In presenting to the Members of the Actuarial Society of Edinburgh the results of my investigation into so practical a matter as that described in the title of this paper, I feel that whatever may be their opinion with regard to the manner in which I have proceeded, and the methods which I have employed in my researches, I am at least absolved from the necessity of apologising for the nature of my subject. A glance at the syllabus of the Society for the current Session is sufficient to establish the fact that scientific inquiries upon theoretical points, and the discussion of matters of practical importance, are alike welcomed as acceptable contributions to its Transactions. But, if I may be permitted to anticipate in a slight measure the course of this investigation, as set forth in the following pages, I would take the opportunity of expressing the hope that my paper may be regarded as possessing some slight interest from the theoretical as well as the practical point of view. It will be my aim to afford such statistics of the Annuity business transacted in this country as the valuable returns to the Board of Trade—an endless source of statistical information upon every point connected with the operations of our Life Assurance Companies—will supply, more particularly with respect to the valuation of such contracts; to construct from data thus obtained a common base, which will enable the relative reserves according to certain mortality tables to be measured—or, as it is technically termed, a “Model Office;” and, finally, to employ this instrument in endeavouring to show the financial results yielded by the application of each of the tables in question.