhl have a result 

 showing marked mother-daughter re- 

 semblance, althougli licredity, as meas- 

 ured by tlip com])arisou of measures 

 taken relatively to the average fertil- 

 ity at the time the individiuil lived, 

 might amount to »//. 



Kdwari) L. Thorndike. 



Teachkks College, 

 New York. 



