Observations on reversionary payments; on schemes for providing annuities for widows, and for persons in old age; and on the method of calculating the values of assurances on lives: to which are added, four essays on different subjects in the doctrine oflife-annuities and political arithmetic. Also, an appendix, containing a compleat set of tables; patrticularly, four new tables, shewing the probabilities of life in various places; and the values of joint lives. A new edition, with a supplement, containing additional observations and tables