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XXX II.— Note on Formulae representing the Fecundity and Fertility of Women. 



By Professor Tait. 



(Received Oct. 1, 1866, and ordered by the Council to be inserted as an Appendix to Dr Duncan's papers in 

 Vol. XXIII., and in the. present volume, of the Transactions.) 



1. Dr Matthews Duncan having requested me to point out to him some 

 simple method of comparing the fertility of different races, I endeavoured, as a 

 preliminary step, to represent by formulae some of the chief results which he has 

 obtained in his very lucid and elaborate papers recently read to this Society, and 

 printed in their Transactions for 1863-4 and for the present session. Some of 

 the formula? which I have obtained are so simple, and accord so well with the 

 tables, that I have thought them worth bringing before the Society. Of course 

 it must be understood that I advocate no theory, and pretend to no physiological 

 knowledge of the question. I merely try to represent, in a simple analytical 

 form, the contents of some of Dr Duncan's tables. 



2. To prevent misconception, let us begin by defining the terms fecundity 

 and fertility as they will be used in this note, unless qualified in some manner. 



By fecundity at a given age we mean the probability that during the lapse 

 of one year of married life, at that age. pregnancy, producing a living child, 

 will ensue. This is, in all likelihood, modified in each individual woman by 

 the previous duration of marriage (see § 10 below). But at present, in dealing 

 with the mass of wives, we omit this consideration. We do not require, in our 

 calculations, to consider any questions connected with the duration of life of 

 husband and wife, of the length of time the child may live, &c, as the numbers 

 in the tables are already influenced by such causes. The numbers in the tables 

 do not usually denote the fecundity as above defined, but are quantities propor- 

 tional to its values. 



By fertility, at any age, we mean the number of children which a married 

 woman of that age is likely to have during the rest of her life, or some numerical 

 multiple of it. 



The subject divides itself into three heads — (I.) The fertility and fecundity 

 of the mass of wives ; (II.) their value for the average individual ; (III.) the 

 relative fertility and fecundity of different races. 



These we proceed to consider in order. 



I. Fertility and Fecundity of the Mass of Wives. 



3. If f represent the fecundity, and F t the fertility at the age of t years, 



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