Although many tables have been graduated in order to study the trend of mortality or express it mathematically, the real object of graduation in practical actuarial work is to provide a sufficiently smooth series of rates of mortality to avoid inconvenience in the calculation of monetary values, particularly perhaps, in the case of joint life functions. The importance of making tables available for practical calculation as soon as possible after the expiration of the period to which the rates of mortality relate necessitates the postponement of any attempt at an extensive mathematical study of the material and we feel that the alternative lies between (1) the use of the rates of mortality already found from the material adjusted as little as is necessary and (2) a Gompertz or Makeham graduation.