This paper was a sequel of a paper read to the Royal Society, and published in the 23d volume of the “Transactions.” That paper was entitled, “On the Variations of the Fertility and Fecundity of Women, according to age;” and among other conclusions therein announced, was one to the effect that fecundity, or likelihood of child-bearing after marriage, increased from the earliest child-bearing age till about twenty-five, and thereafter gradually decreased. In the present paper, the laws regulating such fertility after marriage are demonstrated. The chief data on which the arguments for these laws are based are derived from an analysis of 16,301 families, in connection with which entries were made in 1855 in the public registers for Edinburgh and Glasgow.