3. Note on the Probability that a Marriage entered into by a Man above the Age of 40 will be Fruitful

Extract

When it is desired to disentail a landed estate, it is necessary for the heir in possession, after obtaining the consent of the first substitute heir, to pay to the second and third heirs the estimated value of their expectancy or interest in the estate. In the calculations that have to be made for the purpose of ascertaining this value, the actuary has often to take into account not only the probabilities of life, but the probabilities of marriage and of leaving issue. The heir in possession may be unmarried, in which case he may marry at some future time, and leave a child who would inherit the estate to the exclusion of the subsequent heirs; or the heir in possession may be married but have no children, and the probabilities then to be estimated are (1) that his present wife will have a child at some future time, and (2) that she will die before her husband, that he will then marry a second time, and have issue by his second marriage.