case she may dispose of it as if a single woman. We have then, in the several cases supposed, the following limited interests which may be submitted for valuation to an actuary :-(1) Life interests in possession. (2) Life interests in remainder. (3) Simple reversions subject to such life interests. (4) We may have this much more complicated case, not by any means uncommon, in which the power of appointment does not exist, or has for any reason become inoperative-as, for example, would be the case where it was a joint power, and the death or lunacy of one parent has happened, and the actuary is asked to value the interest of a child who has attained his majority and therewith a vested interest in the fund, subject to be increased by the deaths of his brothers and sisters under age or unmarried, according to the terms of the trust. If there is a large family, the actuary will find in this case ample scope for his ingenuity; but unless the number of very young children is large, will scarcely fail to disappoint his client, with the small value at which he will put his rights of accruer, and possibly be little satisfied himself at the inadequate result of his own labours. (5) We have the interest of the settlor of the fund, probably the father of the lady, if the ultimate reversion is reserved to him and his representatives on the deaths of the husband and wife, and the failure of any issue of the marriage living to attain a vested interest in the fund. (6) Lastly, where the ultimate trust is for the next of kin of the lady, exclusive of the husband when he survives her, we may have the possible interests of a variable class to be ascertained only at her death. Such interests are not likely to be submitted to an actuary for valuation, except in the form of simple reversions, when the reversioner has been ascertained by the death of the first tenant for life. On the hypothesis that that event is still in the future, the student may consult a table deduced from the Statute of distributions of the personal estates of intestates, and from it propose to himself problems of infinite complexity, and sufficient to satisfy the strongest appetite for such mental pabulum. Here, however, he will encounter a contingency which is not susceptible of valuation, namely, that the law, or the construction of the law, shall be the same at the time when he works his solution, and at some future time when he may hope to apply it. As a proof that this is not mere mockery, I may observe that, within the last two years, the Court of Chancery (in re Ross Trusts, L. R., 13 Eq., 293) pointed out the true construction of the statute of Charles the Second in so simple a case as that of determining the shares of grandchildren and great grandchildren in the estate of On the Practice of the Eagle Company with regard to the Assurance of Lives classed as Unsound, and on the Rates of Mortality prevailing amongst the Lives so classed, assured during the Sixty-three Years ending 30 June 1871. By George Humphreys, M.A., Actuary to the Company. Abstract of the Discussion on the preceding On the method of comparing the Expected with the Actual Experience of a Life Insurance Company, as regards the number of Deaths and amount of Claims. By George M. Low, F.F.A., of the English and Scottish Law A comparison of Reserves brought out by the Use of different Data in the Valuation of the Liabilities of a Life Office. By James Valentine, On the Computation of Annuities on Mr. Makeham's Hypothesis. By Emory McClintock, Actuary of the Northwestern Mutual Life Insurance Com- On the Value of a complete Annuity when payable by m equal Instalments in each Year. By Thomas Carr, F.I.A..... "An Estimate of the Degrees of the Mortality of Mankind, drawn from curious Tables of the Births and Funerals at the City of Breslaw; with an Attempt to ascertain the Price of Annuities upon Lives. By Mr. E. Halley, R.S.S". Reprinted from the Philosophical Transactions for PAGE Remarks by Dr. Farr on Halley's table On Lubbock's Formula for Approximating to the Value of a Life Annuity. By T. B. Sprague, M.A., Manager of the Scottish Equitable Life Assur- ance Society, and a Vice-President of the Institute of Actuaries On an application of the Theory of the Composition of Decremental Forces. On the Interpretation of the Statements required by the "Life Assurance Companies Act, 1870", with special reference to the question of Expenses. By David Deuchar, F.I.A., F.F.A., Secretary and Joint Actuary of the Does a Large New Business benefit the Policyholders of a Life Company? By James R. Macfadyen, of the Legal and General Life Assurance Society. On the Mortality of the Clergy. By Herr Heinrich Stüssi, of Zürich. Translated and Abridged by D. A. Bumsted, Fellow of the Institute of On the Rate of Mortality among Adult Government Emigrants on the Voyage to Australia, during the Years 1847-1861 inclusive, as determined from the Reports of the Emigration Commissioners. By J. J. McLauchlan, On the Usefulness of Mathematical Studies to the Actuary.-An Address to the Actuarial Society of Edinburgh. By the Honorary President, T. B. On Mortality Fluctuations. By James R. Macfadyen, of the Legal and Economical Rates of Reserve and Premium. From the Spectator of New 416 Mr. J. J. McLauchlan on the Formulas for the Approximate Determination of the Rate of Interest of an Annuity... 290 JOURNAL OF THE INSTITUTE OF ACTUARIES AND ASSURANCE MAGAZINE. On the Origin and Nature of some of those Limited and Contingent Interests in Property which are commonly submitted to Actuaries for Valuation. By C. J. BUNYON, M.A., Vice-President of the Institute of Actuaries. [Read before the Institute, 28 April 1873.] THE present paper is essentially elementary, and must therefore in a great measure be considered as addressed to the junior members of the Institute, although, perhaps, even to those more experienced persons to whom in the course of years these things have become familiar, a recapitulation, such as I now propose, may not be wholly uninstructive.* These interests, then, appear to divide themselves into two great classes: (1) interests arising under settlements of either real or personal estate, and (2) interests or liabilities which are the fruits of tenure, as in copyholds, or which require valuation on account of the imperfection or limitation of the subject or property to be valued, as in the case of renewable leaseholds, or terms of years in gross, or estates pour autre vie. On the present occasion I propose * The statements of law in this paper are principally taken from "A Profitable Book upon Domestic Law," published by Messrs. Longman & Co., 1873-a volume of legal essays giving in a readable form as much technical information on these subjects as is likely to be useful to persons not actually in legal practice. VOL. XVIII, B |