On various occasions when mortality tables have been prepared in select form difficulty has been experienced in running the select rates into those of an aggregate or ultimate table. The difficulty has been ascribed to various special circumstances, such as further elimination of duplicates at the end of the select period; class selection; and heterogeneity of the data due to the length of the period covered. It seems always to have been taken for granted that, at the end of some period of years, the select rates ought to run into those of an ultimate table.