2. That further investigations should be made into the question of the effect of selection, with the view of deciding whether distinct monetary Tables should be given, applicable to assured lives from which that effect has in a great measure passed away. The graduation of the three Tables, HM, HF, and HMF, was kindly undertaken by Mr. Woolhouse, whose great skill and experience suggested to him a new method, combining in a probably unprecedented degree adaptation for all practical purposes with close adherence to the original facts. As this method cannot fail to be of great interest, the Tables, as adjusted by Mr. Woolhouse, together with his explanation of the process of adjustment, are printed at the end of the Introduction. In order to examine more closely into the question of the effect of selection, a Table of Mortality was deduced from the Observations HM, excluding the years of Assurance o to 4; this was similarly graduated by Mr. Woolhouse. It is designated by the symbol HM(5). The particular period adopted as most suitable generally for exclusion was determined by the marked difference, in the classified original data, between the first five years of assurance and the subsequent periods. It was then decided, after a careful consideration of the whole subject, that Commutation Tables for Single Lives, and Values of Annuities to 4 places of decimals, at 3, 3, 4, 4, 5, and 6 per-cent, should be deduced from the graduated HM and HF Tables. It was also decided that similar Tables, at 3, 3, and 4 per-cent, should be deduced from the HM(5) Table. These were considered sufficient to afford to Life Assurance Companies a basis for approximate valuations of their position and prospects independent of the influence of recent selection. The Table HMF has not been made a basis The Tables for Two Lives comprise an entire set of Joint Life Annuities for every combination of ages from (10, 10) upwards, at 3, 3, and 4 per-cent, as being the rates generally sufficient for official calculations. The values of Annuities on the last survivor of two lives for the same combinations of age are also given at the same rates of interest, and by a simple arrangement fill up, with a new and valuable set of Tables, what would otherwise have been a great waste of space in the Joint Life Columns. The laborious and responsible task of superintending the computation and printing of all these Tables was undertaken in the most disinterested manner by Mr. Peter Gray, whose name will be accepted as a guarantee of the accuracy and consequent value of the completed results. To the Tables themselves Mr. Gray has written an Introduction, fully explaining the methods of formation and various modes of their application. This renders it unnecessary for the Council to do more than draw attention to his clear and able exposition: but they desire, at the same time, to record their sense of the great obligations which all interested in the present work are under to Mr. Gray for his invaluable assistance in its production. Other Tables are required to complete the Canon, such as Single and Annual Premiums for Survivorships and Endowments and the values of Temporary and Deferred Annuities, but it appears to the Council that it would not be advisable to delay any longer the publication of the present volume, which, with these explanations, they now submit to the Profession. The Council have thought it desirable to append to this volume a comprehensive Scheme of Notation, settled by a Special Committee of Actuaries, after long and careful consideration of the subject, aided by valuable suggestions and co-operation from various quarters. The Council believe that this notation will be found extremely well adapted to express all the benefits that occur in practice, and they strongly recommend it for general adoption, in the expectation that its use will contribute materially to advance the study of life contingencies by promoting exactness of thought and expression. LIST OF CONTRIBUTING OFFICES. British Equitable Assurance Company. Briton Medical and General Life Association. Church of England Life Assurance Institution. Clergy Mutual Assurance Society. Clerical, Medical, and General Life Assurance Society. Crown Life Assurance Company. Eagle Insurance Company. English and Scottish Law Life Assurance Association. Equity and Law Life Assurance Society. Friends' Provident Institution. General Reversionary and Investment Company. Law Union Fire and Life Insurance Company. Liverpool, London, and Globe Insurance Company. Metropolitan Life Assurance Society. National Life Assurance Society. National Union Assurance Company. North British and Mercantile Insurance Company. Northern Assurance Company. Pelican Life Assurance Company. Prudential Assurance Company. Royal Farmers' Insurance Company. West of England Fire and Life Insurance Company. Under each of the three Mortality Tables, HM, HF, First, a Table of Elementary Values, with Results deduced from it involving the rate of mortality Secondly, the following Tables involving the rates of both 3. Results deduced from the Commutation Table. The rates of interest will be apparent from the following |