PREFACE. In the early part of the session of 1864, I read a paper before the Actuarial Society of Edinburgh, on the Valuation of Widows' Schemes, and on that occasion I explained the mode of preparation of a few Tables, arranged from the statistics of the Widows' Funds of the Ministers of the Church of Scotland, and of the Burgh and Parochial Schoolmasters in Scotland, exhibiting the law of marriage among the members of these Societies. It occurred to some of the gentlemen present on that occasion, that the publication of these Tables might be useful to Actuaries engaged in the examination of the affairs of such bodies, and I was requested to extend my paper and give it publicity. This, then, is my excuse for offering such an humble work to the profession. I publish it nearly in the same state in which it was originally written, as other engagements have prevented my devoting much additional time to its completion. Having been prepared for a Society, many of whose members had but recently turned their attention to actuarial subjects, there was necessarily much of elementary matter introduced, but I trust that the Tables may be found of service to some Actuaries. I do not know of any already in existence which are exactly similar; at the same time, I do not claim great originality for the idea, as some of them were suggested to me by the perusal of a volume of manuscript tables left by the late eminent Actuary, Griffith Davies, to which I shall afterwards refer in describing my own Tables. I take this opportunity of expressing the obligations under which I lie to Mr Thomson, the Manager of the Standard Life Assurance Company, for placing at my disposal much valuable statistical matter which he had collected during his actuarial career. Indeed, almost all the statistics on which the following Tables are founded were supplied me by Mr Thomson. D. R. W. H. REGISTER PLACE, Edinburgh, 6th March 1868. VI. Value of an Annuity of £1 to the Widows who may be left through the First Marriage of Bachelors, according to the Experience of the Schoolmasters' Widows' VII. Value of an Annuity of £1 to the Widows who may be left through the First Marriage of Bachelors, according to the Experience of the Ministers' Widows' Fund, VIII. Value of £1 to the Widows who may be left through the IX.-XVI. Value of an Annuity of £1 to the Widows who may be left through the Second Marriage of Men whose First XVIII. Value of an Annuity of £1 after the Death of a Widower, and Payable until his Youngest Child reaches 21 XIX. Value of an Annuity of £1, Payable after the Death of a M REMARKS ON THE VALUATION OF WIDOWS' FUNDS. BEFORE the modern system of Life Assurance was introduced, there was no means by which a husband and father could provide an independence for his family in the event of his early death, unless he belonged to some guild or corporation which possessed sufficient funds to offer relief to the destitute families of its members. The first effort in the direction of life assurance was the establishment of Widows' Funds. When these Societies were originally founded the true principles on which they should be established were not understood, and, consequently, great difficulty was experienced in adjusting the rates payable by the members to secure the benefits of the fund. Having no Mortality Tables to assist them, the founders of these Societies endeavoured by an elaborate calculation to ascertain how many widows were likely to come upon the Fund every year, and at what time the number of widows would reach the maximum, after which period the numbers might be expected to remain stationary, or nearly so. These numbers being ascertained, it next became their object to provide an annual fund, sufficient to meet the yearly-increasing amount of annuities, and at the same time to accumulate a capital, the interest of which would, along with the annual rates, be sufficient to pro |