488 PROFESSOR TAIT ON FORMULA REPRESENTING 



This coincidence also is close enough, and would be still closer if we had the 

 numbers for f 50 and upwards, as the smaller numbers in the table, where the 

 deficiency lies, would thus be increased proportionally much more than the 

 larger ones. 



III. Relative Fertility of Different Races. 



12. We may apply the above results to compare the fertility of different 

 races— a problem of considerable interest. We shall not attempt a rigorous 

 solution, for the application of which, indeed, we have no sufficient data ; but 

 shall make one or two postulates, which will probably be easily admitted, and 

 which will enable us to avoid complication. 



13. Suppose that for ten or fifteen years we may consider the number of mar- 

 riages at any given age to remain practically unaltered, we may then consider the 

 births in any one year as represented by the total fertility of those married in that 

 year. That is, the children born in that year of mothers married at 30-34, for 

 instance, are due to those married last year, the year before last, and so on for 

 fifteen years back, at the age of 30-34; and as the number is supposed nearly 

 constant for some years, we have the fertility of all for one year (very nearly) by 

 calculating the total fertility for the rest of their lives of those married in that 

 year. As population, and with it the number of marriages, is generally increasing, 

 this process will slightly exaggerate the numbers sought ; but, in comparing two 

 growing countries, such as England and Scotland, no perceptible error will be 

 introduced. 



14. We next assume that the law of fertility as depending on age is the same 

 in the two countries compared. That is, we assume that 



F't F' t+ i F' t+2 



v — v^ ~ v ~ etCl ' = e ' 



V t ± t +l * t+2 



where e is some definite number ; and F t , F' t represent the fertility in the two 

 races at age t. 



This will evidently be the case if the fertility be really expressible, as above, 

 in the form 



Ft = | k (50 - tf, 



for two such expressions can only differ through the number k ; unless indeed 

 the age at which sterility comes on, here represented by 50, should happen to be 

 greatly different for different races. On this point we have no information. 



15. Let, then, /x t be the number of marriages of women at t years of age in 

 any one year, /3 the number of legitimate births in a year, we have by the above 

 postulates 



= 2/iF = A* 15 F 15 + /e 16 F 16 + • • • + /* 49 F 49- 



