The question ov the calculation ov premiums for the insurance agenst issue to a man at present marryd but without a family, has been on two ocasions bro't under the notis ov the Institute by Mr. Archibald Day. On 31 January 1859 he redd his paper On the determination ov the rates ov Premium for asuring agenst Issue (Journal viii, 127), in which he explaind his proces of calculating, by means ov statistics furnisht by the Registrar General's returns, the present value ov £1 payabl at the end ov the year in which a husband shal contract a second marryge. On 24 March 1862 he redd a stil more important paper, On the statistics ov first and subsequent Marryges among the Familys of the Peerage, considerd specially with reference to the calculation ov Premiums for Asurances agenst Issue, in which the same method was employd to obtain more accurat premiums from the more apropriat statistics furnisht by the peerage familys. The general problem is a very complex one involving several distinct contingencys. Mr. Day delt very succesfully with som ov these contingencys, but his treatment ov the subject was confessedly incomplete, and he himself speaks ov it as giving only a ruf aproximation. He omitted altogether from the calculations the circumstances that the insurance is not payabl until the deth ov the husband after contracting the second marryge, and that ther is a probability ov his second marryge being unfruitful. I hope on som future ocasion to take up the general question and carry the investigation ov it one or two steps beyond the point at which Mr. Day left it, but on the present ocasion I shal deal only with one element involvd in the calculation, namely, the probability ov the remarryge ov a widoer.

A Number of suggestions made at various times by different persons for subjecting Fire Insurance Statistics to systematic treatment were reviewed by Mr. Cornelius Walford some time since in an Article “On the scientific application of Data to the purpose of deducing Rates of Premium for Fire Insurance”, which is published in the April 1878 number of the Assurance Magazine. The present paper is an attempt to lead the investigation into another course, and its purpose is to enunciate a Theory of Statistics in dependence on which algebraic formulae may be constructed and arithmetical calculations made of the values of risks. The particular line it will take is that of averaging quantities, but it could be developed in other directions if that were desirable.

Proceeding, without further preface, to the consideration of the subject, we observe :—

That the readiness with which materials can be ignited by any particular agency varies—

1. In consequence of their constituents being different, as Wool contrasted with Cotton.

2. From the same kinds of substance being in different forms, as timber in logs, deals, shavings, sawdust, or splinters.

3. From substances existing in different states, as flax lying loose in repose, and flax tossed about and being cleaned in a heckling-house.

It is sometimes necessary in disentail proceedings to estimate the probability that a husband, who has been married for several years without having any children, will hereafter have issue, either by his present or by a future wife. The probability of issue by a future wife is a subject comparatively well understood, and it is a recognized part of the business of some insurance companies to grant insurances against the contingency of such issue being left surviving at the death of a married man who has no child. The probability of issue by the present wife has been very little considered, and it is this probability that I propose now to discuss. There are very few statistics that will help us in the matter; in fact, I am only aware of two works in which any such statistics are given. Dr. J. Matthews Duncan gives the following table, in his work Fecundity, Fertility, and Sterility (p. 132, 2nd Ed.) :—

Mr. Charles Ansell, Jun., in his Statistics of Families in the Upper and Professional Classes (page 87) gives a table from which columns (1) to (4) of the table on the opposite page are extracted.