482 



PROFESSOR TAIT ON FORMULA REPRESENTING 



the ordinary laws of probability, if applicable to this question, give us the 

 expression — 



F t =/ t +/ t+1 + . . . +/ 50 = 2f/ t 



assuming that sterility arrives about the age of fifty. 



Before going further, it may be well to verify this formula by comparison with 

 the tables, so that we may be assured of the validity of our reasoning. 



Dr Duncan gives {Trans. R. S. E. 1863-4, p. 358) the following numbers for 

 the wives in Edinburgh and Glasgow, taken as a whole : — 



Age 



15-19 



20-24 



25-29 



30-34 



35-39 



40-44 



45-49 



Fecundity 



50 



418 



34-6 



26-6 



20-4 



8 



1-3 



The two last numbers are probably not so accurate as the others — one from 

 vague statements as to " forty years of age ; " the other on account of some 

 omissions noticed in a footnote to the table. As, unfortunately, we cannot get 

 data for each year separately, we can only test the above formula for intervals of 

 five years. The numbers just given may therefore be taken as proportional to 



/it i f%% . /« ' /m ' fsi ' fa » and /« respectively. 



4. We may now construct the second line of the following table, according to 

 the formula above, by adding to the number for any quinquennial period all 

 those which follow it :• — 



Age 



15-19 



20-24 



25-29 



30-34 



35-39 



40-44 



45-49 



Fertility 



182-7 



132-7 



90-9 



56-3 



297 



9-3 



1-3 



F, 



12 



89 



6 



3-7 



2 



06 



o-i 



The numbers in the last line are proportional to those in the second, on the 

 assumption that a woman of 15-19 will have a family of twelve. 



Dr Duncan quotes (Trans. R. S. E., 1865-6, p. 302) from the Journal of the 

 Statistical Society the following table of values of F t for the mass of married 

 women in the district of St George 1 s-in-the-East. This is, unfortunately, not 

 quite comparable with the last, as the quinquenniads differ by one year of age ; 

 and, besides, the ages at marriage differ in the different columns. But there 

 seems to be no attainable table so nearly approaching what we require for 

 comparison. 



Age. 



16-20 



21-15 



26-30 



31-35 



F t 



10-85 



824 



5-00 



400 



