486 



PROFESSOR TAIT ON FORMULA REPRESENTING 



If we accept 10 children as representing the whole fertility at 15-19, which 

 seems a reasonable assumption, we have 



10 = i/ 17 (43-17) = 13/ 17 . 



Hence / 17 = J£, from which (by proportion) the other values of / are easily 

 found. Hence — 



Age at Marriage. 



Whole Fertility. 



Ft. 



15-19 

 20-24 

 25-26 

 30-34 



100 

 7-7 

 5-5 

 3-4 



100 

 7-4 

 50 

 3-1 



The last column has been added for comparison, so as to show how the later 

 advent of sterility in the more advanced marriages increases the fertility. 



It may be well to notice that the interpretation of the expression / 17 = y§ is, 

 that a wife of 15-19 will, on the average, become pregnant at 1*3 years after mar- 

 riage, that is, she will have a child within about two years of marriage. This 

 limit of time depends, however, on our assumption of 10 children as the measure 

 of the fertility at 15-19, and childless marriages are included in the data. Dr 

 Duncan gives {Trans. R. S. E., 1865-6, p. 297) 152 years as the average interval 

 between marriage and the birth of the first child. The reason of the discrepancy 

 is of course this, that in our calculation the mass of wives is considered, and in 

 Dr Duncan's only fruitful marriages are taken account of. 



II. Fecundity and Fertility of the Average Individual. 



11. If we endeavour to derive formulae of a similar character from the tables 

 of sterility, the results are not quite so simple. Thus we find (Trans. R. S. E., 



1865-6, p. 319)— 



Age at Marriage 



15-19 



20-24 



25-29 



30-34 



35-39 



40-44 



45-49 



Percentage Sterile . 

 Percentage not Sterile 



73 

 927 





 100 



27-7 

 723 



375 

 62-5 



53-2 

 468 



909 

 91 



956 

 44 



From the manner in which this table was formed, it would appear that we are 

 justified in taking the numbers in the last line as proportional to the average 

 fecundity at the respective ages. But the curve representing these numbers 

 differs considerably more from a straight line than that derived from the other 

 tables. It is the dotted curve in the figure. It is true that if we consider the 

 loose way in which women from 30 to 40 call themselves 30, and those from 



