In these days of continuous change in mortality, with the necessity of forecasting in many of our operations, a paper concerned with the graduation of mortality statistics may appear to be academic, the more so if attention is restricted to the fitting of mathematical curves, with or without any attempt to advance that elusive and, as some think, delusive conception, the law of mortality. Nevertheless, it is felt that if progress is to be made in any branch of science, theoretical research and experiment are essential, as also is the publication of the results, unless the work is completely abortive. It has become the fashion to speak of graduation as though its function were restricted to the provision of a practical instrument for monetary calculations; as Todhunter is reputed to have said, the tabulated values of lx are merely successive terms in a commutation column. Notwithstanding this, most of us retain, consciously or unconsciously, a feeling that, underlying all the roughnesses in our data referable to errors of observation and an ever-changing environment, there may be an inherent mathematical system of law and order, which if it could but be discovered would give such insight into the meaning of the unadjusted figures that a considerable advance would be made in the practical application of our science.